sports management 3

Sports Analytics and Data Science

Winning the Game with Methods and Models

THOMAS W. MILLER

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Executive Editor: Jeanne Glasser Levine

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c©2016 by Thomas W. Miller Published by Pearson Education, Inc.

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Library of Congress Control Number: 2015954509

Contents

Preface v

Figures ix

Tables xi

Exhibits xiii

1 Understanding Sports Markets 1

2 Assessing Players 23

3 Ranking Teams 37

4 Predicting Scores 49

5 Making Game-Day Decisions 61

6 Crafting a Message 69

7 Promoting Brands and Products 101

8 Growing Revenues 119

9 Managing Finances 133

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iv Sports Analytics and Data Science

10 Playing What-if Games 147

11 Working with Sports Data 169

12 Competing on Analytics 193

A Data Science Methods 197

A.1 Mathematical Programming 200

A.2 Classical and Bayesian Statistics 203

A.3 Regression and Classification 206

A.4 Data Mining and Machine Learning 215

A.5 Text and Sentiment Analysis 217

A.6 Time Series, Sales Forecasting, and Market Response Models 226

A.7 Social Network Analysis 230

A.8 Data Visualization 234

A.9 Data Science: The Eclectic Discipline 240

B Professional Leagues and Teams 255

Data Science Glossary 261

Baseball Glossary 279

Bibliography 299

Index 329

Preface

“Sometimes you win, sometimes you lose, sometimes it rains.”

—TIM ROBBINS AS EBBY CALVIN LALOOSH IN Bull Durham (1988)

Businesses attract customers, politicians persuade voters, websites cajole visitors, and sports teams draw fans. Whatever the goal or target, data and models rule the day.

This book is about building winning teams and successful sports businesses. Winning and success are more likely when decisions are guided by data and models. Sports analytics is a source of competitive advantage.

This book provides an accessible guide to sports analytics. It is written for anyone who needs to know about sports analytics, including players, managers, owners, and fans. It is also a resource for analysts, data scientists, and programmers. The book views sports analytics in the context of data science, a discipline that blends business savvy, information technology, and modeling techniques.

To use analytics effectively in sports, we must first understand sports— the industry, the business, and what happens on the fields and courts of play. We need to know how to work with data—identifying data sources, gathering data, organizing and preparing them for analysis. We also need to know how to build models from data. Data do not speak for themselves. Useful predictions do not arise out of thin air. It is our job to learn from data and build models that work.

v

vi Sports Analytics and Data Science

The best way to learn about sports analytics and data science is through examples. We provide a ready resource and reference guide for modeling techniques. We show programmers how to solve real world problems by building on a foundation of trustworthy methods and code.

The truth about what we do is in the programs we write. The code is there for everyone to see and for some to debug. Data sets and computer programs are available from the website for the Modeling Techniques se- ries at http://www.ftpress.com/miller/. There is also a GitHub site at https://github.com/mtpa/.

When working on sports problems, some things are more easily accom- plished with R, others with Python. And there are times when it is good to offer solutions in both languages, checking one against the other.

One of the things that distinguishes this book from others in the area of sports analytics is the range of data sources and topics discussed. Many re- searchers focus on numerical performance data for teams and players. We take a broader view of sports analytics—the view of data science. There are text data as well as numeric data. And with the growth of the World Wide Web, the sources of data are plentiful. Much can be learned from public domain sources through crawling and scraping the web and utilizing ap- plication programming interfaces (APIs).

I learn from my consulting work with professional sports organizations. Research Publishers LLC with its ToutBay division promotes what can be called “data science as a service.” Academic research and models can take us only so far. Eventually, to make a difference, we need to implement our ideas and models, sharing them with one another.

Many have influenced my intellectual development over the years. There were those good thinkers and good people, teachers and mentors for whom I will be forever grateful. Sadly, no longer with us are Gerald Hahn Hinkle in philosophy and Allan Lake Rice in languages at Ursinus College, and Herbert Feigl in philosophy at the University of Minnesota. I am also most thankful to David J. Weiss in psychometrics at the University of Minnesota and Kelly Eakin in economics, formerly at the University of Oregon.

Preface vii

My academic home is the Northwestern University School of Professional Studies. Courses in sports research methods and quantitative analysis, mar- keting analytics, database systems and data preparation, web and network data science, web information retrieval and real-time analytics, and data visualization provide inspiration for this book. Thanks to the many stu- dents and fellow faculty from whom I have learned. And thanks to col- leagues and staff who administer excellent graduate programs, including the Master of Science in Predictive Analytics, Master of Arts in Sports Ad- ministration, Master of Science in Information Systems, and the Advanced Certificate in Data Science.

Lorena Martin reviewed this book and provided valuable feedback while she authored a companion volume on sports performance measurement and analytics (Martin 2016). Adam Grossman and Tom Robinson provided valuable feedback about coverage of topics in sports business management. Roy Sanford provided advice on statistics. Amy Hendrickson of TEXnology Inc. applied her craft, making words, tables, and figures look beautiful in print—another victory for open source. Candice Bradley served dual roles as a reviewer and copyeditor for all books in the Modeling Techniques series. And Andy Beaster helped in preparing this book for final production. I am grateful for their guidance and encouragement.

Thanks go to my editor, Jeanne Glasser Levine, and publisher, Pearson/FT Press, for making this book possible. Any writing issues, errors, or items of unfinished business, of course, are my responsibility alone.

My good friend Brittney and her daughter Janiya keep me company when time permits. And my son Daniel is there for me in good times and bad, a friend for life. My greatest debt is to them because they believe in me.

Thomas W. Miller Glendale, California October 2015

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Figures

1.1 MLB, NBA, and NFL Average Annual Salaries 10 1.2 MLB Team Payrolls and Win/Loss Performance (2014 Season) 11 1.3 A Perceptual Map of Seven Sports 13 2.1 Multitrait-Multimethod Matrix for Baseball Measures 25 3.1 Assessing Team Strength: NBA Regular Season (2014–2015) 40 4.1 Work of Data Science 50 4.2 Data and Models for Research 52 4.3 Training-and-Test Regimen for Model Evaluation 54 4.4 Training-and-Test Using Multi-fold Cross-validation 56 4.5 Training-and-Test with Bootstrap Resampling 57 4.6 Predictive Modeling Framework for Team Sports 59 6.1 How Sports Fit into the Entertainment Space (Or Not) 72 6.2 Indices of Dissimilarity Between Pairs of Binary Variables 73 6.3 Consumer Preferences for Dodger Stadium Seating 77 6.4 Choice Item for Assessing Willingness to Pay for Tickets 79 6.5 The Market: A Meeting Place for Buyers and Sellers 80 7.1 Dodgers Attendance by Day of Week 104 7.2 Dodgers Attendance by Month 104 7.3 Dodgers Weather, Fireworks, and Attendance 106 7.4 Dodgers Attendance by Visiting Team 107 7.5 Regression Model Performance: Bobbleheads and Attendance 108 8.1 Competitive Analysis for an NBA Team: Golden State Warriors 129 9.1 Cost-Volume-Profit Analysis 135 9.2 Higher Profits Through Increased Sales 136 9.3 Higher Profits Through Lower Fixed Costs 137 9.4 Higher Profits Through Increased Efficiency 137 9.5 Decision Analysis: Investing in a Sports Franchise (Or Not) 143 10.1 Game-day Simulation (Offense Only) 152

ix

x Sports Analytics and Data Science

10.2 Mets’ Away and Yankees’ Home Data (Offense and Defense) 154 10.3 Balanced Game-day Simulation (Offense and Defense) 155 10.4 Actual and Theoretical Runs-scored Distributions 157 10.5 Poisson Model for Mets vs. Yankees at Yankee Stadium 159 10.6 Negative Binomial Model for Mets vs. Yankees at Yankee Stadium 160 10.7 Probability of Home Team Winning (Negative Binomial Model) 162 10.8 Strategic Modeling Techniques in Sports 164 11.1 Software Stack for a Document Search and Selection System 173 11.2 The Information Supply Chain of Professional Team Sports 174 11.3 Automated Data Acquisition by Crawling, Scraping, and Parsing 177 11.4 Automated Data Acquisition with an API 179 11.5 Gathering and Organizing Data for Analysis 180 A.1 Mathematical Programming Modeling Methods 201 A.2 Evaluating the Predictive Accuracy of a Binary Classifier 212 A.3 Linguistic Foundations of Text Analytics 218 A.4 Creating a Terms-by-Documents Matrix 221 A.5 Data and Plots for the Anscombe Quartet 235 A.6 Visualizing Many Games Across a Season: Differential Runs Plot 236 A.7 Moving Fraction Plot for Basketball 237 A.8 Visualizing Basketball Play-by-Play Data 239 A.9 Data Science: The Eclectic Discipline 241

Tables

1.1 Sports and Recreation Activities in the United States 3 1.2 MLB Team Valuation and Finances (March 2015) 5 1.3 NBA Team Valuation and Finances (January 2015) 6 1.4 NFL Team Valuation and Finances (August 2014) 7 1.5 World Soccer Team Valuation and Finances (May 2015) 8 2.1 Levels of Measurement 29 3.1 NBA Team Records (2014–2015 Season) 39 5.1 Twenty-five States of a Baseball Half-Inning 63 6.1 Dissimilarity Matrix for Entertainment Events and Activities 71 6.2 Consumer Preference Data for Dodger Stadium Seating 76 7.1 Bobbleheads and Dodger Dogs 103 7.2 Regression of Attendance on Month, Day of Week, and Promotion 110 9.1 Discounted Cash Flow Analysis of a Player Contract 139 9.2 Would you like to buy the Brooklyn Nets? 141 10.1 New York Mets’ Early Season Games in 2007 149 10.2 New York Yankees’ Early Season Games in 2007 150 A.1 Three Generalized Linear Models 209 A.2 Social Network Data: MLB Player Transactions 233 B.1 Women’s National Basketball Association (WNBA) 255 B.2 Major League Baseball (MLB) 256 B.3 Major League Soccer (MLS) 257 B.4 National Basketball Association (NBA) 258 B.5 National Football League (NFL) 259 B.6 National Hockey League (NHL) 260

xi

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Exhibits

1.1 MLB, NBA, and NFL Player Salaries (R) 16 1.2 Payroll and Performance in Major League Baseball (R) 18 1.3 Making a Perceptual Map of Sports (R) 19 3.1 Assessing Team Strength by Unidimensional Scaling (R) 43 6.1 Mapping Entertainment Events and Activities (R) 83 6.2 Mapping Entertainment Events and Activities (Python) 86 6.3 Preferences for Sporting Events—Conjoint Analysis (R) 88 6.4 Preferences for Sporting Events—Conjoint Analysis (Python) 99 7.1 Shaking Our Bobbleheads Yes and No (R) 113 7.2 Shaking Our Bobbleheads Yes and No (Python) 116 10.1 Team Winning Probabilities by Simulation (R) 167 10.2 Team Winning Probabilities by Simulation (Python) 168 11.1 Simple One-Site Web Crawler and Scraper (Python) 186 11.2 Gathering Opinion Data from Twitter: Football Injuries (Python) 189 A.1 Programming the Anscombe Quartet (Python) 242 A.2 Programming the Anscombe Quartet (R) 244 A.3 Making Differential Runs Plots for Baseball (R) 245 A.4 Moving Fraction Plot: A Basketball Example (R) 246 A.5 Visualizing Basketball Games (R) 248 A.6 Seeing Data Science as an Eclectic Discipline (R) 252

xiii

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1 Understanding Sports Markets

“Those of you on the floor at the end of the game, I’m proud of you. You played your guts out. I’m only going to say this one time. All of you have the weekend. Think about whether or not you want to be on this team under the following condition: What I say when it comes to this basketball team is the law, absolutely and without discussion.”

—GENE HACKMAN AS COACH NORMAN DALE IN Hoosiers (1986)

In applying the laws of economics to professional sports, we must consider the nature of sports and the motives of owners. Professional sports are different from other forms of business.

There are sellers and buyers of sports entertainment. The sellers are the players and teams within the leagues of professional sports. The buyers are consumers of sports, many of whom never go to games in person but who watch sports on television, listen to the radio, and buy sports team paraphernalia.

Sports compete with other forms of entertainment for people’s time and money. And various sports compete with one another, especially when their seasons overlap. Sports teams produce entertainment content that is distributed through the media. Sports teams license their brand names and logos to other organizations, including sports apparel manufacturers.

1

2 Sports Analytics and Data Science

Sports teams are not independent businesses competing with one another. While players and teams compete on the fields and courts of play, they cooperate with one another as members of leagues. The core product of sports is the sporting contest, a joint product of two or more players or two or more teams.

Fifty-four sports and recreation activities, shown in table 1.1, are tracked by the National Sporting Goods Association (2015), which serves the sporting goods industry. In recent years, participation in baseball, basketball, foot- ball, and tennis has declined, while participation in soccer has increased. There has been growth in individual recreational sports, such as skate- boarding and snowboarding. Of course, levels of participation in sports are not necessarily an indicator of levels of interest in sports as entertainment.

Sports businesses produce entertainment products by cooperating with one another. While it is illegal for businesses in most industries to collude in setting output and prices, sports leagues engage in cooperative output and pricing as a standard part of their business model. The number of games, indeed the entire schedule of games in a sport, is determined by the league. In fact, aspects of professional sports are granted monopoly power by the federal government in the United States.

When developing a model for a typical business or firm, an economist would assume profit maximization as a motive. But for a professional sports team, an owner’s motives may not be so easily understood. While one owner may operate his or her team for profit year by year, another may seek to maximize wins or overall utility. Another may look for capital appreciation—buying, then selling after a few years. Lacking knowledge of owners’ motives, it is difficult to predict what they will do.

Gaining market share and becoming the dominant player is a goal of firms in many industries. Not so in the business of professional sports. If one team were assured of victory in almost all of its contests, interest in those contests could wane. A team benefits by winning more often than losing, but winning all the time may be less beneficial than winning most of the time. Professional sports leagues claim to be seeking competitive balance, although there are dominant teams in many leagues.

Chapter 1. Understanding Sports Markets 3

Table 1.1. Sports and Recreation Activities in the United States

Aerobic Exercising Ice/Figure Skating Archery (Target) In-Line Roller Skating Backpack/Wilderness Camping Kayaking Baseball Lacrosse Basketball Martial Arts/MMA/Tae Kwon Do Bicycle Riding Mountain Biking (Off Road) Billiards/Pool Muzzleloading Boating (Motor/Power) Paintball Games Bowling Running/Jogging Boxing Scuba Diving (Open Water) Camping (Vacation/Overnight) Skateboarding Canoeing Skiing (Alpine) Cheerleading Skiing (Cross Country) Dart Throwing Snowboarding Exercise Walking Soccer Exercising with Equipment Softball Fishing (Fresh Water) Swimming Fishing (Salt Water) Table Tennis/Ping Pong Football (Flag) Target Shooting (Airgun) Football (Tackle) Target Shooting (Live Ammunition) Football (Touch) Tennis Golf Volleyball Gymnastics Water Skiing Hiking Weight Lifting Hockey (Ice) Work Out at Club/Gym/Fitness Studio Hunting with Bow & Arrow Wrestling Hunting with Firearms Yoga

4 Sports Analytics and Data Science

Sports is big business as shown by valuations and finances of the major pro- fessional sports in the United States and worldwide. Data from Forbes for Major League Baseball (MLB), the National Basketball Association (NBA), the National Football League (NFL), and worldwide soccer teams are shown in tables 1.2 through 1.5.

Professional sports teams most certainly compete with one another in the labor market, and labor in the form of star players is in short supply. Some argue that salary caps are necessary to preserve competitive balance. Salary caps also help teams in limiting expenditures on players.

Most professional sports in the United States have salary caps. The 2015 salary cap for NFL teams, with fifty-three player rosters, is set at $143.28 million (Patra 2015). Most teams have payrolls at or near the cap, mak- ing the average salary of an NFL player about $2.7 million. One player on an NFL team may be designated as a franchise player, restricting that player from entering free agency. The league sets minimum salaries for franchise players. For example, a franchise quarterback has a minimum salary of $18.544 million in 2015. The highest annual salary among NFL players is $22 million for Aaron Rodgers, Green Bay Packers quarterback (spotrac 2015c). The minimum annual salary is $420 thousand.

NBA teams have a $70 million salary cap for the 2015–16 season, with penalties for teams going over the cap. Maximum player salaries are based on a percentage of cap and years of service. For example, LeBron James, with ten years of experience, would have a maximum salary of $23 million (Mahoney 2015). New Orleans Pelicans Anthony Davis’ average salary of $29 million is the highest among NBA players (spotrac 2015b). Team rosters include fifteen players under contract, with as many as thirteen available to play in any particular game. The minimum annual salary is $428,498.

Major League Baseball (MLB) has a “luxury tax” for teams with payrolls in excess of $189 million. There is a regular-player roster of twenty-five or twenty-six players for double-header days/nights. A forty-man roster includes players under contract and eligible to play. Between September 1 and the end of the regular season the roster is expanded to forty players. The roster drops back to twenty-five players for the playoffs. The minimum MLB annual salary is $505,700 in 2015. The highest MLB annual salary is $31 million for Miguel Cabrera of the Detroit Tigers (spotrac 2015a).

Chapter 1. Understanding Sports Markets 5

Table 1.2. MLB Team Valuation and Finances (March 2015)

One-Year Current Change Operating

Team Value in Value Debt/Value Revenue Income Rank Team ($ Millions) (Percentage) (Percentage) ($ Millions) ($ Millions)

1 New York Yankees 3,200 28 0 508 8.1 2 Los Angeles Dodgers 2,400 20 17 403 -12.2 3 Boston Red Sox 2,100 40 0 370 49.2 4 San Francisco Giants 2,000 100 4 387 68.4 5 Chicago Cubs 1,800 50 24 302 73.3 6 St Louis Cardinals 1,400 71 21 294 73.6 7 New York Mets 1,350 69 26 263 25.0 8 Los Angeles Angels 1,300 68 0 304 16.7 9 Washington Nationals 1,280 83 27 287 41.4 10 Philadelphia Phillies 1,250 28 8 265 -39.0 11 Texas Rangers 1,220 48 13 266 3.5 12 Atlanta Braves 1,150 58 0 267 33.2 13 Detroit Tigers 1,125 65 15 254 -20.7 14 Seattle Mariners 1,100 55 0 250 26.4 15 Baltimore Orioles 1,000 61 15 245 31.4 16 Chicago White Sox 975 40 5 227 31.9 17 Pittsburgh Pirates 900 57 10 229 43.6 18 Minnesota Twins 895 48 25 223 21.3 19 San Diego Padres 890 45 22 224 35.0 20 Cincinnati Reds 885 48 6 227 2.2 21 Milwaukee Brewers 875 55 6 226 11.3 22 Toronto Blue Jays 870 43 0 227 -17.9 23 Colorado Rockies 855 49 7 214 12.6 24 Arizona Diamondbacks 840 44 17 211 -2.2 25 Cleveland Indians 825 45 9 207 8.9 26 Houston Astros 800 51 34 175 21.6 27 Oakland Athletics 725 46 8 202 20.8 28 Kansas City Royals 700 43 8 231 26.6 29 Miami Marlins 650 30 34 188 15.4 30 Tampa Bay Rays 625 29 22 188 7.9

Source. Badenhausen, Ozanian, and Settimi (2015b).

6 Sports Analytics and Data Science

Table 1.3. NBA Team Valuation and Finances (January 2015)

One-Year Current Change Operating

Team Value in Value Debt/Value Revenue Income Rank Team ($ Millions) (Percentage) (Percentage) ($ Millions) ($ Millions)

1 Los Angeles Lakers 2,600 93 2 293 104.1 2 New York Knicks 2,500 79 0 278 53.4 3 Chicago Bulls 2,000 100 3 201 65.3 4 Boston Celtics 1,700 94 9 173 54.9 5 Los Angeles Clippers 1,600 178 0 146 20.1 6 Brooklyn Nets 1,500 92 19 212 -99.4 7 Golden State Warriors 1,300 73 12 168 44.9 8 Houston Rockets 1,250 61 8 175 38.0 9 Miami Heat 1,175 53 8 188 12.6 10 Dallas Mavericks 1,150 50 17 168 30.4 11 San Antonio Spurs 1,000 52 8 172 40.9 12 Portland Trail Blazers 940 60 11 153 11.7 13 Oklahoma City Thunder 930 58 15 152 30.8 14 Toronto Raptors 920 77 16 151 17.9 15 Cleveland Cavaliers 915 78 22 149 20.6 16 Phoenix Suns 910 61 20 145 28.2 17 Washington Wizards 900 86 14 143 10.1 18 Orlando Magic 875 56 17 143 20.9 19 Denver Nuggets 855 73 1 136 14.0 20 Utah Jazz 850 62 6 142 32.7 21 Indiana Pacers 830 75 18 139 25.0 22 Atlanta Hawks 825 94 21 133 14.8 23 Detroit Pistons 810 80 23 144 17.6 24 Sacramento Kings 800 45 29 125 8.9 25 Memphis Grizzlies 750 66 23 135 10.5 26 Charlotte Hornets 725 77 21 130 1.2 27 Philadelphia 76ers 700 49 21 125 24.4 28 New Orleans Pelicans 650 55 19 131 19.0 29 Minnesota Timberwolves 625 45 16 128 6.9 30 Milwaukee Bucks 600 48 29 110 11.5

Source. Badenhausen, Ozanian, and Settimi (2015a).

Chapter 1. Understanding Sports Markets 7

Table 1.4. NFL Team Valuation and Finances (August 2014)

One-Year Current Change Operating

Team Value in Value Debt/Value Revenue Income Rank Team ($ Millions) (Percentage) (Percentage) ($ Millions) ($ Millions)

1 Dallas Cowboys 3,200 39 6 560 245.7 2 New England Patriots 2,600 44 9 428 147.2 3 Washington Redskins 2,400 41 10 395 143.4 4 New York Giants 2,100 35 25 353 87.3 5 Houston Texans 1,850 28 11 339 102.8 6 New York Jets 1,800 30 33 333 79.5 7 Philadelphia Eagles 1,750 33 11 330 73.2 8 Chicago Bears 1,700 36 6 309 57.1 9 San Francisco 49ers 1,600 31 53 270 24.8 10 Baltimore Ravens 1,500 22 18 304 56.7 11 Denver Broncos 1,450 25 8 301 30.7 12 Indianapolis Colts 1,400 17 4 285 60.7 13 Green Bay Packers 1,375 16 1 299 25.6 14 Pittsburgh Steelers 1,350 21 15 287 52.4 15 Seattle Seahawks 1,330 23 9 288 27.3 16 Miami Dolphins 1,300 21 29 281 8.0 17 Carolina Panthers 1,250 18 5 283 55.6 18 Tampa Bay Buccaneers 1,225 15 15 275 46.4 19 Tennessee Titans 1,160 10 11 278 35.6 20 Minnesota Vikings 1,150 14 43 250 5.3 21 Atlanta Falcons 1,125 21 27 264 13.1 22 Cleveland Browns 1,120 11 18 276 35.0 23 New Orleans Saints 1,110 11 7 278 50.1 24 Kansas City Chiefs 1,100 9 6 260 10.0 25 Arizona Cardinals 1,000 4 15 266 42.8 26 San Diego Chargers 995 5 10 262 39.9 27 Cincinnati Bengals 990 7 10 258 11.9 28 Oakland Raiders 970 18 21 244 42.8 29 Jacksonville Jaguars 965 15 21 263 56.9 30 Detroit Lions 960 7 29 254 -15.9 31 Buffalo Bills 935 7 13 252 38.0 32 St Louis Rams 930 6 12 250 16.2

Source. Badenhausen, Ozanian, and Settimi (2014).

8 Sports Analytics and Data Science

Table 1.5. World Soccer Team Valuation and Finances (May 2015)

One-Year Current Change Operating

Team Value in Value Debt/Value Revenue Income Rank Team ($ Millions) (Percentage) (Percentage) ($ Millions) ($ Millions)

1 Real Madrid 3,263 -5 4 746 170 2 Barcelona 3,163 -1 3 657 174 3 Manchester United 3,104 10 20 703 211 4 Bayern Munich 2,347 27 0 661 78 5 Manchester City 1,375 59 0 562 122 6 Chelsea 1,370 58 0 526 83 7 Arsenal 1,307 -2 30 487 101 8 Liverpool 982 42 10 415 86 9 Juventus 837 -2 9 379 50 10 AC Milan 775 -10 44 339 54 11 Borussia Dortmund 700 17 6 355 55 12 Paris Saint-Germain 634 53 0 643 -1 13 Tottenham Hotspur 600 17 9 293 63 14 Schalke 04 572 -1 0 290 57 15 Inter Milan 439 -9 56 222 -41 16 Atletico de Madrid 436 33 53 231 47 17 Napoli 353 19 0 224 43 18 Newcastle United 349 33 0 210 44 19 West Ham United 309 33 12 186 54 20 Galatasaray 294 -15 17 220 -37

Source. Ozanian (2015).

Chapter 1. Understanding Sports Markets 9

Figure 1.1, a histogram lattice, shows how player salaries compare across the MLB, NBA, and NFL in August 2015. Player salary distributions are positively skewed. The mean salary across NFL players is around $1.7 mil- lion, but the median is $630 thousand. The mean salary across NBA players is around $5.1 million, with median salary $2.8 million. The mean salary across MLB players is around $4.1 million, with the median $1.1 million.

Do team expenditures on players buy success? This is a meaningful ques- tion to ask for leagues that have no salary caps. Szymanski (2015) reports studies showing that between 60 and 90 percent of the variability in U.K. soccer team positions may be explained by wages paid to players. Major League Baseball has a luxury tax in place of a salary cap, and team pay- rolls vary widely in size. The New York Yankees have been known for having the highest payrolls in baseball. Recently, the Los Angeles Dodgers have surpassed the Yankees with the highest player payroll—more than $257 million at the end of the 2014 season (Woody 2014).

Figure 1.2 shows baseball team salaries at the beginning of the 2014 sea- son plotted against the percentage of games won across the regular season. Notice how teams that made the playoffs in 2014, labeled with team ab- breviations, have a wide range of payrolls. While the biggest spenders in baseball are often among the set of teams going to the playoffs, the relation- ship between team payrolls and team performance is weak at best—less than 7 percent of the variability in win/loss percentages is explained by player payrolls.

The thesis of Michael Lewis’ Moneyball (2003) and what has become the ethos of sports analytics is that small-market baseball teams can win by spending their money wisely. Star players demand top salaries due as much to their celebrity status as to their skills. Players with high on-base percentages, overlooked by major-market teams, can be hired at much lower salaries than star players.

Teams, although associated with particular cities, can be known nationwide or worldwide. The media of television and the Internet provide opportu- nities for reaching consumers across the globe. A Super Bowl at the Rose Bowl in Pasadena, California or AT&T Stadium in Arlington, Texas may be attended by around 100 thousand fans (Alder 2015), while U.S. television audiences have grown to over 100 million (statista 2015).

10 Sports Analytics and Data Science

Figure 1.1. MLB, NBA, and NFL Average Annual Salaries

Annual Salary ($ millions)

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National Basketball Association 0.00

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Sources. spotrac (2015a, 2015b, 2015c).

Chapter 1. Understanding Sports Markets 11

Figure 1.2. MLB Team Payrolls and Win/Loss Performance (2014 Season)

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See Appendix B, page 255, for team abbreviations and names.

12 Sports Analytics and Data Science

Media revenues are important to successful sports teams. Other revenues come from business partnerships, sponsorships, advertising, and stadium naming rights. City governments understand well the power of sports to promote business. Locating sports arenas in cities can help to revitalize downtown areas, as demonstrated by the experience of the Oklahoma City Thunder. Indianapolis, Indiana promotes itself as a sports capital with the Colts and Pacers (Rein, Shields, and Grossman 2015).

Teams seek to build their brands, developing a positive reputation in the minds of consumers. Players, like fans, are attracted to teams with a rep- utation for hard work, courage, fair play, honesty, teamwork, and commu- nity service. The character of a team is often as important as its likelihood of winning. The Cubs are associated with Chicago, but Cub fans may be found from Maine to California. This is despite the fact that the Cubs have not won the World Series since 1908. Teams in U.S. professional sports vie to become “America’s team,” with fans across the land wearing their logo- embossed hats and jerseys.

The demand for sports and the feelings of sports consumers are not so eas- ily understood. Fans can be fickle and fandom fleeting. Fans can be loyal to a sport, to a team, or to individual players. Multivariate methods can help us understand how sports consumers think by revealing relationships among products or brands.

Figure 1.3 provides an example, a perceptual map of seven sports. Along the horizontal dimension, we move from individual, non-contact sports on the left-hand side, to team sports with little contact, to team sports with contact on the right-hand side. The vertical dimension, less easily described, may be thought of as relating to the aerobic versus anaerobic nature of sports and to other characteristics such as physicality and skill. Sports such as tennis, soccer, and basketball entail aerobic exercise. These are endurance sports, while football is an example of a sport that involves both aerobic and anaerobic exercise, including intense exercise for short durations. Sports close together on the map have similarities. Baseball and golf, for example, involve special skills, such as precision in hitting a ball. Soccer and hockey involve almost continuous movement and getting a ball through the goal. Football and hockey have high physicality or player contact.

Chapter 1. Understanding Sports Markets 13

Figure 1.3. A Perceptual Map of Seven Sports

First Dimension (Individual/Team, Degree of Contact)

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In many respects, professional sports teams are decidedly different from other businesses. They are in the public eye. They live and die in the media. And a substantial portion of their revenues come from media.

Késenne (2007), Szymanski (2009), Fort (2011), Fort and Winfree (2013), Leeds and von Allmen (2014), and the edited volumes of Humphreys and Howard (2008a, 2008b, 2008c) review sports economics and business issues.

Gorman and Calhoun (1994) and Rein, Shields, and Grossman (2015) fo- cus on alternative sources of revenue for sports teams and how these relate to business strategy. The business of baseball has been the subject of nu- merous volumes (Miller 1990; Zimbalist 1992; Powers 2003; Bradbury 2007; Pessah 2015). And Jozsa (2010) reviews the history of the National Basket- ball Association.

14 Sports Analytics and Data Science

An overview of sports marketing is provided by Mullin, Hardy, and Sut- ton (2014). Rein, Kotler, and Shields (2006) and Carter (2011) discuss the convergence of entertainment and sports. Miller (2015a) reviews methods in marketing data science, including product positioning maps, market seg- mentation, target marketing, customer relationship management, and com- petitive analysis.

Sports also represents a laboratory for labor market research. Sports is one of the few industries in which job performance and compensation are public knowledge. Economic studies examine player performance mea- sures and value of individual players to teams (Kahn 2000; Bradbury 2007). Miller (1991), Abrams (2010), and Lowenfish (2010) review baseball labor relations. And Early (2011) provides insight into labor and racial discrimi- nation in professional sports.

Sports wagering markets have been studied extensively by economists be- cause they provide public information about price, volume, and rates of re- turn. Furthermore, sports betting opportunities have fixed beginning and ending times and published odds or point spreads, making them easier to study than many financial investment opportunities. As a result, sports wagering markets have become a virtual field laboratory for the study of market efficiency. Sauer (1998) provides a comprehensive review of the economics of wagering markets.

When management objectives can be defined clearly in mathematical terms, teams use mathematical programming methods—constrained optimization. Teams attempt to maximize revenue or minimize costs subject to known situational factors. There has been extensive work on league schedules, for which the league objective may be to have teams playing one another an equal number of times while minimizing total distance traveled between cities. Alternatively, league officials may seek home/away schedules, rev- enue sharing formulas, or draft lottery rules that maximize competitive bal- ance. Briskorn (2008) reviews methods for scheduling sports competition, drawing on integer programming, combinatorics, and graph theory. Wright (2009) provides an overview of operations research in sport.

Chapter 1. Understanding Sports Markets 15

Extensive data about sports are in the public domain, readily available in newspapers and online sources. These data offer opportunities for predic- tive modeling and research. Throughout the book we also identify places to apply methods of operations research, including mathematical program- ming and simulation.

Exhibit 1.1 shows an R program for exploring distributions of player salaries across the MLB, NBA, and NFL. The program draws on software for statis- tical graphics from Sarkar (2008).

Exhibit 1.2 (page 18) shows an R program for examining the relationship between MLB payrolls and win-loss performance. The program draws on software for statistical graphics from Wickham and Chang (2014).

Exhibit 1.3 (page 19) shows an R program to obtain a perceptual map of seven sports, showing their relationships with one another. The program draws on modeling software for multidimensional scaling.

16 Sports Analytics and Data Science

Exhibit 1.1. MLB, NBA, and NFL Player Salaries (R)

# MLB, NBA, and NFL Player Salaries (R)

library(lattice) # statistical graphics

# variables in contract data from spotrac.com (August 2015)

# player: player name (contract years)

# position: position on team

# team: team abbreviation

# teamsignedwith: team that signed the original contract

# age: age in years as of August 2015

# years: years as player in league

# contract: dollars in contract

# guaranteed: guaranteed dollars in contract

# guaranteedpct: percentage of contract dollars guaranteed

# salary: annual salary in dollares

# yearfreeagent: year player becomes free agent

#

# additional created variables

# salarymm: salary in millions

# leaguename: full league name

# league: league abbreviation

# read data for Major League Baseball

mlb_contract_data <- read.csv("mlb_player_salaries_2015.csv")

mlb_contract_data$leaguename <- rep("Major League Baseball",

length = nrow(mlb_contract_data))

for (i in seq(along = mlb_contract_data$yearfreeagent))

if (mlb_contract_data$yearfreeagent[i] == 0)

mlb_contract_data$yearfreeagent[i] <- NA

for (i in seq(along = mlb_contract_data$age))

if (mlb_contract_data$age[i] == 0)

mlb_contract_data$age[i] <- NA

mlb_contract_data$salarymm <- mlb_contract_data$salary/1000000

mlb_contract_data$league <- rep("MLB", length = nrow(mlb_contract_data))

print(summary(mlb_contract_data))

# variables for plotting

mlb_data_plot <- mlb_contract_data[, c("salarymm","leaguename")]

nba_contract_data <- read.csv("nba_player_salaries_2015.csv")

nba_contract_data$leaguename <- rep("National Basketball Association",

length = nrow(nba_contract_data))

for (i in seq(along = nba_contract_data$yearfreeagent))

if (nba_contract_data$yearfreeagent[i] == 0)

nba_contract_data$yearfreeagent[i] <- NA

for (i in seq(along = nba_contract_data$age))

if (nba_contract_data$age[i] == 0)

nba_contract_data$age[i] <- NA

nba_contract_data$salarymm <- nba_contract_data$salary/1000000

nba_contract_data$league <- rep("NBA", length = nrow(nba_contract_data))

print(summary(nba_contract_data))

Chapter 1. Understanding Sports Markets 17

# variables for plotting

nba_data_plot <- nba_contract_data[, c("salarymm","leaguename")]

nfl_contract_data <- read.csv("nfl_player_salaries_2015.csv")

nfl_contract_data$leaguename <- rep("National Football League",

length = nrow(nfl_contract_data))

for (i in seq(along = nfl_contract_data$yearfreeagent))

if (nfl_contract_data$yearfreeagent[i] == 0)

nfl_contract_data$yearfreeagent[i] <- NA

for (i in seq(along = nfl_contract_data$age))

if (nfl_contract_data$age[i] == 0)

nfl_contract_data$age[i] <- NA

nfl_contract_data$salarymm <- nfl_contract_data$salary/1000000

nfl_contract_data$league <- rep("NFL", length = nrow(nfl_contract_data))

print(summary(nfl_contract_data))

# variables for plotting

nfl_data_plot <- nfl_contract_data[, c("salarymm","leaguename")]

# merge contract data with variables for plotting

plotting_data_frame <- rbind(mlb_data_plot, nba_data_plot, nfl_data_plot)

# generate the histogram lattice for comparing player salaries

# across the three leagues in this study

lattice_object <- histogram(~salarymm | leaguename, plotting_data_frame,

type = "density", xlab = "Annual Salary ($ millions)", layout = c(1,3))

# print to file

pdf(file = "fig_understanding_markets_player_salaries.pdf",

width = 8.5, height = 11)

print(lattice_object)

dev.off()

18 Sports Analytics and Data Science

Exhibit 1.2. Payroll and Performance in Major League Baseball (R)

# Payroll and Performance in Major League Baseball (R)

library(ggplot2) # statistical graphics

# functions used with grid graphics to split the plotting region

# to set margins and to plot more than one ggplot object on one page/screen

vplayout <- function(x, y)

viewport(layout.pos.row=x, layout.pos.col=y)

# user-defined function to plot a ggplot object with margins

ggplot.print.with.margins <- function(ggplot.object.name,

left.margin.pct=10,

right.margin.pct=10,top.margin.pct=10,bottom.margin.pct=10)

{ # begin function for printing ggplot objects with margins

# margins expressed as percentages of total... use integers

grid.newpage()

pushViewport(viewport(layout=grid.layout(100,100)))

print(ggplot.object.name,

vp=vplayout((0 + top.margin.pct):(100 - bottom.margin.pct),

(0 + left.margin.pct):(100 - right.margin.pct)))

} # end function for printing ggplot objects with margins

# read in payroll and performance data

# including annotation text for team abbreviations

mlb_data <- read.csv("mlb_payroll_performance_2014.csv")

mlb_data$millions <- mlb_data$payroll/1000000

mlb_data$winpercent <- mlb_data$wlpct * 100

cat("\nCorrelation between Payroll and Performance:\n")

with(mlb_data, print(cor(millions, winpercent)))

cat("\nProportion of win/loss percentage explained by payrolls:\n")

with(mlb_data, print(cor(millions, winpercent)^2))

pdf(file = "fig_understanding_markets_payroll_performance.pdf",

width = 5.5, height = 5.5)

ggplot_object <- ggplot(data = mlb_data,

aes(x = millions, y = winpercent)) +

geom_point(colour = "darkblue", size = 3) +

xlab("Team Payroll (Millions of Dollars)") +

ylab("Percentage of Games Won") +

geom_text(aes(label = textleft), size = 3, hjust = 1.3) +

geom_text(aes(label = textright), size = 3, hjust = -0.25)

ggplot.print.with.margins(ggplot_object, left.margin.pct = 5,

right.margin.pct = 5, top.margin.pct = 5, bottom.margin.pct = 5)

dev.off()

Chapter 1. Understanding Sports Markets 19

Exhibit 1.3. Making a Perceptual Map of Sports (R)

# Making a Perceptual Map of Sports (R)

library(MASS) # includes functions for multidimensional scaling

library(wordcloud) # textplot utility to avoid overlapping text

USE_METRIC_MDS <- FALSE # metric versus non-metric toggle

# utility function for converting a distance structure

# to a distance matrix as required for some routines and

# for printing of the complete matrix for visual inspection.

make.distance.matrix <- function(distance_structure)

{ n <- attr(distance_structure, "Size")

full <- matrix(0,n,n)

full[lower.tri(full)] <- distance_structure

full+t(full)

}

# enter data into a distance structure as required for various

# distance-based routines. That is, we enter the upper triangle

# of the distance matrix as a single vector of distances

distance_structure <-

as.single(c(9,11,10,5,14,4,15,6,12,13,16,1,18,2,20,7,3,19,17,8,21))

# provide a character vector of sports names

sport_names <- c("Baseball", "Basketball", "Football",

"Soccer", "Tennis", "Hockey", "Golf")

attr(distance_structure, "Size") <- length(sport_names) # set size attribute

# check to see that the distance structure has been entered correctly

# by converting the distance structure to a distance matrix

# using the utility function make.distance.matrix, which we had defined

distance_matrix <- unlist(make.distance.matrix(distance_structure))

cat("\n","Distance Matrix of Seven Sports","\n")

print(distance_matrix)

if (USE_METRIC_MDS)

{

# apply the metric multidimensional scaling algorithm and plot the map

mds_solution <- cmdscale(distance_structure, k=2, eig=T)

}

# apply the non-metric multidimensional scaling algorithm

# this is more appropriate for rank-order data

# and provides a more satisfactory solution here

if (!USE_METRIC_MDS)

{

mds_solution <- isoMDS(distance_matrix, k = 2, trace = FALSE)

}

20 Sports Analytics and Data Science

pdf(file = "plot_nonmetric_mds_seven_sports.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

# original solution

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2]

# set up the plot but do not plot points... use names for points

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # first page of pdf plots

# We plot the sport names in the locations where points normally go.

text(First_Dimension, Second_Dimension, labels = sport_names,

offset = 0.0, cex = 1.5)

title("Seven Sports (initial solution)")

# reflect the horizontal dimension

# multiply the first dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2]

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # second page of pdf plots

text(First_Dimension, Second_Dimension, labels = sport_names,

offset = 0.0, cex = 1.5)

title("Seven Sports (horizontal reflection)")

# reflect the vertical dimension

# multiply the section dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2] * -1

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # third page of pdf plots

text(First_Dimension, Second_Dimension, labels = sport_names,

offset = 0.0, cex = 1.5)

title("Seven Sports (vertical reflection)")

# multiply the first and second dimensions by -1

# for reflection in both horizontal and vertical directions

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2] * -1

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # fourth page of pdf plots

text(First_Dimension, Second_Dimension, labels = sport_names,

offset = 0.0, cex = 1.5)

title("Seven Sports (horizontal and vertical reflection)")

dev.off() # closes the pdf plotting device

pdf(file = "plot_pretty_original_mds_seven_sports.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

Chapter 1. Understanding Sports Markets 21

First_Dimension <- mds_solution$points[,1] # no reflection

Second_Dimension <- mds_solution$points[,2] # no reflection

# wordcloud utility for plotting with no overlapping text

textplot(x = First_Dimension,

y = Second_Dimension,

words = sport_names,

show.lines = FALSE,

xlim = c(-15, 15), # extent of horizontal axis range

ylim = c(-15, 15), # extent of vertical axis range

xaxt = "n", # suppress tick marks

yaxt = "n", # suppress tick marks

cex = 1.15, # size of text points

mgp = c(0.85, 1, 0.85), # position of axis labels

cex.lab = 1.5, # magnification of axis label text

xlab = "",

ylab = "")

dev.off() # closes the pdf plotting device

pdf(file = "fig_sports_perceptual_map.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

First_Dimension <- mds_solution$points[,1] * -1 # reflect horizontal

Second_Dimension <- mds_solution$points[,2]

# wordcloud utility for plotting with no overlapping text

textplot(x = First_Dimension,

y = Second_Dimension,

words = sport_names,

show.lines = FALSE,

xlim = c(-15, 15), # extent of horizontal axis range

ylim = c(-15, 15), # extent of vertical axis range

xaxt = "n", # suppress tick marks

yaxt = "n", # suppress tick marks

cex = 1.15, # size of text points

mgp = c(0.85, 1, 0.85), # position of axis labels

cex.lab = 1.5, # magnification of axis label text

xlab = "First Dimension (Individual/Team, Degree of Contact)",

ylab = "Second Dimension (Anaerobic/Aerobic, Other")

dev.off() # closes the pdf plotting device

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2 Assessing Players

Pete: “Gus, did you ever think in a million years computers would be a part of this game?” Gus: “Computers? Anyone uses computers doesn’t know a damn thing about this game.” Pete: “You know, if you wanted to, you could access any high school or college roster, pull the stats on any player at any time. You wouldn’t have to waste your time with all these papers.” Gus: “I’m not wasting my time. I enjoy doing this.” Pete: “You know, they got a special program now that can calculate a player’s stats and, based on the competition he’s seen, tell you whether or not he’s ready for the next level. You believe that?” Gus: “Yeah, what else does it tell you? When to scratch your ass?” Pete: “I don’t like them either, but they’re part of the business now.” Gus: “Pete, scouts, good scouts are the heart of this game. They decide who’s gonna play and, if they’re lucky, they decide how it’s gonna be played. But a computer can’t tell if a kid’s got instincts or not, or if he can hit a cut- off man, or hit behind the runner. . . or look into a kid’s face that’s just gone oh-for-four and know if he’s gonna be able to come back like nothing’s hap- pened. No, a computer can’t tell you all that crap, I’ll tell you. No.”

—JOHN GOODMAN AS PETE KLINE, AND CLINT EASTWOOD AS GUS LOBEL

IN Trouble with the Curve (2012)

23

24 Sports Analytics and Data Science

The job of sports performance analytics is to understand how various fac- tors contribute to success on the fields and courts of play, and this job be- gins with measurement. Many factors contribute to success in sport. There are measures that relate to physical stature, biophysics, health, fitness, and conditioning. There is athleticism and measures dealing with speed, power, strength, flexibility, and agility. There are psychological measures of intelli- gence, personality, and attitude. Finally, there are measures relating to pro- ficiency in sport—knowledge, skill, and execution in practice and in games.

Let us step back from the things we see and hear about on a regular basis— the language of sportscasting—and ask basic measurement questions. What do we want from performance measures in sports? What makes a measure reliable? What makes a measure valid?

We use the term reliability to refer to the trustworthiness or repeatability of measurement procedures. We consider the degree to which repeated measures of the same trait at the same time agree with one another, as in test-retest reliability or split-half reliability. When assessed with a multi- item survey, we ask that a measure have internal consistency.

When we talk about validity, we are thinking of the degree to which a mea- sure measures what it is supposed to measure. There are subjective assess- ments of face validity or content validity. We examine measurements to see the degree to which they appear to measure the traits they are supposed to measure.

A more objective approach to validity assessment would be to demonstrate predictive validity. Knowing how two traits are related in theory, we can create measures of those traits and examine the degree to which these mea- sures relate as theory suggests. The meaning of a measure is defined by its relationship to other measures. This is construct validity, a logical extension of predictive validity.

Campbell and Fiske (1959) define reliability and validity as follows:

Reliability is the agreement between two efforts to measure the same trait through maximally similar methods. Validity is represented in the agreement between two attempts to measure the same trait through maximally different methods. (83)

The prototypical measurement study involves the multitrait-multimethod matrix, as shown in figure 2.1

Chapter 2. Assessing Players 25

Figure 2.1. Multitrait-Multimethod Matrix for Baseball Measures

Method 1: Practice Measures

Method 2: Game-Day Measures

Trait A: Hitting Ability

Trait B: Power Hitting

Ability

Trait A: Hitting Ability

Trait B: Power Hitting

Ability

Method 1: Practice Measures

Method 2: Game-Day Measures

Trait A: Hitting Ability

Trait B: Power Hitting Ability

Trait B: Power Hitting Ability

Trait A: Hitting Ability

0.90

0.90

0.80

0.800.30

0.40

0.20

0.20

0.45

0.50

Heterotrait- monomethod

triangle

Heterotrait- heteromethod

triangle

Validity diagonal

Reliability diagonal

Discriminant validity is demonstrated by the relative sizes of correlations in diagonals and triangles:

Method variance is demonstrated by relatively high heterotrait-monomethod correlations when traits are assumed to be uncorrelated.

Convergent validity is demonstrated by high correlations in the validity diagonal.

The meaning of a measure is defined by its relationships to other measures.

26 Sports Analytics and Data Science

The multitrait-multimethod matrix has rows and columns associated with traits (attributes) and methods (measurement procedures). Each element of the matrix represents a trait-method unit. The components of the ma- trix are the reliability diagonal, validity diagonal, heterotrait-monomethod triangles, and heterotrait-heteromethod triangles.

Figure 2.1 shows a hypothetical multitrait-multimethod matrix with four baseball measures. It portrays two underlying traits: general hitting ability and power hitting ability, measuring them both in practice and games. In batting practice, we first ask the player to hit each ball pitched as cleanly as he can and determine the proportion of balls hit in fair territory. Then we ask him to hit each ball pitched as far as he can and determine the pro- portion of balls hit out of the park, much as we would see in a home run derby. For game-day measures, we refer to box scores to obtain the player’s batting average and home run rate (home runs per at bat). This gives four distinct measures. We compute the correlations between all pairs of mea- sures and show the results in the matrix.

To assess reliability for training measures, we would use the same mea- surement procedures on numerous days and compute the average intercor- relation across all pairs of measures. And to assess reliability for game-day measures, we would compute correlations between measures from odd- numbered games with even-numbered games (or alternatively, we could compute correlations between measures across many random split-halves of games and average those correlations). Reliability refers to measures of the same trait in the same way at about the same time. The reliability of sports performance measures is very high because these are objective mea- sures based on counts. Aside from variations across official scorers, there is little subjectivity or opinion involved in these measures. We expect high correlations in the reliability diagonals of the multitrait-multimethod ma- trix.

What else do we expect to see in a multitrait-multimethod matrix? We should see different measures of the same trait correlating positively on the validity diagonal. Hitting in batting practice should have a positive correla- tion with hitting in games. We expect measures of the same trait to correlate more highly with one another than with measures of different traits. Ac- cordingly, we should see higher correlations on the validity diagonal than

Chapter 2. Assessing Players 27

in either the heterotrait-monomethod or the heterotrait-heteromethod tri- angles.

The meaning of a measure is defined by its relationships to other measures. This notion of construct validity is illustrated by the multitrait-multimethod matrix and what Campbell and Fiske (1959) call convergent validity and discriminant validity. Convergent validity refers to the idea that different measures of the same trait should converge. That is, different measures of the same trait or attribute should have relatively high correlations. Discrim- inant validity refers to the notion that measures of different traits should diverge. In other words, measures of different traits should have lower correlations than measures of the same trait. Convergent and discriminant validation are part of what we mean by construct validation. The meaning of a measure is defined in terms of its relationship to other measures.

What we expect in theory depends on the traits being measured. If we took running instead of general hitting ability as our first trait being studied, we would expect very different set of results. In practice, we might also measure a player’s time in the 40-yard dash, perhaps converting the time in milliseconds to miles per hour. For the game-day measures, we refer to box scores to obtain the player’s success rate in stolen bases (stolen bases divided by stolen bases attempted). What would we expect to see for these measures in relation to hitting for power? Running ability and hitting for power would be expected to be uncorrelated or negatively correlated.

Discussions of validity touch on fundamental issues in the philosophy of science—issues of theory construction, measurement, and testability. There are no easy answers here. If the theory is correct and the measures valid, then the pattern of relationships among the measures should be similar to the pattern predicted by theory. To the extent that this is true for observed data, we have partial confirmation of the theory and, at the same time, demonstration of construct validity. But what if the predictions do not pan out? Then we are faced with a dilemma: the theory could be wrong, one or more of the measures could be invalid, or we could have observed an event of low probability with correct theory and valid measures.

28 Sports Analytics and Data Science

Regarding measurement and philosophy of science, I like the umpire story:

After a long day of disputed calls at the ballpark, three umpires are asked to justify their methods. The first umpire, an empiri- cist by persuasion, says, I call them as I see them. The second, with the faith of a philosophical realist, replies, I call them as they are. Not to be outdone, the third umpire, with the self-proclaimed authority of an operationist or logical empiricist, says, The way I call them—that’s the way they are.

S. S. Stevens (1946) wrote On the Theory of Scales of Measurement, an influen- tial article identifying four general types of measures: nominal, ordinal, interval, and ratio. It was the strength of Stevens’ convictions, perhaps more than the strength of his argument, that influenced generations of re- searchers. The words he chose to describe levels of measurement seemed to carry the force of law. He talked about the formal properties of scales and “permissible statistics,” arguing that “the statistical manipulations that can legitimately be applied to empirical data depend on the type of scale” (Stevens 1946, 677). Stevens argued that we could compute means, stan- dard deviations, and correlations with interval and ratio measures, but not with ordinal measures.

Table 2.1 summarizes scale types or levels of measurement from Stevens (1946). The formal definition of a scale type follows from its mathematical properties, or what Stevens called its “mathematical group structure.” This refers to the set of data transformations that, when used on the original measures, will create new measures with the same scale properties as the original measures.

For nominal scales, any one-to-one transformation will preserve the num- ber of categories and, hence, the scale’s essential property. For ordinal scales, any one-to-one monotonic transformation will preserve the property of order. For interval scales, any one-to-one linear transformation, a func- tion of the form y = ax + b, will preserve the properties of the scale. Ratio scales are similar to interval scales, except that the zero point must be pre- served. Accordingly, for ratio scales, a data transformation that preserves its properties must have the form y = ax.

Chapter 2. Assessing Players 29

Table 2.1. Levels of Measurement

Level of Measurement (Scale Type)

Basic Empirical Operations

Mathematical Group Structure

Examples of Permissible Statistics

Nominal

Ordinal

Interval

Ratio

equality, numbers like names

greater than, less than

equality of intervals

equality of ratios

one-to-one correspondence

one-to-one monotonic

one-to-one linear

one-to-one linear, preserving the zero point

number of cases in class, frequency table, modal class

median, percentiles, rank-order correlation

mean, standard deviation, product-moment correlation

same statistics as interval level

Source: Adapted from Stevens (1946).

Researchers following Stevens’ dictums constitute the weak measurement school. They argue that many measures are ordinal rather than interval and that statistics relying on sums or differences, including means and vari- ances, would be inappropriate for ordinal measures. Researchers following the strong statistics school, on the other hand, argue that statistical methods make no explicit assumptions about the meaning of measurements or their relationships to underlying dimensions. Strong statistics can be used with weak measurements.

For practical purposes, we ask whether or not a variable has meaningful magnitude. If a variable is categorical, it lacks meaningful magnitude. One further observation is appropriate for categorical data: we note whether the variable is binary (taking only two possible values) or multinomial (taking more than two possible values). If we can make these simple distinctions across measures, we can do much useful research. Note that most sports performance measures begin as counts, which are ratio measures. And, despite the objections of weak measurement believers, there are many situ- ations in which computing the mean of ranks makes perfectly good sense.

30 Sports Analytics and Data Science

Many sports analysts confuse reliability with stability. In baseball, for ex- ample, they note low correlations for player batting averages from one year to the next or pitcher earned run averages from one year to the next, saying that this is evidence of low reliability. This is incorrect thinking. Baseball measures and sports performance measures in general have very high reli- ability.

Reliability concerns agreement between measures of the same trait in the same way at about the same time. The reliability of sports performance measures is very high because these are objective measures based on counts.

Many sports performance measures rely on the official scoring of events on the field, box scores, and play-by-play logs. Official records, counts, and mathematical formulas for computing performance measures do not change from one observer or one analyst to the next. Many of the newer measures of player and ball location on the fields and courts of play, player running speed, and efficiency in getting to balls in play are obtained through electronic devices with little or no human intervention. These are highly re- liable and trustworthy. What performance measures lack is not reliability, but stability from one year to the next or one game to the next.

Measurement is the assignment of numbers to attributes according to rules, and measurements themselves have certain desirable attributes:

Reliable. A measure should be trustworthy and repeatable. Valid. A measure should measure the attribute it is said to measure. Explicit. Procedures should be unambiguous and defined in detail, so that each research worker obtains the same values when using the measurement procedure. Accessible. A measure should come from data that are easily ob- tained. Tractable. A measure should be easy to work with and easy to utilize in methods and models. Comprehensible. A measure should be simple and straightforward, so it is easily understood and interpreted. Transparent. The method of measurement should be documented fully, so research workers can share results with one another in a spirit of open and honest scientific inquiry. There should be no trade secrets in science.

Chapter 2. Assessing Players 31

Sports performance measures vary widely in the degree to which they pos- sess these attributes. Some measures are dependent on timing or tracking devices in stadia, and may be accessible only to leagues and teams.

Regarding performance on the field, we record play-by-play events, com- pute box scores, and note standings of teams. We develop general measures of offensive and defensive performance and rate players and teams. Base- ball has its Sabermetrics and Moneyball. And other sports have followed suit, designing numerous measures of player performance and using them to make personnel decisions.

Psychometrics has “standardized testing,” defining explicit procedures that all test administrators must follow when making measures. Explicit, unam- biguous procedures promote reliability and reproducibility.

Measures in baseball serve to illustrate measurement principles. Batting average (BA) is a simple proportion with at bats as a devisor. We look for players with batting averages above 0.250, and batting at or above 0.300 is a goal of many hitters. Batting below 0.200, sometimes referred to as “the Mendoza line,” is not a good sign for hitters. Batting average is easily understood, but criticized as a measure of hitting ability because it fails to consider the value of walks. This is a concern about the measure’s validity.

On-base percentage (OBP) is very easy to explain. Using plate appearances rather than at bats in the divisor, OBP reflects the proportion of times that a hitter reaches first base or beyond. For OBP, we look for players whose values are around 0.333, getting on base one in every three plate appear- ances. OBP is well known and well understood, partly as a result of its use in Moneyball (Lewis 2003). But it is criticized because it fails to consider the value of extra-base hits. This, too, is a concern about measurement validity.

Slugging percentage (SLG) is a ratio: the number of total bases per at bat. It is not especially hard to understand, although it is not a percentage as its name would imply. And because it is neither a percentage nor an average, it is difficult to understand. A fan has to be “in the know” to understand that an SLG value of 0.300 as bad or a value of 0.500 as very good. Babe Ruth’s lifetime SLG was 0.690, which is very good. SLG suffers by being less comprehensible than other measures of hitting ability.

32 Sports Analytics and Data Science

On-base percentage plus slugging (OPS) is a simple sum of OBP and SLG. It is neither a percentage like OBP, nor a ratio like SLG. The intent of OPS was to provide an index of ability that would reflect both getting on base and hitting with power. OPS is another measure for which a person needs to be “in the know” to understand. The average regular-season OPS across the thirty MLB teams in the 2014 season was 0.700 (Sports Reference LLC 2015a). OPS makes little intuitive sense. There is no justification for weight- ing OBP and SLG equally in measuring hitting ability, and adding a propor- tion to a ratio gives a measure with no known units. Accordingly, OPS is neither comprehensible nor valid.

Tango, Lichtman, and Dolphin (2007) have created an alternative to OPS called the on-base average (OBA), computed as a weighted linear com- bination of various hitting measures. Their intent is to define a measure that gives reasonable, data-based weights to getting on base and hitting for power, a measure that is then scaled so it has values to conform to OBP. Tango, Lichtman, and Dolphin (2007) make a strong case for using OBA in- stead of OPS. But their method for calculating OBA is complicated.1 OBA cannot be easily explained in words, so it fails as a general index of hitting ability.

Simple, comprehensible measures are preferred to complex measures be- cause simple measures are easier to explain to fans, coaches, and managers. Among the most comprehensible measures are simple percentages or pro- portions computed from the events of a game.

In baseball, much time and effort has been devoted to attempts at finding the best single measure of player prowess. A five-tool player in baseball is a player with strong skills for running, fielding, throwing, hitting, and hitting with power. How can we combine measures of these five traits into a single measure reflecting a player’s contribution to his team?

1 Tango, Lichtman, and Dolphin (2007) provide the formula for weighted on-base average (OBA): wOBA = 0.72 × N I BB + 0.75 × HBP + 0.90 × 1B + 0.92 × RBOE + 1.24 × 2B + 1.56 × 3B + 1.95 × HR

PA where NIBB is the number of intentional bases on balls, HBP is number of times a player is hit by a pitch, 1B is the number of singles, RBOE is the number of times a batter reaches base on an error, 2B is the number of doubles, 3B is the number of triples, and HR is the number of home runs. PA refers to plate appearances, which may or may not exclude bunts, intentional bases on balls, and other events described as “obscure.”

Chapter 2. Assessing Players 33

Comprehensive player evaluation is illustrated by measures of points or wins above replacement. The general idea is to assess player abilities in hitting, fielding, base running, and throwing/pitching relative to a norm group (referred to as replacement players) and then to combine those norm- group-scaled assessments.

We ask, “What is a player’s value to his team? What if he were replaced by another player who is available to play, a player of average ability at the same position?” Wins above replacement is usually expressed in units of wins across the regular season, with ten runs being equivalent to one win. If a player’s wins-above-replacement value is 5, say, then that player’s team can expect to win five fewer games across the entire season if he must be replaced.

Wins-above-replacement measures fail the transparency test when methods of calculation are closely held company secrets. This is a special problem for norm-group-based measures because their meaning rests on the choice of norm group. If we do not know who the replacement players are, then we cannot accurately interpret wins-above-replacement. Furthermore, there is no way of checking the calculations of for-profit companies that refuse to publish their formulas and data. These measures are not in keeping with the spirit of scientific inquiry. They are neither comprehensible nor trans- parent and should be rejected by fans and teams.

For a transparent wins-above-replacement method, we can use openWAR from Baumer, Jensen, and Matthews (2015). Data and programs for this metric are in the public domain.

What about player performance over time? There are truisms in life, and one of those truisms is that the body ages. Much is understood about age effects in baseball and how to model them (Fair 2008). PECOTA, a well known measurement and prediction system, uses player-comparable age curves as its base data.2 Sadly, PECOTA is another method lacking in trans- parency.

2 We know about PECOTA from Silver (2004, 2012), who developed the method for a Baseball Prospectus in 2002–2003. Silver (2012) explains that the name comes from “a marginal infielder with the Kansas City Royals during the 1980s who was nevertheless a constant thorn in the side of my favorite Detroit Tigers.. . . Although Bill Pecota hit just .249 for his career overall, he hit .303 in games against the Tigers.” (Silver 2012, 88)

34 Sports Analytics and Data Science

Fortunately, there are alternatives to PECOTA. Teams desiring age-based measures can compute them directly, obtaining predictions about perfor- mance over the course of a player’s career (Albert and Bennett 2001; Marchi and Albert 2014). Some methods build on Bayesian inference (Albert 2009). Age-based models are most easily developed using tractable measures such as proportions.3 Age-based measures and predictions are especially useful in salary negotiations.

How do we go beyond individual player performance to look at a player’s contribution to his team? Therein lies a fundamental question in sports analytics. Anyone who knows sports knows that a good team is worth more than the sum of its parts. And it should come as no surprise that a dysfunctional team is worth less than the sum of its parts. This is to say that team effects should be considered when predicting winners and losers.

Baseball may be less susceptible to team effects than other sports. On a baseball diamond, Tinker-to-Evers-to-Chance works fine, even when Tin- kers, Evers, and Chance are not speaking with one another. Baseball is distinct from many other team sports in being defined by many individual matchups, one batter facing one pitcher, then another pitcher facing an- other batter—the events are discrete and easily identifiable as belonging to one player or another.

In most team sports, players complement one another. Some players are described as “team players,” because they help their teammates play better. Stockton and Malone worked together as a unit on the Utah Jazz. Their classic pick-and-roll made the Jazz a difficult team to beat for many years. Their individual performance measures from those years are inextricably intertwined (Oliver 2004).

By their very nature, basketball and many other team sports present special problems in evaluating individual players. A player’s value on one team

3 For an age-based measure, we could work with the proportion of hits in at bats (batting average BA), on-base percentage (OBP), or the proportion of home runs in at bats. We think of observations at time t as probabilities pt and employ the logit transform, using the log of the odds ratio. The resulting model takes the form of a logistic regression with a quadratic term in the linear predictor:

log ( pt

1 − pt

) = β0 + β1 xt + β2 xt

2

where xt is a player’s age at time t. With fitted parameters in hand (or posterior distributions for those parameters in a Bayesian context), we work backwards to obtain a player’s age curve. We find the value of the performance measure next year p(t+1) associated with the player’s age next year x(t+1).

Chapter 2. Assessing Players 35

may be quite different from his value on another team. This is revealed in the free-agency market where bids for a player vary widely across bidding teams. And this explains why player trades can benefit all teams involved.

Player evaluation has become a hot topic among the consumers of sport due in large measure to the growth in fantasy sports. Fantasy sports has an individual-player focus, with fantasy teams being little more than the sum of their player component parts. In this regard, fantasy sports are pure fantasy. They do not reflect the way players work together as a team.

Performance measures can be quite useful to coaches, managers, and own- ers. Measures of athleticism and sport proficiency are well documented in Martin (2016), with summary principles outlined in Martin and Miller (in press).

For references on measurement reliability and validity, we refer to the lit- erature of psychometrics (Gulliksen 1950; Cronbach 1951; Ghiselli 1964; Nunnally 1967; Nunnally and Bernstein 1994; Lord and Novick 1968; Fiske 1971; Brown 1976). Betz and Weiss (2001) and Allen and Yen (2002) intro- duce concepts of measurement theory. Item response theory is discussed by Rogers, Swaminathan, and Hambleton (1991). Articles in the volume edited by Shrout and Fiske (1995) provide many examples of multitrait- multimethod matrices and review quantitative methods available for the analysis of such matrices. Lumley (2010) discusses sample survey design and analysis in the R programming environment. For R functions in psy- chometrics, see Revelle (2014). Reviews of the weak measurements versus strong statistics controversy and its relevance (or lack of relevance) to sci- ence and statistical inference have been presented by Baker, Hardyck, and Petrinovich (1966) and Velleman and Wilkinson (1993).

Measurement theory applies equally well to text measures and designed surveys. We work with term frequencies within documents and term fre- quencies adjusted by overall corpus term frequencies. We assign scores to text messages and posts. We utilize methods of natural language process- ing to detect features in text and to annotate documents (Bird, Klein, and Loper 2009; Pustejovsky and Stubbs 2013). These are measurements.

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3 Ranking Teams

Gillon: “So you saying that our boxing here in Diggstown is not to your satisfaction, Mister . . . ?” Caine: “Caine. Gabriel Caine?” Gillon: “John Gillon. Nice to meet you.” Caine: “Hey, can I be frank with you?” Gillon: “Please.” Caine: “It’s never too satisfying knowing who’s gonna win every time. You know what I mean? Take this mamluke in the white trunks over here. Half way through the first fight, I knew he’ll be kissing canvas. And varoom, he’s already done it twice. So what do you think? Is he going to kiss canvas a third time? Yes.” Gillon: “What you’re saying is that you think this man in the red trunks is going to win this fight.” Caine: “Is there like an acoustical problem in here? I didn’t say I think he’s going to win this fight. I said I know he’s going to win this fight. Hey, I gotta split. By the way, I’d bet a thousand on it.” Gillon: “But would you bet two thousand bucks on it?” Cain: “What? Are you kidding?” Gillon: “There’s two things we never joke about in Diggstown, Mr. Caine: our boxing and our betting.”

—BRUCE DERN AS GILLON AND JAMES WOODS AS CAINE IN Diggstown (1992)

37

38 Sports Analytics and Data Science

The meaning of a measure is defined by its relationships with other mea- sures, and the strength of a team is defined in relation to other teams. When picking winning teams, it is not sufficient to consider individual player statistics. We must see how teams compete with one another.

Measurement is the assignment of numbers to attributes according to rules. And just as we assign numbers to player performance attributes, we can as- sign numbers to teams. When working with team performance, we usually generate ratings and rankings.

There is debate about how to rank teams, especially when teams have lim- ited opportunity to play one another. Most of us remember the extensive controversies surrounding the Bowl Championship Series (BCS) for college football prior to the introduction of a limited playoff program. And there remains controversy about which teams should qualify for the playoffs due to strength-of-schedule differences across teams.

Compared with college athletics, professional team sports have more bal- ance across league schedules, but perfect balance does not exist. Divisions and conferences are not equal in player abilities, and teams play more of their games with other teams in their own conferences and divisions.

Consider the problem of assessing team strength in the National Basketball Association. Table 3.1 shows the NBA team win/loss records at the close of the regular season 2014–2015. Eight teams from each conference make the playoffs. Western Conference teams are at a disadvantage because there are more strong teams in that conference. NBA schedules are not balanced.

How shall we judge or rank teams, given imbalance in team schedules? One way employs unidimensional scaling from psychometrics, which uses team win/loss data from games. Win/loss data are paired comparisons, one team over another in each game.

To employ unidimensional scaling, we construct a matrix with the number of times each team beats each other team. This matrix is converted to a matrix of proportions, which are then averaged across rows or columns and referred to a standard normal distribution. As a final step in the process, we set a desired mean and standard deviation for scale scores. The method automatically adjusts for strength of schedule while defining interval-level measures from what were originally paired comparisons.

Chapter 3. Ranking Teams 39

Table 3.1. NBA Team Records (2014–2015 Season)

Conference Division Team Name (Playoff *) Abbreviation Wins Losses P(Win)

Eastern Atlantic Boston Celtics* BOS 40 42 0.488 Brooklyn Nets* BKN 38 44 0.463 New York Knicks NYK 17 65 0.207 Philadelphia 76ers PHI 18 64 0.220 Toronto Raptors* TOR 49 33 0.598

Central Chicago Bulls* CHI 50 32 0.610 Cleveland Cavaliers* CLE 53 29 0.646 Detroit Pistons DET 32 50 0.390 Indiana Pacers IND 38 44 0.463 Milwaukee Bucks* MIL 41 41 0.500

Southeast Atlanta Hawks* ATL 60 22 0.732 Charlotte Hornets CHA 33 49 0.402 Miami Heat MIA 37 45 0.451 Orlando Magic ORL 25 57 0.305 Washington Wizards* WAS 46 36 0.561#DIV/0!#DIV/0!

Western Southwest Dallas Mavericks* DAL 50 32 0.610 Houston Rockets* HOU 56 26 0.683 Memphis Grizzlies* MEM 55 27 0.671 New Orleans Pelicans* NOP 45 37 0.549 San Antonio Spurs* SAS 55 27 0.671

Northwest Denver Nuggets DEN 30 52 0.366 Minnesota Timberwolves MIN 16 66 0.195 Oklahoma City Thunder OKC 45 37 0.549 Portland Trail Blazers* POR 51 31 0.622 Utah Jazz UTA 38 44 0.463

Pacific Golden State Warriors* GSW 67 15 0.817 Los Angeles Clippers* LAC 56 26 0.683 Los Angeles Lakers LAL 21 61 0.256 Phoenix Suns PHX 39 43 0.476 Sacramento Kings SAC 29 53 0.354

40 Sports Analytics and Data Science

Figure 3.1. Assessing Team Strength: NBA Regular Season (2014–2015)

400 450 500 550 600

Team Scale Scores Adjusted for Strength of Schedule

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Figure 3.1 shows the results of a unidimensional scaling of box score data from the 2014–2015 NBA season. A team of average strength would have a score of 500 on this scale, with the standard deviation across teams set to 100. Unidimensional scales reflect differences between teams in strength, not just rank orders of teams. Note the strength of the Golden State Warriors relative to other teams. From the unidimensional scaling alone, we would have predicted the Golden State Warriors to be victorious in the playoffs.

Another method for rating teams based on wins and losses comes from work on chess player rankings by Árpád Élö (1903–1992). The Elo system has been adapted to professional team sports in the United States and is the basis of Jeff Sagarin’s rankings in USA Today.

In ranking sports teams, we can go beyond binary win/loss data to con- sider the margin of victory or game point differentials. Again we must account for variability in team schedules. When looking at points scored in games, we must also adjust for games involving extra innings in baseball or overtime periods in football or basketball.

Chapter 3. Ranking Teams 41

Another consideration when working with scores relates to very high scor- ing games. These may result from games involving teams that are unevenly matched (“blowouts”) or games that have little bearing on team possibili- ties for moving into the playoffs. In games such as these, teams may be using second string or bench players in place of their usual lineups. Some adjustment of game scores would be appropriate in such instances.

Other approaches to team rankings involve developing separate measures or ranks for offensive and defensive performance, which are later combined into a single measure or rank. Sometimes it makes sense to employ a mul- tivariate approach, accounting for team performance on many measures and/or across many player positions. Strength profiles for teams may be represented in parallel coordinate plots.

Teams want to build future winners. General managers wonder about the characteristics that make winning more likely. Teams can improve through player drafts, free agent acquisitions, promotion of players from minor leagues, and player trades. And player performance measures evaluated in the context of current team performance measures can point to the player additions that are most beneficial to a team. A general manager can assess a team’s ranking with and without the addition of new players.

Player selection problems have multiple constraints. There are constraints on team size and composition. There is often a salary cap constraint. The decision variables are binary—each available player is either selected for the team or not. Problems such as this are known as multidimensional knapsack problems (MKP) and have been studied extensively in operations research (Fréville 2004; Kellerer, Pferschy, and Pisinger 2004). Guttag (2013) provides an introduction to knapsack problems using Python examples. See the overview of mathematical programming presented in appendix A (page 200).

Having determined player rosters, team managers and coaches must de- cide on player starting lineups for each game. Again, we can provide sug- gestions using methods of constrained optimization such as mathematical programming. With the extensive data that are available today, it is possible to build credible models for improving the performance of teams.

42 Sports Analytics and Data Science

Sports team rankings and models for predicting sporting event outcomes have garnered considerable attention from mathematicians as well as sports enthusiasts. Langville and Meyer (2012) provide a comprehensive review of rating and ranking algorithms and methods. Ranking methods, the use of rankings in the design of sporting tournaments, and the seeding of teams in tournaments have been discussed extensively (Thompson 1975; Groen- eveld 1990; Appleton 1995; Carlin 1996; West 2006). There has been special interest in National Football League games (Thompson 1975; Stern 1991; Glickman and Stern 1998). And much has been written about rating and ranking strategies for picking winning brackets in the men’s Division One NCAA basketball tournament, known as March Madness (Schwertman, Mc- Cready, and Howard 1991; Schwertman, Schenk, and Holbrook 1996; Carlin 1996; Kaplan and Garstka 2001; West 2006).

Unidimensional scaling and the method of paired comparisons have long histories in measurement theory and statistics. Paired comparisons have been used in taste-testing experiments, psychophysical investigations, pref- erence scaling, and studies of consistency across judges (inter-rater relia- bility), as well as in ranking players and teams. The extensive literature in this field, documented in Davidson and Farquhar (1976), dates back to early work by Thurstone (1927) and Guilford (1936), who used normal dis- tribution theory to obtain scale scores for underlying psychological dimen- sions. In the statistical literature, Bradley and Terry (1952) introduced tra- ditional logistic or logit models for analyzing paired comparisons. Reviews of paired comparison methods have been provided by Torgerson (1958), David (1963), and Bradley (1976).

Exhibit 3.1 shows an R program for unidimensional scaling of box scores from the 2014–2015 NBA season. These provided the basis for construct- ing matrices of wins and proportions of wins across the season. The matrix of proportions is used to compute average schedule-adjusted proportions, which are then referred to a standard normal distribution. As a final step in the process, we set the desired mean and standard deviation for univari- ate scale scores. The program employs standard R graphics to plot results from this unidimensional scaling. Included in the program are matrices for performing other types of team rankings, including those that take account of runs scored by winning and losing teams.

Chapter 3. Ranking Teams 43

Exhibit 3.1. Assessing Team Strength by Unidimensional Scaling (R)

# Assessing Team Strength by Unidimensional Scaling (R)

# NBA Regular Season 2014-2015 data from Basketball-Reference.com

# read comma-delimited text file to create data frame

nba_input <- read.csv("basketball_2014_2015_season.csv",

stringsAsFactors = FALSE)

# add record number to records

record_number <- seq(nrow(nba_input))

nba_scores <- cbind(data.frame(record_number), nba_input)

# explore the data

with(nba_scores, plot(home_points, visitor_points))

with(nba_scores, table(overtime))

# define minutes played using overtime information

nba_scores$minutes <- rep(48, length = nrow(nba_scores)) # standard game

for (i in seq(along = nba_scores$minutes)) {

if(nba_scores$overtime[i] == "OT")

nba_scores$minutes[i] <- nba_scores$minutes[i] + 5 # 1 OT period

if(nba_scores$overtime[i] == "2OT")

nba_scores$minutes[i] <- nba_scores$minutes[i] + 10 # 2 OT periods

if(nba_scores$overtime[i] == "3OT")

nba_scores$minutes[i] <- nba_scores$minutes[i] + 15 # 3 OT periods

}

with(nba_scores, table(overtime, minutes)) # check minute calculations

# compute points per minute for each team

nba_scores$visitor_ppm <- nba_scores$visitor_points / nba_scores$minutes

nba_scores$home_ppm <- nba_scores$home_points / nba_scores$minutes

# check calculations

print(head(nba_scores))

print(tail(nba_scores))

# explore points-per-minute data

with(nba_scores, plot(home_ppm, visitor_ppm))

# read in team names and abbreviations

team_info <- read.csv("nba_team_names_abbreviations.csv",

stringsAsFactors = FALSE)

# append team information to nba_scores data frame

list_of_team_names <- team_info$team_name

# first do the visitor team

nba_scores$visitor_conference <- rep("", length = nrow(nba_scores))

nba_scores$visitor_division <- rep("", length = nrow(nba_scores))

nba_scores$visitor_code <- rep("", length = nrow(nba_scores))

44 Sports Analytics and Data Science

for (i in seq(along = list_of_team_names)) {

this_team_info <-

team_info[(team_info$team_name == list_of_team_names[i]),]

indices_for_visitor_team <-

which (nba_scores$visitor_team == list_of_team_names[i])

for (j in seq(along = indices_for_visitor_team)) {

nba_scores$visitor_conference[indices_for_visitor_team[j]] <-

this_team_info$conference[1]

nba_scores$visitor_division[indices_for_visitor_team[j]] <-

this_team_info$division[1]

nba_scores$visitor_code[indices_for_visitor_team[j]] <-

this_team_info$abbreviation[1]

}

}

# next do the home team

nba_scores$home_conference <- rep("", length = nrow(nba_scores))

nba_scores$home_division <- rep("", length = nrow(nba_scores))

nba_scores$home_code <- rep("", length = nrow(nba_scores))

for (i in seq(along = list_of_team_names)) {

this_team_info <-

team_info[(team_info$team_name == list_of_team_names[i]),]

indices_for_home_team <-

which (nba_scores$home_team == list_of_team_names[i])

for (j in seq(along = indices_for_home_team)) {

nba_scores$home_conference[indices_for_home_team[j]] <-

this_team_info$conference[1]

nba_scores$home_division[indices_for_home_team[j]] <-

this_team_info$division[1]

nba_scores$home_code[indices_for_home_team[j]] <-

this_team_info$abbreviation[1]

}

}

# define winning team (Visitor or Home)

nba_scores$win_visitor_home <- rep("Home", length = nrow(nba_scores))

for (i in seq(along = nba_scores$record_number))

if (nba_scores$visitor_ppm[i] > nba_scores$home_ppm[i])

nba_scores$win_visitor_home[i] <- "Visitor"

# who wins more games.. visitor or home team

with(nba_scores, table(win_visitor_home))

with(nba_scores, plot(home_ppm, visitor_ppm))

# define winning and losing teams by three-character abbreviation/code

nba_scores$win_team_code <- rep("", length = nrow(nba_scores))

nba_scores$lose_team_code <- rep("", length = nrow(nba_scores))

for (i in seq(along = nba_scores$record_number)) {

if (nba_scores$visitor_ppm[i] > nba_scores$home_ppm[i]) {

nba_scores$win_team_code[i] <- nba_scores$visitor_code[i]

nba_scores$lose_team_code[i] <- nba_scores$home_code[i]

}

Chapter 3. Ranking Teams 45

if (nba_scores$visitor_ppm[i] < nba_scores$home_ppm[i]) {

nba_scores$win_team_code[i] <- nba_scores$home_code[i]

nba_scores$lose_team_code[i] <- nba_scores$visitor_code[i]

}

}

# check the nba_scores data frame

print(head(nba_scores))

print(tail(nba_scores))

# create OKC data frame for testing and visualization example

OKC_visitor <- nba_scores[(nba_scores$visitor_code == "OKC"),]

OKC_home <- nba_scores[(nba_scores$home_code == "OKC"),]

OKC_data <- rbind(OKC_visitor, OKC_home)

OKC_data <- OKC_data[sort.list(OKC_data$record_number),]

# save file for Oklahoma City Thunder for data visualization work

write.csv(OKC_data, file = "okc_data_2014_2015.csv", row.names = FALSE)

# write win team score and lose team score in points per minute

nba_scores$win_team_ppm <- rep(0, length = nrow(nba_scores))

nba_scores$lose_team_ppm <- rep(0, length = nrow(nba_scores))

for (i in seq(along = nba_scores$record_number)) {

if (nba_scores$visitor_ppm[i] > nba_scores$home_ppm[i]) {

nba_scores$win_team_ppm[i] <- nba_scores$visitor_ppm[i]

nba_scores$lose_team_ppm[i] <- nba_scores$home_ppm[i]

}

if (nba_scores$visitor_ppm[i] < nba_scores$home_ppm[i]) {

nba_scores$win_team_ppm[i] <- nba_scores$home_ppm[i]

nba_scores$lose_team_ppm[i] <- nba_scores$visitor_ppm[i]

}

}

# compute margin of victory in points per minute

nba_scores$margin_ppm <- nba_scores$win_team_ppm - nba_scores$lose_team_ppm

# initialize matrices for entire set of 30 teams

ordered_team_codes <- sort(team_info$abbreviation)

# total number of wins

wins_mat <- matrix(0, nrow = 30, ncol = 30,

dimnames = list(ordered_team_codes, ordered_team_codes))

prop_mat <- wins_mat # proportion wins

ppm_mat <- wins_mat # sum of ppm scores

# build matrices for entire set of 30 teams

for (i in seq(along = nba_scores$record_number)) {

# tally the number of times team k beats team j

wins_mat[nba_scores$lose_team_code[i], nba_scores$win_team_code[i]] <-

wins_mat[nba_scores$lose_team_code[i], nba_scores$win_team_code[i]] + 1

# sum the ppm scores for teams and enter in ppm_mat

# two enteries needed for each record in nba_scores

46 Sports Analytics and Data Science

ppm_mat[nba_scores$lose_team_code[i], nba_scores$win_team_code[i]] <-

ppm_mat[nba_scores$lose_team_code[i], nba_scores$win_team_code[i]] +

nba_scores$win_team_ppm[i]

ppm_mat[nba_scores$win_team_code[i], nba_scores$lose_team_code[i]] <-

ppm_mat[nba_scores$win_team_code[i], nba_scores$lose_team_code[i]] +

nba_scores$lose_team_ppm[i]

}

# check wins_mat entries... should be 82 games for every team

for (j in 1:length(ordered_team_codes))

print(sum(wins_mat[,j]) + sum(wins_mat[j,]))

# compute matrix of proportions prop_mat

# proportion of times team j beats team k

for(j in 1:length(ordered_team_codes)) { # begin outer for-loop

for(k in 1:length(ordered_team_codes)) { # begin inner for-loop

if (j == k) prop_mat[j,k] <- NA # set diagonal entries missing

if (j > k) { # begin outer if-block

between_team_games <-

wins_mat[ordered_team_codes[j],ordered_team_codes[k]] +

wins_mat[ordered_team_codes[k],ordered_team_codes[j]]

# if teams never play others within the season

# we set the entry in the cell

# to be the mean of the team

if (between_team_games == 0) { # begin first inner if-block

prop_mat[j,k] <- sum(wins_mat[j,]) /

(sum(wins_mat[,j]) + sum(wins_mat[j,]))

prop_mat[k,j] <- sum(wins_mat[k,]) /

(sum(wins_mat[,k]) + sum(wins_mat[k,]))

} # end first inner if-block

# when teams play other teams at least once

# we compute the proportion of times they beat one another

if (between_team_games > 0) { # begin second inner if-block

prop_mat[j,k] <-

wins_mat[ordered_team_codes[j],ordered_team_codes[k]]/

between_team_games

prop_mat[k,j] <-

wins_mat[ordered_team_codes[k],ordered_team_codes[j]]/

between_team_games

} # end second inner if-block

} # end outer if-block

} # end inner for-loop

} # end outer for-loop

# check prop_mat against known results for the season

# results should be close but not exact

# because prop_mat adjusts for strength of schedule

for(i in seq(along = ordered_team_codes))

cat("\n", ordered_team_codes[i], ":", mean(prop_mat[,i], na.rm = TRUE))

Chapter 3. Ranking Teams 47

# unidimensional scaling work begins here

# begin by defining the paired_comparisons scaling matrix

pc_mat <- prop_mat

for(j in 1:length(ordered_team_codes))

for(k in 1:length(ordered_team_codes))

if (j == k) pc_mat[j,k] <- 0.50 # set diagonal entries missing

nobjects <- length(ordered_team_codes)

mean_pc_mat <- numeric(nobjects)

object_quantile <- numeric(nobjects)

for(j in 1:nobjects)

{

mean_pc_mat[j] <- mean(pc_mat[,j])

object_quantile[j] <- qnorm(mean_pc_mat[j])

}

# user-defined function provides mean 500 standard deviation 100

z.score.converter <- function(z) {round(((100*z) + 500),digits=0)}

scale_score <- numeric(nobjects)

for(j in 1:nobjects)

scale_score[j] <- z.score.converter(object_quantile[j])

sorted_team_info <- team_info[sort.list(team_info$abbreviation),]

sorted_team_info$scale_score <- scale_score

sorted_team_info$name_with_score <- rep("", length = nrow(sorted_team_info))

for(i in seq(along = ordered_team_codes))

sorted_team_info$name_with_score[i] <-

paste(sorted_team_info$team_name[i],

" (", sorted_team_info$scale_score[i], ")", sep = "")

scaling_frame <-

sorted_team_info[,c("abbreviation", "team_name",

"name_with_score", "scale_score")]

names(scaling_frame) <-

c("object.name", "long.object.name",

"long.object.name.with.score", "scale_score")

ordered_scaling_frame <-

scaling_frame[sort.list(scale_score, decreasing=FALSE),]

# plotting to external pdf file using standard R graphics

pdf(file = "fig_unidimensional_scaling_analysis.pdf",

width = 11, height = 8.5)

text.angle = 45

par(mfrow=c(1,1), xpd=NA, cex=1, yaxt= "n" , lwd=3, bty="n",

srt=text.angle, mar=c(5, 0, 4, 0) + 0.1)

48 Sports Analytics and Data Science

plot(ordered_scaling_frame$scale_score,

rep(0.1,length(ordered_scaling_frame$scale_score)), type="h",

xlab=paste("Team Scale Scores Adjusted for Strength of Schedule"),

ylab="",

ylim=c(0,2),

xlim=c(min(ordered_scaling_frame$scale_score) - 50,

max(ordered_scaling_frame$scale_score) + 50))

text(ordered_scaling_frame$scale_score + 40,

rep(0.65,length(ordered_scaling_frame$scale_score)),

ordered_scaling_frame$long.object.name.with.score, pos=2, cex=1)

dev.off()

4 Predicting Scores

“You know what the difference between hitting .250 and .300 is? It’s 25 hits. Twenty-five hits in 500 at-bats is 50 points. OK? There’s six months in a season. That’s about 25 weeks. That means if you get one extra flare a week. Just one. A gork. You get a ground ball with eyes. You get a dying quail. Just one more dying quail a week, and you go to Yankee Stadium.”

—KEVIN COSTNER AS CRASH DAVIS IN Bull Durham (1988)

Sporting events take place in a public arena. We know the managers and players. We know their salaries, and we have extensive information about their performance. We know who wins, and we know who loses. The data are available and easily accessible. These data, both text and numbers, come to us in time and place. And the analysis of these data may be carried out using methods well known to data scientists.

Competitive advantage—the extra inches, hits, and free throws—can be gained through the use of predictive models. Just as we can predict which customers will buy products or which stocks will outperform the market, we can predict which players and teams will succeed on the fields and courts of play. Just as easily as we can guide the decisions of manufacturers and retailers, we can guide the decisions of coaches and general managers in sports.

49

50 Sports Analytics and Data Science

Figure 4.1. Work of Data Science

Measure

Model

Predict Test

Question

? Report

Data

By analyzing sports data, we may learn that bunting to advance a runner in baseball or punting on fourth down in football are not good ideas. We may discover that the most valuable basketball player is not the one who scores the most points or makes the highest percentage of three-point shots, but the one who helps his teammates score. Through analytics, we discover many small findings of interest or curiosity in sports. But more importantly, we gain insight into sports business management and strategy.

Just as we can view sports in a larger context as entertainment, we can view sports analytics within the larger context of data science. Information technology professionals deliver data as data. Statisticians and machine learning experts focus on models. Data scientists, building on a foundation of data and models, tell a story that others can understand. They are con- cerned with prediction, testing, and interpreting model results, and if the data and models warrant, recommending management action. The work of data science, illustrated in figure 4.1, involves learning from data and models and helping managers make informed decisions. We begin with a question. We end with a story, a report to management.

Predictive models come in two general forms, referred to as classification and regression. Classification concerns predicting a future class or category. Will the consumer of sports buy a ticket to the game? If she buys a ticket to the game, will it be a ticket for a standard, preferred, or a box seat. Perhaps she becomes a loyal fan of the team. If so, will she buy a season ticket for next year?

Chapter 4. Predicting Scores 51

With classification, we predict consumer choices or discrete responses. With regression, on the other hand, we predict a response with meaningful mag- nitude. How many dollars will be spent on tickets? How much will be spent on concessions? How many tickets will be sold to the game? What will be in the number of runs or points scored by the home team? What will be the right fielder’s batting average next year? How many yards will the fullback run next week? What kind of salary will a player receive when he becomes a free agent?

A model is a representation of things, a rendering or description of reality. A typical model in data science is an attempt to relate one set of variables to another. Limited, imprecise, but useful, a model helps us to make sense of the world. A model is more than just talk because it is based on data.

We can think of data science as the new statistics, a blending of model- ing techniques, information technology, and business savvy. Data science apprehends a data-intensive world, requiring a multidisciplinary skill set essential for success in business, nonprofit organizations, and government. Data science is predictive analytics. Whether forecasting sales or market shares, finding a good retail site or investment opportunity, identifying consumer segments and target markets, or assessing the potential of new products or risks for existing products, modeling methods in predictive an- alytics provide the key.

Data scientists speak the language of business—accounting, finance, mar- keting, and management. They know about information technology, in- cluding data structures, algorithms, and object-oriented programming. They understand statistical modeling, machine learning, and mathematical pro- gramming. Data scientists are methodological eclectics, drawing from many scientific disciplines and translating the results of empirical research into words and pictures that management can understand.

Data science, as with much of statistics, involves searching for meaningful relationships among variables and representing those relationships in mod- els. There are response variables—things we are trying to predict. There are explanatory variables or predictors—things that we observe, manipulate, or control and might relate to the response.

52 Sports Analytics and Data Science

Figure 4.2. Data and Models for Research

Traditional Research

Model

Real Data

Data-Adaptive Research

Real Data

Model

Model-Dependent Research

Model

Generated Data

Real Data

Prediction problems are defined by their width or number of potential pre- dictors and by their depth or number of observations in the data set. It is the number of potential predictors in business, marketing, and investment analysis that causes the most difficulty. There can be thousands of potential predictors with weak relationships to the response. With the aid of com- puters, hundreds or thousands of models can be fit to subsets of the data and tested on other subsets of the data, providing an evaluation of each predictor. Predictive modeling involves finding good subsets of predictors. Models that fit the data well are better than models that fit the data poorly. Simple models are better than complex models.

Consider three general approaches to research and modeling: traditional, data-adaptive, and model-dependent. Figure 4.2 illustrates the approaches. With a traditional approach, statistical inference and modeling begin with the specification of a theory or model. We use methods such as linear re- gression and logistic regression to estimate parameters for linear predictors. Classical or Bayesian methods of statistical inference may be employed. We fit models to data and check models with diagnostics. We validate models before using them to make predictions.

Chapter 4. Predicting Scores 53

When we employ a data-adaptive approach, we begin with data and search through those data to find useful predictors. We give little thought to the- ories or hypotheses prior to running the analysis. This is the world of ma- chine learning, sometimes called statistical learning or data mining. Data- adaptive methods adapt to the available data, representing nonlinear rela- tionships and interactions among variables. The data determine the model. Data-adaptive methods are data-driven. As with traditional models, we validate data-adaptive models before using them to make predictions.

Model-dependent research is the third approach. It begins with the spec- ification of a model and uses that model to generate data, predictions, or recommendations. Simulations and mathematical programming methods, primary tools of operations research, are examples of model-dependent research. When employing a model-dependent or simulation approach, models are improved by comparing generated data with real data. We ask whether simulated consumers, firms, and markets behave like real con- sumers, firms, and markets. The comparison with real data serves as a form of validation.

Data may be organized by observational unit, time, and space. The observa- tional or cross-sectional unit could be an individual consumer or business or any other basis for collecting and grouping data. Data are organized in time by seconds, minutes, hours, days, and so on. Space or location is often defined by longitude and latitude. As we consider sports analytics problems in this book, we touch on many types of models, including cross- sectional, time series, and spatial data models.

Whatever the structure of the data and associated models, prediction is the unifying theme. We use the data we have to predict data we do not yet have, recognizing that prediction is a precarious enterprise. It is the process of extrapolating and forecasting. And model validation is essential to the process.

How do we test the accuracy of a predictive model? We employ a training- and-test regimen. As in economic and financial research, we see how well we can predict the past before we attempt to predict the future. That is, we use more distant past observations to predict less distant past observations. If we are working with a sixteen-week football season, for example, we use the first ten weeks’ data to predict what will happen in the eleventh week.

54 Sports Analytics and Data Science

Figure 4.3. Training-and-Test Regimen for Model Evaluation

Develop models

Validation Set

Training Set

Test Set

Test Set

Training Set

Complete Data Set Complete Data Set

Evaluate models

Evaluate the selected model

Select the best model based on validation set performance

Develop models

Evaluate models

Two-way Partition Three-way Partition

Then we use the first eleven weeks’ data to predict what will happen in the twelfth week, and so on. Measures of uncertainty in predicting the past help us to assess uncertainty about predicting the future.

To make predictions, we may employ classical or Bayesian methods. Or we may dispense with traditional statistics entirely and rely on machine learning algorithms. We do what works. Our approach to data science is based on a simple premise:

The value of a model lies in the quality of its predictions.

Indices such as the Akaike information criterion (AIC) or the Bayes infor- mation criterion (BIC) help us to to judge one model against another, pro- viding a balance between goodness-of-fit and parsimony. Central to our approach is a training-and-test regimen. We partition sample data into train- ing and test sets. We build our model on the training set and evaluate it on the test set. Simple two- and three-way data partitioning are shown in figure 4.3.

Chapter 4. Predicting Scores 55

A random splitting of a sample into training and test sets could be fortu- itous, especially when working with small data sets, so we sometimes con- duct statistical experiments by executing a number of random splits and averaging performance indices from the resulting test sets. There are exten- sions to and variations on the training-and-test theme.

One variation on the training-and-test theme is multi-fold cross-validation, illustrated in figure 4.4. We partition the sample data into M folds of ap- proximately equal size and conduct a series of tests. For the five-fold cross- validation shown in the figure, we would first train on sets B through E and test on set A. Then we would train on sets A and C through E, and test on B. We continue until each of the five folds has been utilized as a test set. We assess performance by averaging across the test sets. In leave-one-out cross-valuation, the logical extreme of multi-fold cross-validation, there are as many test sets as there are observations in the sample.

Another variation on the training-and-test regimen is the class of boot- strap methods. If a sample approximates the population from which it was drawn, then a sample from the sample (what is known as a resample) also approximates the population. A bootstrap procedure, as illustrated in fig- ure 4.5, involves repeated resampling with replacement. We take many random samples with replacement from the sample, and for each of these resamples, we compute a statistic of interest. The bootstrap distribution of the statistic approximates the sampling distribution of that statistic.

What is the value of the bootstrap? It frees us from having to make as- sumptions about the population distribution. We can estimate standard er- rors and make probability statements working from the sample data alone. The bootstrap may also be employed to improve estimates of prediction er- ror within a leave-one-out cross-validation process. Cross-validation and bootstrap methods are reviewed in Davison and Hinkley (1997), Efron and Tibshirani (1993), and Hastie, Tibshirani, and Friedman (2009).

Much of what passes as sports analytics is performance measurement alone. In baseball, as we have discussed, there is debate about which is the best measure of hitting prowess: batting average, on-base percentage, slugging percentage, or some combination of these. But when we need to make a prediction, we can dispense with arguments about measurement validity and use the combination of measures that provides the best prediction.

56 Sports Analytics and Data Science

Figure 4.4. Training-and-Test Using Multi-fold Cross-validation

Randomly divide the sample into folds of approximately equal size:

Each fold serves once as a test fold:

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Iteration 5

A B C D E

Test

Train Train Train

Train

Train Train Train Train

Train Train Train Train

Train

Train TrainTrain

TrainTrainTrain Train

Test

Test

Test

Test

Chapter 4. Predicting Scores 57

Figure 4.5. Training-and-Test with Bootstrap Resampling

Sample

Population

Bootstrap Sample 1

Bootstrap Sample 2

Bootstrap Sample B

Random sample of size n

Random sample of size n with replacement

Random sample of size n with replacement Random sample

of size n with replacement

S*1 S*2 S*B

Bootstrap Sampling Distribution for the Statistic S

S*BS*2S*1The quantities , , . . . , represent the statistic S computed from B bootstrap samples.

58 Sports Analytics and Data Science

Building a predictive model is a matter of finding the right combination of measures to provide trustworthy predictions. We select measures or explanatory variables. We select the type of modeling method to be em- ployed. And with traditional statistical methods, we specify the mathemat- ical form of models and estimate the weights to apply to measures.

The simplest of models are those that employ a linear predictor, adding one variable effect to another with regression coefficients as weights. More com- plicated models consider interactions among explanatory variables. These may take a linear form as well, but they are more likely to employ a data- adaptive method, using a machine learning algorithm to extract the model specification from the data themselves.

With hundreds or thousands of measures or explanatory variables from which to choose, there will be millions of possible model specifications. Selecting the right method and the right model specification—this is the art and science of predictive modeling. There are many modeling tech- niques from which to choose, including traditional linear regression, tree- structured regression, and neural networks, among others.

Often a researcher will test a number of techniques to see which technique or combination of techniques works best. An approach that works well in many contexts is an ensemble technique that combines many small, sim- ple models into a large, more complex model. For example, we could use tree-structured regression for each of a number of performance measures in baseball, and then average their forecasts to get a summary prediction.

To determine the accuracy, goodness, or utility of a model, we choose a measure of accuracy. We could use the percentage error in prediction, the mean-square error in prediction, or the correlation between observed scores and the predicted scores.

A good choice for measuring the accuracy of a regression model is the squared correlation of observed scores with predicted scores, also known as the coefficient of determination. The coefficient of determination can be interpreted as a proportion. It is the proportion of response variance ac- counted for by the predictive model. As a proportion, it varies between zero and one in all settings. When the coefficient of determination is zero, the model is of no value in predicting the future. Perfect predictive power would yield a coefficient of determination equal to one.

Chapter 4. Predicting Scores 59

Figure 4.6. Predictive Modeling Framework for Team Sports

Sports Database and Game-day Information

Visiting Team Offense

Home Team Offense

Game-day Simulator

Predicted probabilities of winning for visiting and home teams

Selected explanatory variables

Expected scoring by visiting team

Expected scoring by home team

Home Team Defense

Visiting Team Defense

Selected explanatory variables

Source. Miller (2008).

Miller (2008) presents a generic, data-driven approach to picking a winning team, as shown in figure 4.6. The modeling framework follows the prin- ciples of predictive inference. Explanatory variables relate to past player and team performance. These are used to predict runs or points scored by opposing teams. We note where and when games are played and other con- ditions that may affect game outcomes. Starting pitchers, for example, are especially important in predicting outcomes in baseball.

The framework allows distinct sets of explanatory variables to be used for visiting and home teams. The drivers of success for the Yankees may be different from the drivers of success for the Red Sox, the drivers for the Red Sox different from the Angels, the Angels different from the Dodgers, and so on. For each team, the things that matter when playing at home may be different from the things that matter when playing away.

Various measures of win/loss strength and offensive and defensive per- formance may be used as explanatory variables. An important part of the modeling framework is game-day simulation, which we illustrate in chap- ter 10 with an example from Major League Baseball.

60 Sports Analytics and Data Science

One approach to game-day modeling is to predict runs or points scored and runs or points allowed for each team and then use simulation to convert these into binary win/loss predictions. A second approach is to treat the problem as a logistic regression, predicting the win/loss response directly. A third approach is to use multivariate regression to predict visiting and home team runs concurrently.

Think of a game as a multivariate or, more precisely, a bivariate regression problem—we predict two scores simultaneously, scores of home and vis- iting teams. Then we translate each pair of predicted scores into a binary classification—either the home team wins or the visiting team wins. With predictions of winners in hand, it is a simple matter to see what happens in actual games and compute the proportion of correct predictions, an index of predictive accuracy well understood by managers and sports enthusiasts.

Predictive models can be traditional or data-adaptive, or a combination of the two. As always, a training-and-test regimen is employed in the evalua- tion of models.

The data of sports and the predictive models that draw on these data can provide competitive advantage. We may see a time when the smartest, best informed, and most technologically advanced teams are the ones that win.

5 Making Game-Day Decisions

Jimmy: “Taking a little day trip?” Dottie: “No, Bob and I are driving back to Oregon.” Jimmy: “You know, I really thought you were a ball player.” Dottie: “Well, you were wrong.” Jimmy: “Was I?” Dottie: “Yeah, it is only a game, Jimmy. It’s only a game. And I have Bob. I don’t need this. I don’t.” Jimmy: “I gave away five years at the end of my career to drinking. Five years. And now there isn’t anything I wouldn’t give to get back one day of it.” Dottie: “Well, we’re different.” Jimmy: “Chicken shit, Dottie. If you want to go back to Oregon and make a hundred babies, great. I’m in no position to tell anyone how to live. But sneaking out like this, quitting—you’ll regret it the rest of your life. Baseball is what gets inside of you. It’s what lights you up. You can’t deny that.” Dottie: “It just got too hard.” Jimmy: “It’s supposed to be hard. If it wasn’t hard, everyone would do it. The hard is what makes it great.”

—TOM HANKS AS JIMMY DUGAN AND GEENA DAVIS AS DOTTIE HINSON

IN A League of Their Own (1992)

61

62 Sports Analytics and Data Science

To show how data can inform game-day decisions, it is convenient to begin with baseball because baseball may be described as a sequence of discrete events. Play stops and play starts in baseball—there is no continuous clock or time limit. Among the sports, analytics in baseball is the most advanced, with extensive documentation in the public domain.

Table 5.1 shows the twenty-five states of a baseball half-inning, along with the expected runs to be scored by the time the inning ends. The expected runs in this table are computed from play-by-play records across all regular season games in 2014 (FanGraphs.com 2015).

Every baseball half-inning is a sequence of events or transitions from one state to another. It begins with no outs and no one on base (state code [0000]). It ends with three outs, referred to as an absorbing state or sink (state code [END]). There are also probabilities associated with going from one state to another—these are called transition probabilities in the lan- guage of Markov chains, and they can be estimated from baseball play- by-play data.

A pitcher’s perfect inning is represented by the sequence {[0000], [1000], [2000], [END]}. If a pitcher were to allow three runners on base through walks, say, and then strike out the side, the sequence of baseball states would be represented as {[0000], [0100], [0110],[0111], [1111], [2111], [END]}.

A no-out walk with no runners on first base would take a team from [0000] to [0100], which has the same effect as a single with with no runners on base. In fact, a walk is the same as a single with one or two outs, moving from state [1000] to [1100] or from [2000] to [2100]. Quite often, however, a walk is not as good as a hit, because a hit potentially moves base runners further toward home. With a runner on first base, for example, a single could move that runner to third. With no outs, we often see a transition from [0100] to [0101], whereas a walk with no outs and a runner on first is represented as a transition from [0100] to [0110].

We can use baseball states and their associated expected runs data to pro- vide advice to managers and coaches making game-day decisions. Suppose we begin with a runner on first with no outs, represented as [0100]. We note its associated expected runs 0.831. A batter coming to home plate could at- tempt a sacrifice bunt. If successful, that sacrifice bunt would move the team to the state [1010] with its associated expected runs 0.644.

Chapter 5. Making Game-Day Decisions 63

Table 5.1. Twenty-five States of a Baseball Half-Inning

State Expected Code Outs First Second Third Runs

[0000] 0 0 0 0 0.461 [1000] 1 0 0 0 0.234 [2000] 2 0 0 0 0.095

[0100] 0 1 0 0 0.831 [1100] 1 1 0 0 0.489 [2100] 2 1 0 0 0.214

[0010] 0 0 1 0 1.068 [1010] 1 0 1 0 0.644 [2010] 2 0 1 0 0.305

[0001] 0 0 0 1 1.426 [1001] 1 0 0 1 0.865 [2001] 2 0 0 1 0.413

[0110] 0 1 1 0 1.373 [1110] 1 1 1 0 0.908 [2110] 2 1 1 0 0.343

[0101] 0 1 0 1 1.798 [1101] 1 1 0 1 1.140 [2101] 2 1 0 1 0.471

[0011] 0 0 1 1 1.920 [1011] 1 0 1 1 1.354 [2011] 2 0 1 1 0.570

[0111] 0 1 1 1 2.282 [1111] 1 1 1 1 1.520 [2111] 2 1 1 1 0.736

[END] 0.000

Runners on Base

Expected runs estimates from FanGraphs.com (2015).

64 Sports Analytics and Data Science

It is not hard to understand why baseball analysts eschew the sacrifice bunt—giving up an out to move a runner to second base lowers the ex- pected runs for the team at bat. To make matters worse, not all sacrifice bunts are successful. If a bunt fails to move the runner to second base (due to being popped up, having the runner thrown out at second, or hav- ing the bunt fouled off on a third strike), then the result of the failed bunt moves the team from state [0100] to [1100] with its associated expected runs 0.489. A bunt with no outs sometimes results in a double play, leaving the team in the precarious position of two outs and no runners on base—state [2000] with expected runs 0.095. To provide a complete strategic analy- sis, we would consider all possibilities, including a bunt going for a hit, which moves the team from a no-outs state [0100] to [0110] with expected runs 1.373. Each transition from state to state has an associated probability. Strategic in-game analysis is a matter of computing expected runs across mutually exclusive outcomes or events.

To illustrate probability analysis across mutually exclusive events, consider another in-game decision in baseball, a player’s attempt to steal second base with no outs. Across Major League Baseball, the success rate of stealing second base is about 70 percent. With no outs, a successful steal takes a team from [0100] to [0010], moving expected runs from 0.831 to 1.068. An unsuccessful steal, however, moves the team to [1000] with expected runs 0.243. Computing the expected runs of stealing with no outs, we have

(0.70 × 1.068) + (0.30 × 0.243) = 0.748 + 0.073 = 0.821 So stealing second with no outs is not a good idea when the probability of being called “safe” at second is 0.70, the league average. Should the manager signal a steal? That depends on the baserunner’s speed on the base paths, the pitcher’s speed in delivering the ball to home plate, the catcher’s ability to throw runners out, and the skill of middle infielders in tagging runners out—all of which vary from one set of players to the next.

There are many factors to consider in making in-game decisions in base- ball, and for each factor there are relevant data to evaluate given the play- by-play record of past games. Because baseball is clearly represented as discrete states and player responsibilities are clearly identified, baseball an- alysts can evaluate alternative strategies by drawing on the history of the game and player-specific data. The analysis is a straightforward application of mathematics and probability theory.

Chapter 5. Making Game-Day Decisions 65

In evaluating alternative strategies, baseball analysts utilize expected runs estimates relevant to the teams and players in each game and the field of play. Weather conditions and the time of the game (day or night) can also affect expected runs. Some ball parks, such as Coors Field in Denver and Fenway Park in Boston, are known to be favorable to hitters, yielding higher expected runs across all in-game states. Other parks, such as U.S. Cellular Field in Chicago and AT&T Park in San Francisco, are more favor- able to pitchers, yielding lower expected runs (ESPN.com 2015). Umpires at home plate can also affect expected runs due to differences in how balls and strikes are called. An umpire with a wide strike zone favors pitchers, resulting in lower expected runs across all in-game states. See Weinstock (2012) for evidence of umpire individual differences in strike zone areas.

The baseball manager determines the starting line-up, when to pull the starting pitcher, when to pinch hit, when to bunt or hit away, when to steal second, third, or home, and when to request replay review of an umpire’s call. There are those “hidden rules of baseball” that are understood by the best managers and coaches in the game (Thorn and Palmer 1985; Keri 2006; Tango, Lichtman, and Dolphin 2007). The mantra of Sabermetrics is to use objective evidence from baseball to evaluate past player performance and inform in-game decisions. And baseball lovers have long had a fascination with data (Schwarz 2004; James 2010).

Baseball provides a model for strategic analysis—we identify alternative strategies for each play and compute expected results for each strategy. To the extent that other sports can emulate baseball’s discrete state-to-state model, they too provide opportunities for strategic analysis with math and probability theory. This is the challenge—to convert continuous action in sports such as basketball, soccer, and hockey into discrete events and to convert offensive and defensive player positions in these sports and foot- ball into a finite set of states.

Key in basketball is the decision about which five players to put in the game at any given time, player matchups in guarding opposing players, and the type of defense to employ. A notable case comes from the 2015 NBA Finals. After the Cleveland Cavaliers and Golden State Warriors had split two ini- tial overtime games, there was a dramatic turn of events between games three and four of the series.

66 Sports Analytics and Data Science

In game three of the 2015 NBA Finals, with Cavs guard Kyrie Irving out for the rest of the season with a fractured left knee, LeBron James took charge, playing 46 of the 48 minutes and scoring 40 points. The Cavs won game three 96 to 91, despite scoring only 24 points in the fourth period, compared to the Warriors’ 36.

Steve Kerr, manager of the Golden State Warriors, had not started Andre Iguodala all season. But because of Iguodala’s prowess in guarding James, Kerr put Andre in the starting lineup in game four. Iguodala and his team- mates managed to limit James to 20 points, and the Warriors won game four 103 to 82, with Iguodala and Steph Curry each scoring 22 points.

Iguodala remained in the Warriors’ starting lineup for the last two games of the series. LeBron James continued to have an amazing series in terms of minutes played and points scored, but his productivity was kept in check by Iguodala and the Warriors. On the offensive side, Andre Iguodala and Steph Curry scored 14 and 37 points, respectfully, in the Warriors’ 104-91 victory in game five, and they each scored 25 points in the Warriors’ 105-97 victory in the game six series finale.1

Basketball is a team sport, and, except for performance at the free throw line, it is difficult to assess the performance of any one player. Nonetheless, data relating to player performance under alternative matchups can guide coaching decisions. Individual matchups in basketball, as in many sports, can spell the difference between winning and losing.

Mathematical programming (integer programming, in particular) can help coaches in defining lineup and playing-time game plans. The objective is to score the most points over four twelve-minute periods. Only five of thir- teen players may be on court at once, and each player may have a playing time constraint, defined by his age, physical condition, and susceptibility to injury. A coach can impose player position or player type constraints— two guards (one point guard and one shooting guard), two forwards (one power forward), and one center. Despite the many uncertainties involved in assessing individual player contribution in sports such as basketball, we can take each player’s expected contribution to team points as a starting point in models.

1 Regarding the 2015 NBA Finals, see the National Basketball Association (2015) for Finals box scores and see Jenkins (2015a, 2015b) for additional commentary.

Chapter 5. Making Game-Day Decisions 67

The NBA provides member teams with standard data sets for all games, including box scores and play-by-play data. The NBA provides extensive basketball data from 1946 to present—these historical box scores and play- by-play data are in the public domain.

The “hot hand” in basketball, like hitting streaks and slumps in baseball, has generated considerable interest in the statistical community. Sports enthusiasts and coaches may be surprised to learn that there is little con- vincing evidence that these are anything but runs of good fortune or bad luck. Bar-Eli, Avugos, and Raab (2006) provide a comprehensive review of research in this area.

Commercial data sources complement NBA-distributed data, offering more detailed or more granular records of each game. There are videos and an- notated videos, computer-vision-aided observations and in-person obser- vations. NBA teams can purchase these data and make use of them to obtain competitive advantage. Current spatial data sources, for example, show the position of every player and the ball twenty-five times a second. As sports analysts and data scientists work with these data sources, we can expect new measures and models to emerge, and many of these measures and models will inform in-game decisions.

For football in-game decisions, coaches have offensive and defensive for- mations to consider, whether to run or pass, and whether to punt or go for it on fourth and one (or two, or more yards to go). Much has been written about football strategy and coaches’ thinking (American Football Coaches Association 1999b, 1999a). The challenge is to convert coaching wisdom and practice into discrete sets of offensive and defensive actions and to trace the success of those actions. Data, measures, and models some- times contradict conventional approaches to coaching. One area of special note is punting on fourth down, which many sports analysts view as a poor decision (Romer 2006; Berri and Schmidt 2010; Moskowitz and Wertheim 2011).

Among sports writers, there is widespread use of the word “strategy” to mean what are actually “tactics.” We have continued with this practice in the present chapter. Business managers, on the other hand, make a clear distinction between the terms, with “strategy“ referring to an overall ap- proach to competition and “tactics” referring to the operational details.

68 Sports Analytics and Data Science

Teams in all sports can utilize mathematical programing to define player lineups and in-game strategies to maximize expected scoring, subject to constraints. Review of strategic alternatives with mathematical program- ming are illustrated in the edited volume by Ladany and E.Machol (1977). And contributors to the Journal of Quantitative Analysis in Sports have been most influential in developing predictive models to guide strategy.

Lindsey (1963) provided strategic analysis in baseball, setting the stage for subsequent work with expected runs across possible game situations or states. Books by Kemeny and Snell (1976), Ross (2014), Puterman (2005), and Privault (2013) review the mathematics of Markov chains. Bukiet, El- liotte, and Palacios (1997) and Albert (2003) illustrate Markov chain analysis of baseball. Marchi and Albert (2014) provide R programs for computing expected runs and for simulating baseball games with Markov chains.

Baumer and Zimbalist (2014) provide a comprehensive review of Saber- metrics and its relevance to baseball strategy. They critique Moneyball, both the Lewis’ (2003) book and the movie, showing how these popular works present an inaccurate and incomplete rendering of Sabermetric thought.

For further discussion of basketball analytics, see Oliver (2004), Winston (2009), Shea and Baker (2013), Shea (2014), and Martin (2016). For foot- ball analytics and strategy see Carroll, Palmer, and Thorn (1988) and Carrol et al. (1998). Brown (2015) and Dresow (2015) document football coaching strategies, but present little analytics. Those interested in understanding the philosophy of one coach in particular, Bill Belichick, can refer to Hal- berstam (2005) and Belichick (2008). Soccer strategy is reviewed in books by Wells (2008) and Wilson (2008).

6 Crafting a Message

Dan: “Kalb.” Eugene: “Thanks for the Lakers Tickets.” Dan: “You bet.” Eugene: “The seats were terrific. But I’m still not going to advertise in the magazine. My son-in-law tells me that people don’t read much any more. Too much effort moving their eyes back and forth. So we’re going to put most of our budget into television, radio, Internet.” Dan: “OK.” Eugene: “OK? What does that mean?” Dan: “I’m not going to try to sell you.” Eugene: “Why the hell not? You’re a salesman.” Dan: “Yeah, just not a very good one. That’s all.” Eugene: “I’ll say.” Dan: “But I am going to ask you one favor. I’m going to leave you an issue of the magazine. And I’m personally going to send you a new one every week. Now I’ll call you in a few weeks. And if you want to, we’ll talk. There’s a great article in there comparing today’s quarterbacks with Johnny Unitas.” Eugene: “Unitas would kick their butts. So this is your sales pitch?” Dan: “I’ve been with the magazine for twenty years. I believe in it.”

—DENNIS QUAID AS DAN FOREMAN AND PHILIP BAKER HALL AS EUGENE KALB IN In Good Company (2004)

69

70 Sports Analytics and Data Science

Crafting a message, marketing communications, brand development, sales, and marketing are important to professional sports teams, just as they are to any business. There are ticket pricing, concessions, and team-branded mer- chandise options to consider. There are advertisers, sponsors, and business partnerships to pursue. Teams need to get people’s attention, to attract in- terest, and ultimately to build loyalty. Teams benefit when they turn sports consumers into fans.

Data science methods and models have wide applicability on the business side of professional sports. Sports teams benefit by having an understand- ing of sports and entertainment markets.

To show how sport fits into the entertainment space, we begin with a simple example. Consider seven event entertainment or activity options available to Washington D.C. consumers in the fall:

Comedy at Warner Theater (Comedy)

National Symphony Orchestra (Symphony)

National Zoological Park (Zoo)

Popular Music at EagleBank Arena (Pop Music)

Smithsonian Museum (Museum)

Washington Capitals Game (Hockey)

Washington Redskins Game (Football)

Noting similarities among activities, we can see how they relate to one an- other in the entertainment space. When studying small sets of activities, we can seek direct ratings or rankings across all pairs of activities. With k activities there will be k(k − 1)/2 pairs or combinations of two activities. With seven activities, there are 7(7−1)2 = 21 pairs of activities. So we can use twenty-one similarity ratings to construct a distance matrix showing how far each activity is from every other activity.

We can represent similarity ranks in a matrix. Table 6.1 shows the lower triangle of a data matrix for the seven activities in the Washington D.C. area. Because larger numbers correspond to larger differences between activities, we call this a dissimilarity or distance matrix. We can use this matrix to construct a product positioning map.

Chapter 6. Crafting a Message 71

Table 6.1. Dissimilarity Matrix for Entertainment Events and Activities

Comedy Symphony Zoo Pop Music Museum Hockey Football

Comedy - Symphony 6 -

Zoo 11 10 - Pop Music 5 3 9 -

Museum 8 2 4 7 - Hockey 15 19 17 13 21 - Football 14 18 16 12 20 1 -

Similarity judgments are especially useful in product or service categories for which attributes are difficult to identify or describe, such as categories defined by style, look, odor, or flavor. The resulting distance or dissimi- larity matrix serves as input to multidimensional scaling algorithms, which produce product positioning maps. The distance or dissimilarity matrix can also serve as input to cluster analysis algorithms, which organize products or services into groups.

When studying a large group of products and services, we might use data about product attributes or consumer ratings of product attributes as input to multidimensional scaling or cluster analysis. For this work we would use multivariate distance measures to construct the distance matrix.

Figure 6.1 shows the product positioning or perceptual map of the activities in Washington D.C. area. In many research contexts, products or services close together on maps represent potential substitutes for one another. In the eyes of this consumer, sports are seen as decidedly different from other entertainment events and activities. Seeing a football game is not a substi- tute for going to a museum or listening to a symphony orchestra, whereas seeing a football game may well be a substitute for seeing a hockey game.

We call a product positioning map a perceptual map because it is a rendering of consumer perceptions of activities—in this case one consumer’s percep- tions. And it is not too hard to imagine how making a map of products in space for one consumer could translate into making a map for many con- sumers. We would ask a group of consumers to rank pairs of activities on similarity and then place average ranks in the dissimilarity matrix.

72 Sports Analytics and Data Science

Figure 6.1. How Sports Fit into the Entertainment Space (Or Not)

First Dimension

S ec

on d

D im

en si

on

Comedy

Symphony

Zoo

Pop Music

Museum Hockey Football

Multidimensional scaling uses dissimilarities or distances as inputs, pro- viding a map as output. The orientation of the map is arbitrary. We can rotate the map without changing the solution. We can develop a reflection of the map without changing the solution. We can exchange the top for the bottom or the left for the right without changing the solution.

Maps based on different similarity metrics will also differ. To assess simi- larity between activities, products, or brands, we often use the Jaccard dis- similarity index (see figure 6.2). When different multivariate methods yield decidedly different results, as they often do, we use our best judgment to choose a solution that will be easiest to communicate to management.

Whether concerned with new or current products and services, product positioning is an important part of business and marketing strategy. There are basic questions to address: What constitutes the category of products? How do products within a category compare with one another? What can a organization do to distinguish its products and services from those offered by other organizations?

Chapter 6. Crafting a Message 73

Figure 6.2. Indices of Dissimilarity between Pairs of Binary Variables

First Binary Variable

Second Binary Variable

YES

YES

NO

NO

a b

c d

b + da + c

a + b

c + d

a + b + c + d = n

Jaccard Index of Similarity:

Proportion of Similar Observations (Simple Matching Coefficient):

Jaccard Index of Dissimilarity:

Proportion of Dissimilar Observations:

marginal frequencies for the first binary variable (row marginals)

marginal frequencies for the second binary variable (column marginals)

total frequency (number of observations)

a + b + c + d b + c

a + b + c + d a + d

a + b + c a

a + b + c b + c

The Jaccard index of dissimilarity is obtained from a two-by-two table for bi- nary variables. The table above shows how to compute the Jaccard indices of similarity and dissimilarity from the frequencies a, b, c, and d in the two-by- two table. In many research problems the Jaccard index of dissimilarity makes more sense as an index of dissimilarity than the proportion of dissimilar ob- servations. For pairs of low-incidence binary variables, the proportion of dis- similar observations is low because most observations are in the NO/NO cell of the two-by-two table. These NO/NO observations are more a reflection of low-incidence than similarity between the binary variables. In computing the Jaccard dissimilarity index, we drop the NO/NO cell frequency, thus avoid- ing problems with low-incidence binary variables. Similarity and dissimi- larity indices play an important role in such methods as multidimensional scaling, cluster analysis, and nearest-neighbor analysis. Market basket anal- ysis often begins with consumers or individual market baskets defining the rows of a binary data matrix and products or services defining the columns. Indices of similarity show how likely it is that two products will be included in a shopper’s market basket. Further discussion of indices of similarity and dissimilarity may be found in Kaufman and Rousseeuw (1990).

74 Sports Analytics and Data Science

Product positioning maps are especially useful in product planning and competitive analysis. Products close to one another in space may be thought of as substitute products or close competitors. Open areas in the product space may represent opportunities for new, differentiated products. These same technologies may be applied to brands to obtain information about brand positioning and to guide branding strategy.

Product or brand positioning may be studied in concert with product and brand preferences, yielding a joint perception/preference mapping of prod- ucts or brands in space. Critical to strategic product positioning are areas of the product space most desirable to consumers. Product managers like to find areas of the product space where there are many potential customers and few competitive brands or products.

Multivariate methods study relationships among many variables. The lan- guage of principal components, factor analysis, multidimensional scaling, and other multivariate methods suggests that we are trying to identify un- derlying or latent dimensions in the data. We want to reduce the number of dimensions being considered, so we can focus on the most critical or salient dimensions.

Cluster analysis, a class of multivariate methods, represents an alternative to multidimensional scaling. Quite often, products or activities within the same cluster are potential substitutes for one another. Cluster analysis is also appropriate for classification problems in which classes are not known in advance. Products that are similar to one another in terms of their values on measured attributes in the data set get placed in the same cluster. Prod- ucts within a cluster should be more similar to one another than they are to objects in other clusters.

Going to a museum or zoo involves active participation, walking while ob- serving. Listening to a symphony or watching a movie, on the other hand, are passive activities, sitting while observing. Just as entertainment events and activities differ from one another, consumers differ from one another. We often use cluster analysis to identify market segments or groups of con- sumers that differ from one another. Sports fans are not a homogeneous group. They come from all economic levels and educational backgrounds. There is wide variability as well in active participants in sports, an addi- tional factor for defining segments.

Chapter 6. Crafting a Message 75

We choose methods of analysis appropriate for the data and the business problem at hand. We choose methods for presenting results that are both appropriate for the data and meaningful to management. A plot of points in two dimensions is easier to understand than a large table of numbers. It is hard to see relationships in large matrices of correlations or dissimilarities, but it is not so hard to see relationships in maps.

Conjoint analysis is a modeling method particularly useful in sports mar- keting. Managers often ask about what drives buyer choice. They want to know what is important to choice or which factors determine choice. To the extent that buyer behavior is affected by product features, brand, and price, managers are able to influence buyer behavior, increasing demand, revenue, and profitability.

Ask buyers what they want, and they may say, the best of everything. Ask them what they would like to spend, and they may say, as little as possi- ble. There are limitations to assessing buyer willingness to pay and product preferences with direct-response rating scales, or what are sometimes called self-explicative scales. Simple rating scale items arranged as they often are, with separate questions about product attributes, brands, and prices, fail to capture tradeoffs that are fundamental to consumer choice. To learn more from buyer surveys, we provide a context for responding and then gather as much information as we can. This is what conjoint and choice studies do, and many of them do it quite well.

Conjoint analysis is really conjoint measurement. Marketing analysts present product profiles to consumers. Product profiles are defined by their at- tributes. By ranking, rating, or choosing products, consumers reveal their preferences for products and the corresponding attributes that define prod- ucts. The computed attribute importance values and part-worths associ- ated with levels of attributes represent measurements that are obtained as a group or jointly—thus the name conjoint analysis. The task—ranking, rating, or choosing—can take many forms.

When doing traditional conjoint analysis, we utilize regression analysis and sum contrasts, so that the sum of fitted coefficients across the levels of each attribute is zero. The fitted regression coefficients represent conjoint mea- sures of utility called part-worths. Part-worths reflect the strength of indi- vidual consumer preferences for each level of each attribute in the study.

76 Sports Analytics and Data Science

Table 6.2. Consumer Preference Data for Dodger Stadium Seating

question price seating boxvip frontrow promotion ranking

1 Price $45 Reserved Box/VIP NO Front Row NO None 10 2 Price $20 Field Box/VIP NO Front Row NO Ball 16 3 Price $20 Reserved Box/VIP YES Front Row YES Bobblehead 13 4 Price $45 Loge Box/VIP NO Front Row YES Bobblehead 11 5 Price $20 Loge Box/VIP YES Front Row NO None 14 6 Price $95 Loge Box/VIP NO Front Row NO Cap 6 7 Price $70 Field Box/VIP NO Front Row YES None 12 8 Price $70 Reserved Box/VIP YES Front Row NO Cap 7 9 Price $45 Top Deck Box/VIP YES Front Row NO Ball 3 10 Price $95 Reserved Box/VIP NO Front Row YES Ball 5 11 Price $70 Top Deck Box/VIP NO Front Row NO Bobblehead 2 12 Price $70 Loge Box/VIP YES Front Row YES Ball 9 13 Price $95 Field Box/VIP YES Front Row NO Bobblehead 8 14 Price $20 Top Deck Box/VIP NO Front Row YES Cap 4 15 Price $45 Field Box/VIP YES Front Row YES Cap 15 16 Price $95 Top Deck Box/VIP YES Front Row YES None 1

Positive part-worths add to a product’s value in the mind of the consumer. Negative part-worths subtract from that value. When we sum across the part-worths of a product, we obtain a measure of the utility or benefit to the consumer. A linear model fit to preference rankings is an example of traditional conjoint analysis, a modeling technique designed to show how product attributes affect purchasing decisions.

To demonstrate conjoint analysis, we consider seating and ticket prices at Dodger Stadium. There are four large seating areas for fans: field, loge, re- served, and top deck. A “loge,” according to Webster’s Collegiate Dictionary (eleventh ed.), is “a raised section or level of seats in a sports stadium.” At Dodger Stadium, field level seats are closest to the field of play. Next is the loge level, followed by reserved seating. The top level is far removed from the field of play. Ticket prices vary widely across and within these areas, where sections within the areas might be described as “Front Row,” “Box,” or “VIP,” for example. One other factor included in this demonstra- tion study is promotions or give-aways. Some games might have a ball, bobblehead doll, or cap promotion available to the first fifty thousand fans. Table 6.2 shows ranking data for one fan across sixteen product profiles for Dodger Stadium seating. To display the results of the conjoint analysis, we use a special type of dot plot called the spine chart, shown in figure 6.3.

Chapter 6. Crafting a Message 77

Figure 6.3. Consumer Preferences for Dodger Stadium Seating

Seating Area 53.25% Field (4.25) � Loge (1.50) �

Reserved (0.25) � Top Deck (−6.00) �

Ticket Price 35.06% Price $20 (3.25) � Price $45 (1.25) � Price $70 (−1.00) � Price $95 (−3.50) �

Promotion 6.49% Ball (−0.25) �

Bobblehead (−0.00) � Cap (−0.50) �

None (0.75) �

Box/VIP 2.60% Box/VIP NO (−0.25) �

Box/VIP YES (0.25) �

Front Row 2.60% Front Row NO (−0.25) �

Front Row YES (0.25) �

−10 −5 0 +5 +10 Part−WorthPart−WorthInternal consistency: 0.98

Seating Area 53.25% Field (4.25) � Loge (1.50) �

Reserved (0.25) � Top Deck (−6.00) �

Ticket Price 35.06% Price $20 (3.25) � Price $45 (1.25) � Price $70 (−1.00) � Price $95 (−3.50) �

Promotion 6.49% Ball (−0.25) �

Bobblehead (−0.00) � Cap (−0.50) �

None (0.75) �

Box/VIP 2.60% Box/VIP NO (−0.25) �

Box/VIP YES (0.25) �

Front Row 2.60% Front Row NO (−0.25) �

Front Row YES (0.25) �

78 Sports Analytics and Data Science

In the spine chart, part-worths can be displayed on a common part-worths scale across attributes. The vertical line in the center, the spine, is anchored at zero. The part-worth of each level of each attribute is displayed as a dot with a connecting horizontal line, extending from the spine. Preferred product or service characteristics have positive part-worths and fall to the right of the spine. Less preferred product or service characteristics fall to the left of the spine. The relative importance of attributes in a conjoint anal- ysis is defined using the ranges of part-worths within attributes. These importance values are scaled so the sum across all attributes is 100 percent.

What does the spine chart say about this consumer’s seating preferences? It shows that the seating area is of primary importance. Next in order of importance is price. Location within the general seating area, defined by “Front Row,” “Box,” or “VIP” designations, is considerably less important than general seating area itself. Promotions appear to have little import, as this consumer may prefer no promotions to receiving a ball, cap, or bobble- head doll.

This simple study measures consumer preferences for seating. It should come as no surprise that seats closer to the field are preferred or that lower prices are preferred. But the real value of a study like this comes in what it shows us about consumer willingness to pay.

To assess willingness to pay within the context of conjoint measures, we note the part-worth differential across the range of ticket prices. From fig- ure 6.3, we see that a part-worth of 3.25 corresponds to a ticket price of $20. Similarly, a part worth of -3.50 corresponds to a ticket price of $95. A few simple calculations provide a dollar-metric for part-worths:

|3.25 − (−3.50)| = 6.75 part-worth differential (utils) |20 − 95| = 75 ticket price differential (dollars)

6.75 utils = 75 dollars

1 util = 11.11 dollars

Each unit of part-worth (call it a util for want of a better term) is worth $11.11 to this consumer. And for this consumer the part-worth difference between a field level seat and a loge seat is |4.25 − 1.50| = 2.75 utils. So this consumer would be willing to spend 2.75 × 11.11 = 30.55 dollars more for a field seat than a loge seat.

Chapter 6. Crafting a Message 79

Figure 6.4. Choice Item for Assessing Willingness to Pay for Tickets

Loge Level Box Seat Front Row Bobblehead Doll

$70

Reserved Level VIP Seating Middle Row Baseball Cap

$45

Top Level General Seating Middle Row No Promotion

$20

None

Select the ticket you would most likely purchase. Or if you would be unlikely to purchase any of these tickets, select None.

Traditional conjoint analysis fits a linear model to each individual’s ratings or rankings, thus measuring the utility or part-worth of each level of each attribute, as well as the relative importance of attributes. Traditional con- joint analysis is one of many types of conjoint analysis (Orme 2013).

To assess willingness to pay more fully, we would employ a choice-based conjoint approach including a none alternative. Figure 6.4 shows what a choice item would look like in such a study. We present numerous choice items to each consumer respondent and use methods of discrete choice analysis to estimate part-worths and attribute importance. Miller (2015a) shows how to use Bayesian hierarchical models to analyze choice data. Talluri and van Ryzin (2004) describe discrete choice methods in revenue management, as appropriate for assessing willingness to pay in capacity- limited, variable-pricing problems, such as airline and stadium seating.

The measures we obtain from conjoint studies may be analyzed to identify consumer segments. We can use conjoint measures to predict consumer choices in the marketplace. We can draw on the results of conjoint studies to perform marketplace simulations, exploring alternative product designs and pricing policies. Consumers reveal their preferences in responses to surveys and ultimately in choices they make in the marketplace.

80 Sports Analytics and Data Science

Figure 6.5. The Market: A Meeting Place for Buyers and Sellers

Products Sellers

Buyers

Market

Seller History

Sector

Features Brands

Segment

Attitudes

Preferences Goals/Wants

Needs Budget

Prices

Buyer History

Source: Miller (2015a).

Figure 6.5 provides a framework for understanding buyers’ and sellers’ choices in a market. A market is a place where buyers and sellers get to- gether. Buyers represent the demand side, and sellers the supply side. We use methods and models to predict what will happen in a market, how much of a product will be sold and what will happen with prices. Studying the behavior of markets in the aggregate is the work of economics. Market- ing research and data science study market segments and the behavior of buyers within segments.

Professional sports teams can ask basic questions about buyers. Consumers and fans have varied histories, preferences, and attitudes. Some consumers are fans of a particular team, others are fans of a particular sport, and still others are fans of sports in general. A team’s market should not be seen as limited to the city where that team resides. There are opportuni- ties for revenue growth through national branding and media contracts. Location-bound sports stadia have limited capacity. Sporting events dis- tributed through media have no such limits.

Chapter 6. Crafting a Message 81

What is the market for a team? Many Cub fans across the nation have little connection with Chicagoland. The Dallas Cowboys can be described as “America’s team” by fans who have little intention to visit Texas. Small- market teams such as the Green Bay Packers of the NFL or the Oklahoma City Thunder of the NBA can build fan bases well beyond their city limits. To use a sports analogy, media “level the playing field” between small- and major-market teams.

Data science methods and models are relevant to all markets, business-to- consumer and business-to-business markets alike, and they are certainly relevant to professional sports marketing. Blattberg, Kim, and Neslin (2008) and Miller (2015a) review methods and models relevant to the general do- main of marketing data science. Rein, Kotler, and Shields (2006) show how general marketing principles apply to professional sports team marketing.

Preference scaling has a long history in psychometrics (Thurstone 1927; Young and Householder 1938; Richardson 1938). Guilford (1954, first pub- lished in 1936) and Torgerson (1958) provided in-depth treatments. Tra- ditional unidimensional scaling methods, building as they do on a paired comparison preference matrix, may be used for data arising from actual paired comparisons, rank orders, and multiple rank orders, as well as from best-worst scaling items, choice studies, pick lists, and elimination pick lists. Miller (2015a) provides examples.

There are many good sources for learning about multidimensional scaling (Davison 1992; Cox and Cox 1994; Carroll and Green 1997; Borg and Groe- nen 2010). Lilien and Rangaswamy (2003) discuss methods for the joint mapping of perception and preference. R software for multidimensional scaling is described in Venables and Ripley (2002).

Multivariate methods are reviewed by Seber (2000), Manly (1994), Sharma (1996), Gnanadesikan (1997), Johnson and Wichern (1998), and Izenman (2008). Principal component biplots represent an alternative to multidimen- sional scaling plots (Gabriel 1971; Gower and Hand 1996). Biplots allow us to plot consumers and products/brands in the same space.

Conjoint measurement, a critical tool of marketing data science, focuses on buyers or the demand side of markets. The method was originally devel- oped by Luce and Tukey (1964). Orme (2013) presents a comprehensive review of conjoint methods.

82 Sports Analytics and Data Science

Exhibit 6.1 shows the R program for product positioning using the enter- tainment event and activities example. The R program draws on the work of Ripley et al. (2015). We show the corresponding Python program in ex- hibit 6.2.

Exhibits 6.3 and 6.4 show R and Python programs for analyzing ranking or rating data for consumer preferences. The programs perform traditional conjoint analysis. The R program shows how to construct a spine chart, which is a customized data visualization for conjoint and choice studies. Using standard R graphics, the program builds this chart one point, line, and text string at a time. The precise placement of points, lines, and text is under program control.

Chapter 6. Crafting a Message 83

Exhibit 6.1. Mapping Entertainment Events and Activities (R)

# Product Positioning of Entertainment Events and Activities (R)

library(MASS) # includes functions for multidimensional scaling

library(wordcloud) # textplot utility to avoid overlapping text

USE_METRIC_MDS <- FALSE # metric versus non-metric toggle

# utility function for converting a distance structure

# to a distance matrix as required for some routines and

# for printing of the complete matrix for visual inspection.

make.distance.matrix <- function(distance_structure)

{ n <- attr(distance_structure, "Size")

full <- matrix(0,n,n)

full[lower.tri(full)] <- distance_structure

full+t(full)

}

# enter data into a distance structure as required for various

# distance-based routines. That is, we enter the upper triangle

# of the distance matrix as a single vector of distances

distance_structure <-

as.single(c(6,11,5,8,15,14,10,3,2,19,18,9,4,17,16,7,13,12,21,20,1))

# provide a character vector of entertainment event or activity names

activity_names <-

c("Comedy", "Symphony", "Zoo", "Pop Music", "Museum", "Hockey", "Football")

attr(distance_structure, "Size") <- length(activity_names) # set size attribute

# check to see that the distance structure has been entered correctly

# by converting the distance structure to a distance matrix

# using the utility function make.distance.matrix, which we had defined

distance_matrix <- unlist(make.distance.matrix(distance_structure))

cat("\n","Distance Matrix of Seven Activities","\n")

print(distance_matrix)

if (USE_METRIC_MDS)

{

# apply the metric multidimensional scaling algorithm and plot the map

mds_solution <- cmdscale(distance_structure, k=2, eig=T)

}

# apply the non-metric multidimensional scaling algorithm

# this is more appropriate for rank-order data

# and provides a more satisfactory solution here

if (!USE_METRIC_MDS)

{

mds_solution <- isoMDS(distance_matrix, k = 2, trace = FALSE)

}

84 Sports Analytics and Data Science

pdf(file = "plot_nonmetric_mds_seven_activities.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

# original solution

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2]

# set up the plot but do not plot points... use names for points

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # first page of pdf plots

# We plot the sport names in the locations where points normally go.

text(First_Dimension, Second_Dimension, labels = activity_names,

offset = 0.0, cex = 1.5)

title("Seven Activities (initial solution)")

# reflect the horizontal dimension

# multiply the first dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2]

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # second page of pdf plots

text(First_Dimension, Second_Dimension, labels = activity_names,

offset = 0.0, cex = 1.5)

title("Seven Activities (horizontal reflection)")

# reflect the vertical dimension

# multiply the section dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2] * -1

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # third page of pdf plots

text(First_Dimension, Second_Dimension, labels = activity_names,

offset = 0.0, cex = 1.5)

title("Seven Activities (vertical reflection)")

# multiply the first and second dimensions by -1

# for reflection in both horizontal and vertical directions

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2] * -1

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-15, 15), ylim = c(-15, 15)) # fourth page of pdf plots

text(First_Dimension, Second_Dimension, labels = activity_names,

offset = 0.0, cex = 1.5)

title("Seven Activities (horizontal and vertical reflection)")

dev.off() # closes the pdf plotting device

pdf(file = "plot_pretty_original_mds_seven_activities.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

Chapter 6. Crafting a Message 85

First_Dimension <- mds_solution$points[,1] # no reflection

Second_Dimension <- mds_solution$points[,2] # no reflection

# wordcloud utility for plotting with no overlapping text

textplot(x = First_Dimension,

y = Second_Dimension,

words = activity_names,

show.lines = FALSE,

xlim = c(-15, 15), # extent of horizontal axis range

ylim = c(-15, 15), # extent of vertical axis range

xaxt = "n", # suppress tick marks

yaxt = "n", # suppress tick marks

cex = 1.15, # size of text points

mgp = c(0.85, 1, 0.85), # position of axis labels

cex.lab = 1.5, # magnification of axis label text

xlab = "First Dimension",

ylab = "Second Dimension")

dev.off() # closes the pdf plotting device

86 Sports Analytics and Data Science

Exhibit 6.2. Mapping Entertainment Events and Activities (Python)

# Product Positioning of Entertainment Events and Activities (Python)

# prepare for Python version 3x features and functions

from __future__ import division, print_function

# import packages for multivariate analysis

import numpy as np # arrays and numerical processing

import scipy

import matplotlib.pyplot as plt # 2D plotting

# alternative distance metrics for multidimensional scaling

from sklearn.metrics import euclidean_distances

from sklearn.metrics.pairwise import linear_kernel as cosine_distances

from sklearn.metrics.pairwise import manhattan_distances as manhattan_distances

from sklearn import manifold # multidimensional scaling

# These are the original data from one respondent

# Pairs of activities are judged on their similarity

# Smaller numbers are more similar to one another

# Zero on the diagonal means no difference

# 0 6 11 5 8 15 14 Comedy

# 6 0 10 3 2 19 18 Symphony

# 11 10 0 9 4 17 16 Zoo

# 5 3 9 0 7 13 12 Pop Music

# 8 2 4 7 0 21 20 Museum

# 15 19 17 13 21 0 1 Hockey

# 14 18 16 12 20 1 0 Football

# define a numpy array for these data

distance_matrix = np.array([\

[0, 6, 11, 5, 8, 15, 14],\

[6, 0, 10, 3, 2, 19, 18],\

[11, 10, 0, 9, 4, 17, 16],\

[5, 3, 9, 0, 7, 13, 12],\

[8, 2, 4, 7, 0, 21, 20],\

[15, 19, 17, 13, 21, 0, 1],\

[14, 18, 16, 12, 20, 1, 0]])

# check to see that the distance structure has been entered correctly

print(distance_matrix)

print(type(distance_matrix))

# apply the multidimensional scaling algorithm and plot the map

mds_method = manifold.MDS(n_components = 2, random_state = 9999,\

dissimilarity = ’precomputed’)

mds_fit = mds_method.fit(distance_matrix)

mds_coordinates = mds_method.fit_transform(distance_matrix)

activity_label = ["Comedy", "Symphony", "Zoo", \

"Pop Music", "Museum", "Hockey", "Football"]

Chapter 6. Crafting a Message 87

# plot mds solution in two dimensions using activity labels

# defined by multidimensional scaling

plt.figure()

plt.scatter(mds_coordinates[:,0],mds_coordinates[:,1],\

facecolors = ’none’, edgecolors = ’none’) # points in white (invisible)

labels = activity_label

for label, x, y in zip(labels, mds_coordinates[:,0], mds_coordinates[:,1]):

plt.annotate(label, (x,y), xycoords = ’data’)

plt.xlabel(’First Dimension’)

plt.ylabel(’Second Dimension’)

plt.show()

plt.savefig(’fig_positioning_products_mds_activities_python.pdf’,

bbox_inches = ’tight’, dpi=None, facecolor=’w’, edgecolor=’b’,

orientation=’landscape’, papertype=None, format=None,

transparent=True, pad_inches=0.25, frameon=None)

88 Sports Analytics and Data Science

Exhibit 6.3. Preferences for Sporting Events—Conjoint Analysis (R)

# Consumer Preferences for Sporting Events---Conjoint Analysis (R)

library(support.CEs) # package for survey construction

# generate a balanced set of product profiles for survey

# varies with each call to the function

# so each individual gets a different set of sixteen items

provider.survey <- Lma.design(attribute.names =

list(price = c("PRICE $20","PRICE $45","PRICE $70","PRICE $95"),

seating = c("Field","Loge","Reserved","Top Deck"),

boxvip = c("Box/VIP NO","Box/VIP YES"),

frontrow = c("Front Row NO","Front Row YES"),

promotion = c("Ball","Bobblehead","Cap","None")),

nalternatives = 1, nblocks=1, seed = 7777)

print(questionnaire(provider.survey)) # print survey design for review

sink("questions_for_survey.txt") # send survey to external text file

questionnaire(provider.survey)

sink() # send output back to the screen

print.digits <- 2 # set number of digits on print and spine chart

# user-defined function for printing conjoint measures

if (print.digits == 2)

pretty.print <- function(x) {sprintf("%1.2f",round(x,digits = 2))}

if (print.digits == 3)

pretty.print <- function(x) {sprintf("%1.3f",round(x,digits = 3))}

# ---------------------------------------------------------------

# user-defined function for printing conjoint measures

# spine chart accommodates up to 45 part-worths on one page

# |part-worth| <= 40 can be plotted directly on the spine chart

# |part-worths| > 40 can be accommodated through

# standardization# user-defined function for spine chart

# ---------------------------------------------------------------

spine.chart <- function(conjoint.results,

color.for.part.worth.point = "blue",

color.for.part.worth.line = "blue",

left.side.symbol.to.print.around.part.worths = "(",

right.side.symbol.to.print.around.part.worths = ")",

left.side.symbol.to.print.around.importance = "",

right.side.symbol.to.print.around.importance = "",

color.for.printing.importance.text = "dark red",

color.for.printing.part.worth.text = "black",

draw.gray.background = TRUE,

draw.optional.grid.lines = TRUE,

print.internal.consistency = TRUE,

fix.max.to.4 = FALSE,

put.title.on.spine.chart = FALSE,

title.on.spine.chart = paste("TITLE GOES HERE IF WE ASK FOR ONE",sep=""),

plot.framing.box = TRUE,

do.ordered.attributes = TRUE) {

Chapter 6. Crafting a Message 89

# fix.max.to.4 option to override the range for part-worth plotting

if(!do.ordered.attributes) effect.names <- conjoint.results$attributes

if(do.ordered.attributes) effect.names <-

conjoint.results$ordered.attributes

number.of.levels.of.attribute <- NULL

for(index.for.factor in seq(along=effect.names))

number.of.levels.of.attribute <- c(number.of.levels.of.attribute,

length(conjoint.results$xlevels[[effect.names[index.for.factor]]]))

# total number of levels needed for vertical length of spine the spine plot

total.number.of.levels <- sum(number.of.levels.of.attribute)

# define size of spaces based upon the number of part-worth levels to plot

if(total.number.of.levels <= 20) {

smaller.space <- 0.01

small.space <- 0.02

medium.space <- 0.03

large.space <- 0.04

}

if(total.number.of.levels > 20) {

smaller.space <- 0.01 * 0.9

small.space <- 0.02 * 0.9

medium.space <- 0.03 * 0.9

large.space <- 0.04 * 0.9

}

if(total.number.of.levels > 22) {

smaller.space <- 0.01 * 0.85

small.space <- 0.02 * 0.85

medium.space <- 0.03 * 0.825

large.space <- 0.04 * 0.8

}

if(total.number.of.levels > 25) {

smaller.space <- 0.01 * 0.8

small.space <- 0.02 * 0.8

medium.space <- 0.03 * 0.75

large.space <- 0.04 * 0.75

}

if(total.number.of.levels > 35) {

smaller.space <- 0.01 * 0.65

small.space <- 0.02 * 0.65

medium.space <- 0.03 * 0.6

large.space <- 0.04 * 0.6

}

# of course there is a limit to how much we can plot on one page

if (total.number.of.levels > 45)

stop("\n\nTERMINATED: More than 45 part-worths on spine chart\n")

90 Sports Analytics and Data Science

part.worth.plotting.list <- conjoint.results$part.worths

# check the range of part-worths to see which path to go down for plotting

# initialize these toggles to start

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.10 <- FALSE

max.is.less.than.4 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

if (max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 40) {

max.is.less.than.40 <- TRUE

max.is.less.than.20 <- FALSE

max.is.less.than.10 <- FALSE

max.is.less.than.4 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

}

if (max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 20) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- TRUE

max.is.less.than.10 <- FALSE

max.is.less.than.4 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

}

if(max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 10) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.10 <- TRUE

max.is.less.than.4 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

}

if (max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 4) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.4 <- TRUE

max.is.less.than.10 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

}

Chapter 6. Crafting a Message 91

if(max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 2) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.4 <- FALSE

max.is.less.than.10 <- FALSE

max.is.less.than.2 <- TRUE

max.is.less.than.1 <- FALSE

}

if(max(abs(min(unlist(part.worth.plotting.list),na.rm=TRUE)),

max(unlist(part.worth.plotting.list),na.rm=TRUE)) <= 1) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.4 <- FALSE

max.is.less.than.10 <- FALSE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- TRUE

}

# sometimes we override the range for part-worth plotting

# this is not usually done... but it is an option

if (fix.max.to.4) {

max.is.less.than.40 <- FALSE

max.is.less.than.20 <- FALSE

max.is.less.than.10 <- FALSE

max.is.less.than.4 <- TRUE

max.is.less.than.2 <- FALSE

max.is.less.than.1 <- FALSE

}

if (!max.is.less.than.1 & !max.is.less.than.2 & !max.is.less.than.4 &

!max.is.less.than.10 & !max.is.less.than.20 & !max.is.less.than.40)

stop("\n\nTERMINATED: Spine chart cannot plot |part-worth| > 40")

# determine point positions for plotting part-worths on spine chart

if (max.is.less.than.1 | max.is.less.than.2 | max.is.less.than.4 |

max.is.less.than.10 | max.is.less.than.20 | max.is.less.than.40) {

# begin if-block plotting when all part-worths in absolute value

# are less than one of the tested range values

# part-worth positions for plotting

# end if-block plotting when all part-worths in absolute value

# are less than one of the tested range values

# offsets for plotting vary with the max.is.less.than setting

if(max.is.less.than.1) {

list.scaling <- function(x) {0.75 + x/5}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

if(max.is.less.than.2) {

list.scaling <- function(x) {0.75 + x/10}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

92 Sports Analytics and Data Science

if(max.is.less.than.4) {

list.scaling <- function(x) {0.75 + x/20}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

if(max.is.less.than.10) {

list.scaling <- function(x) {0.75 + x/50}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

if(max.is.less.than.20) {

list.scaling <- function(x) {0.75 + x/100}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

if(max.is.less.than.40) {

list.scaling <- function(x) {0.75 + x/200}

part.worth.point.position <-

lapply(part.worth.plotting.list,list.scaling)

}

part.worth.point.position <- lapply(part.worth.plotting.list,list.scaling)

}

if (plot.framing.box) plot(c(0,0,1,1),c(0,1,0,1),xlab="",ylab="",

type="n",xaxt="n",yaxt="n")

if (!plot.framing.box) plot(c(0,0,1,1),c(0,1,0,1),xlab="",ylab="",

type="n",xaxt="n",yaxt="n", bty="n")

if (put.title.on.spine.chart) {

text(c(0.50),c(0.975),pos=3,labels=title.on.spine.chart,cex=01.5)

y.location <- 0.925 # starting position with title

}

if (!put.title.on.spine.chart) y.location <- 0.975 # no-title start

# store top of vertical line for later plotting needs

y.top.of.vertical.line <- y.location

x.center.position <- 0.75 # horizontal position of spine

# begin primary plotting loop

# think of a plot as a collection of text and symbols on screen or paper

# we are going to construct a plot one text string and symbol at a time

# (note that we may have to repeat this process at the end of the program)

for(k in seq(along=effect.names)) {

y.location <- y.location - large.space

Chapter 6. Crafting a Message 93

text(c(0.4),c(y.location),pos=2,

labels=paste(effect.name.map(effect.names[k])," ",sep=""),cex=01.0)

text(c(0.525),c(y.location),pos=2,col=color.for.printing.importance.text,

labels=paste(" ",left.side.symbol.to.print.around.importance,

pretty.print(

unlist(conjoint.results$attribute.importance[effect.names[k]])),"%",

right.side.symbol.to.print.around.importance,sep=""),cex=01.0)

# begin loop for printing part-worths

for(m in seq(1:number.of.levels.of.attribute[k])) {

y.location <- y.location - medium.space

text(c(0.4),c(y.location),pos=2,

conjoint.results$xlevel[[effect.names[k]]][m],cex=01.0)

# part.worth.label.data.frame[k,m],cex=01.0)

text(c(0.525),c(y.location),pos=2,

col=color.for.printing.part.worth.text,

labels=paste(" ",left.side.symbol.to.print.around.part.worths,

pretty.print(part.worth.plotting.list[[effect.names[k]]][m]),

right.side.symbol.to.print.around.part.worths,sep=""),cex=01.0)

points(part.worth.point.position[[effect.names[k]]][m],y.location,

type = "p", pch = 20, col = color.for.part.worth.point, cex = 2)

segments(x.center.position, y.location,

part.worth.point.position[[effect.names[k]]][m], y.location,

col = color.for.part.worth.line, lty = 1, lwd = 2)

}

}

y.location <- y.location - medium.space

# begin center axis and bottom plotting

y.bottom.of.vertical.line <- y.location # store top of vertical line

below.y.bottom.of.vertical.line <- y.bottom.of.vertical.line - small.space/2

if (!draw.gray.background) {

# four optional grid lines may be drawn on the plot parallel to the spine

if (draw.optional.grid.lines) {

segments(0.55, y.top.of.vertical.line, 0.55,

y.bottom.of.vertical.line, col = "black", lty = "solid", lwd = 1)

segments(0.65, y.top.of.vertical.line, 0.65,

y.bottom.of.vertical.line, col = "gray", lty = "solid", lwd = 1)

segments(0.85, y.top.of.vertical.line, 0.85,

y.bottom.of.vertical.line, col = "gray", lty = "solid", lwd = 1)

segments(0.95, y.top.of.vertical.line, 0.95,

y.bottom.of.vertical.line, col = "black", lty = "solid", lwd = 1)

}

}

94 Sports Analytics and Data Science

# gray background for plotting area of the points

if (draw.gray.background) {

rect(xleft = 0.55, ybottom = y.bottom.of.vertical.line,

xright = 0.95, ytop = y.top.of.vertical.line, density = -1, angle = 45,

col = "light gray", border = NULL, lty = "solid", lwd = 1)

# four optional grid lines may be drawn on the plot parallel to the spine

if (draw.optional.grid.lines) {

segments(0.55, y.top.of.vertical.line, 0.55,

y.bottom.of.vertical.line, col = "black", lty = "solid", lwd = 1)

segments(0.65, y.top.of.vertical.line, 0.65,

y.bottom.of.vertical.line, col = "white", lty = "solid", lwd = 1)

segments(0.85, y.top.of.vertical.line, 0.85,

y.bottom.of.vertical.line, col = "white", lty = "solid", lwd = 1)

segments(0.95, y.top.of.vertical.line, 0.95,

y.bottom.of.vertical.line, col = "black", lty = "solid", lwd = 1)

}

}

# draw the all-important spine on the plot

segments(x.center.position, y.top.of.vertical.line, x.center.position,

y.bottom.of.vertical.line, col = "black", lty = "dashed", lwd = 1)

# horizontal line at top

segments(0.55, y.top.of.vertical.line, 0.95, y.top.of.vertical.line,

col = "black", lty = 1, lwd = 1)

# horizontal line at bottom

segments(0.55, y.bottom.of.vertical.line, 0.95, y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1)

# plot for ticks and labels

segments(0.55, y.bottom.of.vertical.line,

0.55, below.y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1) # tick line at bottom

segments(0.65, y.bottom.of.vertical.line,

0.65, below.y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1) # tick line at bottom

segments(0.75, y.bottom.of.vertical.line,

0.75, below.y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1) # tick line at bottom

segments(0.85, y.bottom.of.vertical.line,

0.85, below.y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1) # tick line at bottom

segments(0.95, y.bottom.of.vertical.line,

0.95, below.y.bottom.of.vertical.line,

col = "black", lty = 1, lwd = 1) # tick line at bottom

Chapter 6. Crafting a Message 95

# axis labels vary with the max.is.less.than range being used

if (max.is.less.than.1) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-1","-0.5","0","+0.5","+1"),cex=0.75)

if (max.is.less.than.2) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-2","-1","0","+1","+2"),cex=0.75)

if (max.is.less.than.4) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-4","-2","0","+2","+4"),cex=0.75)

if (max.is.less.than.10) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-10","-5","0","+5","+10"),cex=0.75)

if (max.is.less.than.20) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-20","-10","0","+10","+20"),cex=0.75)

if (max.is.less.than.40) text(c(0.55,0.65,0.75,0.85,0.95),

rep(below.y.bottom.of.vertical.line,times=5),

pos=1,labels=c("-40","-20","0","+20","+40"),cex=0.75)

y.location <- below.y.bottom.of.vertical.line - small.space

text(.75,y.location,pos=1,labels=c("Part-Worth"),

cex=0.95)

y.location <- below.y.bottom.of.vertical.line - small.space

text(0.75,y.location,pos=1,labels=c("Part-Worth"), cex=0.95)

if(print.internal.consistency) {

y.location <- y.location - medium.space

text(c(0.525),c(y.location),pos=2,labels=paste("Internal consistency: ",

pretty.print(conjoint.results$internal.consistency),

sep=""))

}

# if we have grid lines we may have plotted over part-worth points

# if we have a gray background then we have plotted over part-worth points

# so let us plot those all-important part-worth points and lines once again

if(draw.gray.background || draw.optional.grid.lines) {

y.location <- y.top.of.vertical.line # retreive the starting value

# repeat the primary plotting loop

for(k in seq(along=effect.names)) {

y.location <- y.location - large.space

text(c(0.4),c(y.location),pos=2,

labels=paste(effect.name.map(effect.names[k])," ",sep=""),cex=01.0)

96 Sports Analytics and Data Science

text(c(0.525),c(y.location),pos=2,col=color.for.printing.importance.text,

labels=paste(" ",left.side.symbol.to.print.around.importance,

pretty.print(

unlist(conjoint.results$attribute.importance[effect.names[k]])),"%",

right.side.symbol.to.print.around.importance,sep=""),cex=01.0)

# begin loop for printing part-worths

for(m in seq(1:number.of.levels.of.attribute[k])) {

y.location <- y.location - medium.space

text(c(0.4),c(y.location),pos=2,

conjoint.results$xlevel[[effect.names[k]]][m],cex=01.0)

text(c(0.525),c(y.location),

pos=2,col=color.for.printing.part.worth.text,

labels=paste(" ",left.side.symbol.to.print.around.part.worths,

pretty.print(part.worth.plotting.list[[effect.names[k]]][m]),

right.side.symbol.to.print.around.part.worths,sep=""),cex=01.0)

points(part.worth.point.position[[effect.names[k]]][m],y.location,

type = "p", pch = 20, col = color.for.part.worth.point, cex = 2)

segments(x.center.position, y.location,

part.worth.point.position[[effect.names[k]]][m], y.location,

col = color.for.part.worth.line, lty = 1, lwd = 2)

}

}

}

}

# user-defined function for plotting descriptive attribute names

effect.name.map <- function(effect.name) {

if(effect.name=="price") return("Ticket Price")

if(effect.name=="seating") return("Seating Area")

if(effect.name=="boxvip") return("Box/VIP")

if(effect.name=="frontrow") return("Front Row")

if(effect.name=="promotion") return("Promotion")

}

# read in conjoint survey profiles with respondent ranks

conjoint.data.frame <- read.csv("sporting_event_ranking.csv")

# set up sum contrasts for effects coding as needed for conjoint analysis

options(contrasts=c("contr.sum","contr.poly"))

# main effects model specification

main.effects.model <-

{ranking ~ price + seating + boxvip + frontrow + promotion}

# fit linear regression model using main effects only (no interaction terms)

main.effects.model.fit <- lm(main.effects.model, data=conjoint.data.frame)

print(summary(main.effects.model.fit))

# save key list elements of the fitted model as needed for conjoint measures

conjoint.results <-

main.effects.model.fit[c("contrasts","xlevels","coefficients")]

conjoint.results$attributes <- names(conjoint.results$contrasts)

Chapter 6. Crafting a Message 97

# compute and store part-worths in the conjoint.results list structure

part.worths <- conjoint.results$xlevels # list of same structure as xlevels

end.index.for.coefficient <- 1 # intitialize skipping the intercept

part.worth.vector <- NULL # used for accumulation of part worths

for(index.for.attribute in seq(along=conjoint.results$contrasts)) {

nlevels <- length(unlist(conjoint.results$xlevels[index.for.attribute]))

begin.index.for.coefficient <- end.index.for.coefficient + 1

end.index.for.coefficient <- begin.index.for.coefficient + nlevels -2

last.part.worth <- -sum(conjoint.results$coefficients[

begin.index.for.coefficient:end.index.for.coefficient])

part.worths[index.for.attribute] <-

list(as.numeric(c(conjoint.results$coefficients[

begin.index.for.coefficient:end.index.for.coefficient],

last.part.worth)))

part.worth.vector <-

c(part.worth.vector,unlist(part.worths[index.for.attribute]))

}

conjoint.results$part.worths <- part.worths

# compute and store part-worth ranges for each attribute

part.worth.ranges <- conjoint.results$contrasts

for(index.for.attribute in seq(along=conjoint.results$contrasts))

part.worth.ranges[index.for.attribute] <-

dist(range(conjoint.results$part.worths[index.for.attribute]))

conjoint.results$part.worth.ranges <- part.worth.ranges

sum.part.worth.ranges <- sum(as.numeric(conjoint.results$part.worth.ranges))

# compute and store importance values for each attribute

attribute.importance <- conjoint.results$contrasts

for(index.for.attribute in seq(along=conjoint.results$contrasts))

attribute.importance[index.for.attribute] <-

(dist(range(conjoint.results$part.worths[index.for.attribute]))/

sum.part.worth.ranges) * 100

conjoint.results$attribute.importance <- attribute.importance

# data frame for ordering attribute names

attribute.name <- names(conjoint.results$contrasts)

attribute.importance <- as.numeric(attribute.importance)

temp.frame <- data.frame(attribute.name,attribute.importance)

conjoint.results$ordered.attributes <-

as.character(temp.frame[sort.list(

temp.frame$attribute.importance,decreasing = TRUE),"attribute.name"])

# respondent internal consistency added to list structure

conjoint.results$internal.consistency <- summary(main.effects.model.fit)$r.squared

# user-defined function for printing conjoint measures

if (print.digits == 2)

pretty.print <- function(x) {sprintf("%1.2f",round(x,digits = 2))}

98 Sports Analytics and Data Science

if (print.digits == 3)

pretty.print <- function(x) {sprintf("%1.3f",round(x,digits = 3))}

# report conjoint measures to console

# use pretty.print to provide nicely formated output

for(k in seq(along=conjoint.results$ordered.attributes)) {

cat("\n","\n")

cat(conjoint.results$ordered.attributes[k],"Levels: ",

unlist(conjoint.results$xlevels[conjoint.results$ordered.attributes[k]]))

cat("\n"," Part-Worths: ")

cat(pretty.print(unlist(conjoint.results$part.worths

[conjoint.results$ordered.attributes[k]])))

cat("\n"," Attribute Importance: ")

cat(pretty.print(unlist(conjoint.results$attribute.importance

[conjoint.results$ordered.attributes[k]])))

}

# plotting of spine chart begins here

# all graphical output is routed to external pdf file

pdf(file = "fig_zsports_willingness_to_pay.pdf", width=8.5, height=11)

spine.chart(conjoint.results)

dev.off() # close the graphics output device

Chapter 6. Crafting a Message 99

Exhibit 6.4. Preferences for Sporting Events—Conjoint Analysis (Python)

# Consumer Preferences for Sporting Events---Conjoint Analysis (Python)

# prepare for Python version 3x features and functions

from __future__ import division, print_function

# import packages for analysis and modeling

import pandas as pd # data frame operations

import numpy as np # arrays and math functions

import statsmodels.api as sm # statistical models (including regression)

import statsmodels.formula.api as smf # R-like model specification

from patsy.contrasts import Sum

# read in conjoint survey profiles with respondent ranks

conjoint_data_frame = pd.read_csv(’sporting_event_ranking.csv’)

# set up sum contrasts for effects coding as needed for conjoint analysis

# using C(effect, Sum) notation within main effects model specification

main_effects_model = ’ranking ~ C(price, Sum) + C(seating, Sum) + \

C(boxvip, Sum) + C(frontrow, Sum) + C(promotion, Sum)’

# fit linear regression model using main effects only (no interaction terms)

main_effects_model_fit = \

smf.ols(main_effects_model, data = conjoint_data_frame).fit()

print(main_effects_model_fit.summary())

conjoint_attributes = [’price’, ’seating’, ’boxvip’, ’frontrow’, ’promotion’]

# build part-worth information one attribute at a time

level_name = []

part_worth = []

part_worth_range = []

end = 1 # initialize index for coefficient in params

for item in conjoint_attributes:

level_set = set(conjoint_data_frame[item])

nlevels = len(level_set)

level_name.append(list(sorted(list(level_set))))

begin = end

end = begin + nlevels - 1

new_part_worth = list(main_effects_model_fit.params[begin:end])

new_part_worth.append((-1) * sum(new_part_worth))

part_worth_range.append(max(new_part_worth) - min(new_part_worth))

part_worth.append(new_part_worth)

# end set to begin next iteration

# compute attribute relative importance values from ranges

attribute_importance = []

for item in part_worth_range:

attribute_importance.append(round(100 * (item / sum(part_worth_range)),2))

# user-defined dictionary for printing descriptive attribute names

effect_name_dict = {’price’ : ’Ticket Price’, \

’seating’ : ’Seating Area’,’boxvip’ : ’Box/VIP’, \

’frontrow’ : ’Front Row’, ’promotion’ : ’Promotion’}

100 Sports Analytics and Data Science

# report conjoint measures to console

index = 0 # initialize for use in for-loop

for item in conjoint_attributes:

print(’\nAttribute:’, effect_name_dict[item])

print(’ Importance:’, attribute_importance[index])

print(’ Level Part-Worths’)

for level in range(len(level_name[index])):

print(’ ’,level_name[index][level], part_worth[index][level])

index = index + 1

7 Promoting Brands and Products

Hobbs: “Still dogging me, huh, Max?”

Max: “Yeah. End of the road, Hobbs.”

Hobbs: “Want to hear what I think our chances are?”

Max: “So, you read my mind.”

Hobbs: “That takes all of three seconds.”

Max: “They come and they go, Hobbs. They come and they go. I’m guess- ing I’m going to be around here a lot longer than you or anyone else around here. I’m here to protect the game.”

Hobbs: “Who’s game?”

Max: “I do it by making or breaking the likes of you.”

Hobbs: “Did you ever play ball, Max?”

Max: “No, never have. But I make it a little more fun to watch. You see, it happens today whether you’re a goat or a hero. You’re gonna make me a quick story. Hey, see you around.”

—ROBERT REDFORD AS ROY HOBBS, AND ROBERT DUVAL AS MAX MERCY

IN The Natural (1984)

101

102 Sports Analytics and Data Science

It was a Thursday night in July. I was thinking about going to the ballpark. The Los Angeles Dodgers were playing the Colorado Rockies, and I was supposed to get an Adrian Gonzalez bobblehead with my ticket. Although I was not excited about the bobblehead, seeing a ball game at Dodger Sta- dium sounded like great fun. In April and May the Dodgers’ record had not been the best, but things were looking better by July. I wondered if bobble- heads would bring additional fans to the park. Dodgers management may have been wondering the same thing, or perhaps making plans for Yasiel Puig bobbleheads.

Suppose we were working for the Dodgers and wanted to learn about pro- motions and their effect on attendance. We call this example Bobbleheads and Dodger Dogs or Shaking Our Bobbleheads Yes and No. The example draws on Major League Baseball data from the 2012 season.

Relevant data for Dodgers’ home games are shown in table 7.1. Dodger Stadium, with a capacity of 56,000, is the largest ballpark in the world. We can see that Dodger Stadium was filled to capacity only twice in 2012. There were two cap promotions and three shirt promotions in 2012, not enough to draw meaningful inferences. Fireworks were used thirteen times on Friday nights, and once on the Fourth of July. The eleven bobblehead promotions occurred on night games, six of those being Tuesday nights.

Exploratory graphics help us find models that might work for predicting attendance and evaluating the effect of promotions on attendance. Figure 7.1 shows distributions of attendance across days of the week, and figure 7.2 shows attendance by month. Box plots like these reveal the overall values of the data, with the boxes covering the middle fifty percent or so of the distribution and with the center line representing the median. The dotted lines or whiskers extend to more extreme values in the distribution.1 By looking at the box plots, we can make comparisons by day and by month across the distributions of attendance.

1 To determine the length of the whiskers, we first compute the interquartile range, which is the distance between the 25th percentile and the 75th percentile. The end-points of the whiskers are defined by what are called adjacent values. The upper whisker extends to the upper adjacent value, a point one- and-a-half times the interquartile range above the upper end of the box. Or, if the maximum value in the distribution is less than that, the upper whisker extends to that maximum value. We often think of outliers as being points outside the whiskers; these outlier points are plotted as open circles. Box plots were the invention of John Tukey (1977).

Chapter 7. Promoting Brands and Products 103

Table 7.1. Bobbleheads and Dodger Dogs

month day attend day_of_week opponent temp skies day_night cap shirt fireworks bobblehead

APR 10 56000 Tuesday Pirates 67 Clear Day NO NO NO NO APR 11 29729 Wednesday Pirates 58 Cloudy Night NO NO NO NO APR 12 28328 Thursday Pirates 57 Cloudy Night NO NO NO NO APR 13 31601 Friday Padres 54 Cloudy Night NO NO YES NO APR 14 46549 Saturday Padres 57 Cloudy Night NO NO NO NO APR 15 38359 Sunday Padres 65 Clear Day NO NO NO NO APR 23 26376 Monday Braves 60 Cloudy Night NO NO NO NO APR 24 44014 Tuesday Braves 63 Cloudy Night NO NO NO NO APR 25 26345 Wednesday Braves 64 Cloudy Night NO NO NO NO APR 27 44807 Friday Nationals 66 Clear Night NO NO YES NO APR 28 54242 Saturday Nationals 71 Clear Night NO NO NO YES APR 29 48753 Sunday Nationals 74 Clear Day NO YES NO NO MAY 7 43713 Monday Giants 67 Clear Night NO NO NO NO MAY 8 32799 Tuesday Giants 75 Clear Night NO NO NO NO MAY 9 33993 Wednesday Giants 71 Clear Night NO NO NO NO MAY 11 35591 Friday Rockies 65 Clear Night NO NO YES NO MAY 12 33735 Saturday Rockies 65 Clear Night NO NO NO NO MAY 13 49124 Sunday Rockies 70 Clear Day NO NO NO NO MAY 14 24312 Monday Snakes 67 Clear Night NO NO NO NO MAY 15 47077 Tuesday Snakes 70 Clear Night NO NO NO YES MAY 18 40906 Friday Cardinals 64 Clear Night NO NO YES NO MAY 19 39383 Saturday Cardinals 67 Clear Night NO NO NO NO MAY 20 44005 Sunday Cardinals 77 Clear Night NO NO NO NO MAY 25 36283 Friday Astros 59 Cloudy Night NO NO YES NO MAY 26 36561 Saturday Astros 61 Cloudy Night NO NO NO NO MAY 27 33306 Sunday Astros 70 Clear Day NO NO NO NO MAY 28 38016 Monday Brewers 73 Clear Night NO NO NO NO MAY 29 51137 Tuesday Brewers 74 Clear Night NO NO NO YES MAY 30 25509 Wednesday Brewers 69 Clear Night NO NO NO NO MAY 31 26773 Thursday Brewers 70 Clear Night NO NO NO NO JUN 11 50559 Monday Angels 68 Clear Night NO YES NO NO JUN 12 55279 Tuesday Angels 66 Cloudy Night NO NO NO YES JUN 13 43494 Wednesday Angels 67 Clear Night NO NO NO NO JUN 15 40432 Friday White Sox 67 Clear Night NO NO YES NO JUN 16 45210 Saturday White Sox 68 Clear Night NO NO NO NO JUN 17 53504 Sunday White Sox 74 Clear Day NO NO NO NO JUN 28 49006 Thursday Mets 75 Clear Night NO NO NO YES JUN 29 49763 Friday Mets 72 Clear Night NO NO YES NO JUN 30 44217 Saturday Mets 78 Clear Day NO NO NO NO JUL 1 55359 Sunday Mets 75 Clear Night NO NO NO YES JUL 2 34493 Monday Reds 70 Clear Night NO NO NO NO JUL 3 33884 Tuesday Reds 70 Cloudy Night YES NO NO NO JUL 4 53570 Wednesday Reds 70 Clear Night NO NO YES NO JUL 13 43873 Friday Padres 76 Cloudy Night NO NO YES NO JUL 14 54014 Saturday Padres 75 Clear Night NO NO NO YES JUL 15 39715 Sunday Padres 77 Clear Day NO NO NO NO JUL 16 32238 Monday Phillies 67 Clear Night NO NO NO NO JUL 17 53498 Tuesday Phillies 70 Clear Night NO NO NO NO JUL 18 39955 Wednesday Phillies 80 Cloudy Day NO NO NO NO JUL 30 33180 Monday Snakes 73 Clear Night NO NO NO NO JUL 31 52832 Tuesday Snakes 75 Cloudy Night NO NO NO YES AUG 1 36596 Wednesday Snakes 79 Clear Day NO NO NO NO AUG 3 43537 Friday Cubs 73 Clear Night NO NO YES NO AUG 4 46588 Saturday Cubs 73 Cloudy Night NO NO NO NO AUG 5 42495 Sunday Cubs 83 Clear Day YES NO NO NO AUG 6 32659 Monday Rockies 79 Clear Night NO NO NO NO AUG 7 55024 Tuesday Rockies 80 Clear Night NO NO NO YES AUG 8 37084 Wednesday Rockies 84 Clear Night NO NO NO NO AUG 20 36878 Monday Giants 80 Clear Night NO NO NO NO AUG 21 56000 Tuesday Giants 75 Clear Night NO NO NO YES AUG 22 40173 Wednesday Giants 75 Clear Night NO NO NO NO AUG 24 39805 Friday Marlins 71 Clear Night NO NO YES NO AUG 25 40284 Saturday Marlins 70 Clear Night NO NO NO NO AUG 26 41907 Sunday Marlins 81 Clear Day NO NO NO NO AUG 30 54621 Thursday Snakes 80 Clear Night NO NO NO YES AUG 31 37622 Friday Snakes 77 Clear Night NO NO YES NO SEP 1 35992 Saturday Snakes 81 Clear Night NO NO NO NO SEP 2 31607 Sunday Snakes 89 Clear Day NO NO NO NO SEP 3 33540 Monday Padres 84 Cloudy Night NO NO NO NO SEP 4 40619 Tuesday Padres 78 Clear Night NO YES NO NO SEP 5 50560 Wednesday Padres 77 Cloudy Night NO NO NO NO SEP 13 43309 Thursday Cardinals 80 Clear Night NO NO NO NO SEP 14 40167 Friday Cardinals 85 Clear Night NO NO YES NO SEP 15 42449 Saturday Cardinals 95 Clear Night NO NO NO NO SEP 16 35754 Sunday Cardinals 86 Clear Day NO NO NO NO SEP 28 37133 Friday Rockies 77 Clear Night NO NO YES NO SEP 29 40724 Saturday Rockies 84 Cloudy Night NO NO NO NO SEP 30 35607 Sunday Rockies 95 Clear Day NO NO NO NO OCT 1 33624 Monday Giants 86 Clear Night NO NO NO NO OCT 2 42473 Tuesday Giants 83 Clear Night NO NO NO NO OCT 3 34014 Wednesday Giants 82 Cloudy Night NO NO NO NO

104 Sports Analytics and Data Science

Figure 7.1. Dodgers Attendance by Day of Week

Mon Tue Wed Thur Fri Sat Sun

25

30

35

40

45

50

55

Day of Week

A tte

nd an

ce (t

ho us

an ds

)

Figure 7.2. Dodgers Attendance by Month

April May June July Aug Sept Oct

25

30

35

40

45

50

55

Month

A tte

nd an

ce (t

ho us

an ds

)

Chapter 7. Promoting Brands and Products 105

We can explore these data further using a lattice of scatter plots. In figure 7.3 we map the relationship between temperature and attendance, controlling for time of game (day or night) and clear or cloudy skies. On day games with clear skies, we see what appears to be a moderate inverse relationship between temperature and attendance. Day games are usually on Sunday, and in 2012 all but one of those games was played under clear skies—a benefit of being in Los Angeles.

More telling perhaps are strip plots of attendance by opponent or visiting team; these are the univariate scatter plots in figure 7.4. Opponents from the large metropolitan areas (the New York Mets, Chicago Cubs and White Sox, Los Angeles Angels, and Washington D.C. Nationals) are consistently associated with higher attendance. But there are seventeen visiting teams in this study, and only eighty-one games or observations. Accordingly, uti- lizing the visiting team as a categorical predictor presents problems.

To advise management regarding promotions, we would like to know if promotions have a positive effect on attendance, and if they do have a pos- itive effect, how much might that effect be. So we build a linear model for predicting attendance using month, day of the week, and an indicator variable for the bobblehead promotion, and then we see how well it works. We enter these explanatory variables in a particular order so we can an- swer the basic question: “Do bobblehead promotions increase attendance, controlling for the date of the game (month and day of the week)?” Being data scientists, we employ a training-and-test regimen to provide an honest evaluation of the model’s predictive performance.

For the Los Angeles Dodgers bobblehead promotion, the fitted model does a good job of predicting higher attendance at games when bobbleheads are distributed. Our computer programs can provide indices of goodness of fit, but, more importantly, they can provide predictions of attendance that we can display on scatter plots.

How does a training-and-test regimen play out for the model we have de- veloped for the Dodgers? Figure 7.5 provides a picture of model perfor- mance that data scientists and business managers can understand. The model fit to the training set holds up when used with the test set.

106 Sports Analytics and Data Science

Figure 7.3. Dodgers Weather, Fireworks, and Attendance

Temperature (Degrees Fahrenheit)

A tte

nd an

ce (t

ho us

an ds

)

30

40

50

60 70 80 90

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�

Cloudy Day

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Clear Night

60 70 80 90

30

40

50

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Cloudy Night

Fireworks No Fireworks �

Chapter 7. Promoting Brands and Products 107

Figure 7.4. Dodgers Attendance by Visiting Team

Attendance (thousands)

Angels

Astros

Braves

Brewers

Cardinals

Cubs

Giants

Marlins

Mets

Nationals

Padres

Phillies

Pirates

Reds

Rockies

Snakes

White Sox

30 40 50

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Day Night �

108 Sports Analytics and Data Science

Figure 7.5. Regression Model Performance: Bobbleheads and Attendance

Actual Attendance (thousands)

P re

di ct

ed A

tte nd

an ce

(t ho

us an

ds )

30

40

50

60

30 40 50 60

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TRAIN

30 40 50 60

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TEST

Bobbleheads No Bobbleheads �

ln figure 7.5, TRAIN refers to the training set, the data on which we fit the model and TEST refers to the hold-out-data on which we test our model. Running the code for this example, we would see that, in the test set, more than 45 percent of the variance in attendance is accounted for by the lin- ear model—this is the square of the correlation of observed and predicted attendance. To explain a model to management, however, it is better to show a performance graph than to talk about squared correlation coeffi- cients, mean squared errors of prediction, or other model summary statis- tics. This is one graph among many possible graphs that we could have produced for the Dodgers. It shows the results of one particular random splitting of the data into training and test.

Running the code for the study on the complete set of home game data for the Los Angeles Dodgers in 2012 would yield a set of regression coeffi- cients, estimates of the parameters in the linear model, as shown in table 7.2. A sequential analysis of variance shows a statistically significant effect for the bobblehead promotion, controlling for month and day of the week. A test of residuals from the model would identify any statistically significant outliers—there were none for this problem. Most importantly, the model

Chapter 7. Promoting Brands and Products 109

can provide an assessment of the effect of the bobblehead promotion. In particular, we can see that bobblehead promotions have the potential of in- creasing attendance by 10,715 fans per game, all other things being equal.

The baseball promotions example was chosen to be simple in structure, so that ordinary least squares regression could be employed. This is a cross- sectional study with the baseball game serving as the unit of analysis.

More complicated models are possible, and diagnostic plots can provide additional information for the data scientist seeking to improve the model we specified. Nonetheless, it is interesting to note how much information a linear regression model can provide. Predictive models like the one used in this small example, with results presented in graphical summaries, can help guide management decisions.

One of the things that distinguishes data science from statistics is its focus on business requirements. In evaluating the utility of a model, the data scientist considers financial criteria as well as statistical criteria. And, in presenting predictions to management, she provides financial analysis as well as a description of the statistical model itself.

Using the fitted predictive model for the Dodgers bobblehead promotion, we can predict the attendance for each game in the forthcoming season, and we can predict this attendance with and without a bobblehead promotion. Knowing fixed and variable costs associated with a bobblehead promotion, as well as expected revenues from ticket sales and concessions, we can help the Los Angeles Dodgers assess the financial contribution of bobblehead promotions.

Considering costs for the forthcoming season in this example, the unit cost of a bobblehead doll is expected to be no more than $3 when ordered in quantities of at least 20,000. Bobbleheads are provided to the first 50,000 fans entering Dodger Stadium. To complete our work, then, we would use cost/volume/profit analysis to assess profit contribution.2

2 Cost/volume/profit analysis is a common technique in management accounting. It is sometimes called break even analysis or cost/benefit analysis. There are challenges in carrying out a financial analysis for Dodgers’ promotions because ticket prices vary by the type of game and seating location. Ticket prices for (four-star) bobblehead games in 2013 varied from $20 for a top deck seat to $120 for a VIP field box seat. These prices were raised in 2014 to $25 for a top deck seat to $140 for a VIP field box seat. A portion of ticket revenues goes to support concessions and additional staff needed to distribute bobbleheads. We would obtain these cost estimates from Dodger management.

110 Sports Analytics and Data Science

Table 7.2. Regression of Attendance on Month, Day of Week, and Bobblehead Promotion

Response: Attendance

Month (May) −2,385.625

Month (June) 7,163.234∗∗

Month (July) 2,849.828

Month (August) 2,377.924

Month (September) 29.030

Month (October) −662.668

Day of Week (Tuesday) 7,911.494∗∗∗

Day of Week (Wednesday) 2,460.023

Day of Week (Thursday) 775.364

Day of Week (Friday) 4,883.818∗

Day of Week (Saturday) 6,372.056∗∗

Day of Week (Sunday) 6,724.003∗∗∗

Bobblehead Promotion (YES) 10,714.900∗∗∗

Constant 33,909.160∗∗∗

Observations 81 R2 0.544 Adjusted R2 0.456 Residual Std. Error 6, 120.158(d f = 67) F statistic 6.158∗∗∗(d f = 13; 67)

Notes: ∗∗∗Significant at the 1 percent level. ∗∗Significant at the 5 percent level. ∗Significant at the 10 percent level.

Chapter 7. Promoting Brands and Products 111

Among Major League Baseball teams, the Dodgers had the third highest at- tendance in 2012 and the highest attendance in 2013 and 2014 (Knight 2015). The Dodgers are one of many MLB teams using promotions to increase at- tendance. Reports suggest that bobblehead promotions in particular are on the rise, with 2.27 million dolls distributed in 2012 (Broughton 2012) and an estimated 2.7 million dolls in 2013 (Foster 2013).

Promotions such as the bobblehead promotion do more than simply drive up attendance. They also reinforce the name of the brand in the minds of consumers. Advertising and promotion are the “promotion” part of the marketing mix or the four Ps: product, price, promotion, and place. Here “product” relates to product or service, and “price” is simply price. The word “place” refers to channels of distribution (face-to-face selling, whole- sale, retail, brick-and-mortar, mail-order, online, or mobile). Advertising and promotion are thought of as distinct fields of study by marketing aca- demics. Advertising refers to the message, the marketing communication, while promotion is what firms do in addition to the message.

As we have shown, traditional regression models are especially relevant to these areas of inquiry. Useful sources for regression modeling include Kutner, Nachtsheim, Neter, and Li (2004), Ryan (2008), and Chatterjee and Hadi (2012). For guidance in R programming for regression, see Venables and Ripley (2002), Fox and Weisberg (2011), and Fox (2014).

Moving beyond traditional linear models, we can consider modern, data- adaptive regression methods, as reviewed by Izenman (2008) and Hastie, Tibshirani, and Friedman (2009). We provide additional discussion of tra- ditional and data-adaptive (machine learning) methods in appendix A.

For an overview of advertising and promotion, marketing management textbooks may be consulted (Dickson 1997; Kotler and Keller 2012). Market response models attempt to predict sales and market shares across products within categories. These build upon econometric and time series methods. Hanssens, Parsons, and Schultz (2001) discuss market response modeling. Lilien and Rangaswamy (2003) suggest applications of market response modeling in sales force and channel management.

112 Sports Analytics and Data Science

For those wishing to explore models across all Major League Baseball teams, complete promotion and attendance data for all teams for the 2012 sea- son are provided on the publisher’s website http://www.ftpress.com/ miller/ and on GitHub at https://github.com/mtpa/.3 These data have a format similar to the Dodgers data in table 7.1, except that there are extra columns for the year and home team. Having data for all teams allows us to explore alternative modeling approaches, such as building a model for each team, aggregate models for groups of teams, or hierarchical models for game-day observations within teams. When predicting attendance at Major League Baseball parks, we would need to consider the fact that ballparks are often filled to capacity. Special models may be required to accommodate this high-end censoring (Lemke, Leonard, and Tlhokwane 2010).

The R program Shaking Our Bobbleheads Yes and No is shown in exhibit 7.1 and draws on packages for regression and graphics by Fox (2014) and Sarkar (2014), respectively. A similar Python program is shown in exhibit 7.2.

3 Major League Baseball data for promotions and attendance during the 2012 season were collected by Erica Costello. She graciously contributed these data so others could learn from them.

Chapter 7. Promoting Brands and Products 113

Exhibit 7.1. Shaking Our Bobbleheads Yes and No (R)

# Predictive Model for Los Angeles Dodgers Promotion and Attendance (R)

library(car) # special functions for linear regression

library(lattice) # graphics package

# read in data and create a data frame called dodgers

dodgers <- read.csv("dodgers.csv")

print(str(dodgers)) # check the structure of the data frame

# define an ordered day-of-week variable

# for plots and data summaries

dodgers$ordered_day_of_week <- with(data=dodgers,

ifelse ((day_of_week == "Monday"),1,

ifelse ((day_of_week == "Tuesday"),2,

ifelse ((day_of_week == "Wednesday"),3,

ifelse ((day_of_week == "Thursday"),4,

ifelse ((day_of_week == "Friday"),5,

ifelse ((day_of_week == "Saturday"),6,7)))))))

dodgers$ordered_day_of_week <- factor(dodgers$ordered_day_of_week, levels=1:7,

labels=c("Mon", "Tue", "Wed", "Thur", "Fri", "Sat", "Sun"))

# exploratory data analysis with standard graphics: attendance by day of week

with(data=dodgers,plot(ordered_day_of_week, attend/1000,

xlab = "Day of Week", ylab = "Attendance (thousands)",

col = "violet", las = 1))

# when do the Dodgers use bobblehead promotions

with(dodgers, table(bobblehead,ordered_day_of_week)) # bobbleheads on Tuesday

# define an ordered month variable

# for plots and data summaries

dodgers$ordered_month <- with(data=dodgers,

ifelse ((month == "APR"),4,

ifelse ((month == "MAY"),5,

ifelse ((month == "JUN"),6,

ifelse ((month == "JUL"),7,

ifelse ((month == "AUG"),8,

ifelse ((month == "SEP"),9,10)))))))

dodgers$ordered_month <- factor(dodgers$ordered_month, levels=4:10,

labels = c("April", "May", "June", "July", "Aug", "Sept", "Oct"))

# exploratory data analysis with standard R graphics: attendance by month

with(data=dodgers,plot(ordered_month,attend/1000, xlab = "Month",

ylab = "Attendance (thousands)", col = "light blue", las = 1))

# exploratory data analysis displaying many variables

# looking at attendance and conditioning on day/night

# the skies and whether or not fireworks are displayed

library(lattice) # used for plotting

# let us prepare a graphical summary of the dodgers data

group.labels <- c("No Fireworks","Fireworks")

114 Sports Analytics and Data Science

group.symbols <- c(21,24)

group.colors <- c("black","black")

group.fill <- c("black","red")

xyplot(attend/1000 ~ temp | skies + day_night,

data = dodgers, groups = fireworks, pch = group.symbols,

aspect = 1, cex = 1.5, col = group.colors, fill = group.fill,

layout = c(2, 2), type = c("p","g"),

strip=strip.custom(strip.levels=TRUE,strip.names=FALSE, style=1),

xlab = "Temperature (Degrees Fahrenheit)",

ylab = "Attendance (thousands)",

key = list(space = "top",

text = list(rev(group.labels),col = rev(group.colors)),

points = list(pch = rev(group.symbols), col = rev(group.colors),

fill = rev(group.fill))))

# attendance by opponent and day/night game

group.labels <- c("Day","Night")

group.symbols <- c(1,20)

group.symbols.size <- c(2,2.75)

bwplot(opponent ~ attend/1000, data = dodgers, groups = day_night,

xlab = "Attendance (thousands)",

panel = function(x, y, groups, subscripts, ...)

{panel.grid(h = (length(levels(dodgers$opponent)) - 1), v = -1)

panel.stripplot(x, y, groups = groups, subscripts = subscripts,

cex = group.symbols.size, pch = group.symbols, col = "darkblue")

},

key = list(space = "top",

text = list(group.labels,col = "black"),

points = list(pch = group.symbols, cex = group.symbols.size,

col = "darkblue")))

# employ training-and-test regimen for model validation

set.seed(1234) # set seed for repeatability of training-and-test split

training_test <- c(rep(1,length=trunc((2/3)*nrow(dodgers))),

rep(2,length=(nrow(dodgers) - trunc((2/3)*nrow(dodgers)))))

dodgers$training_test <- sample(training_test) # random permutation

dodgers$training_test <- factor(dodgers$training_test,

levels=c(1,2), labels=c("TRAIN","TEST"))

dodgers.train <- subset(dodgers, training_test == "TRAIN")

print(str(dodgers.train)) # check training data frame

dodgers.test <- subset(dodgers, training_test == "TEST")

print(str(dodgers.test)) # check test data frame

# specify a simple model with bobblehead entered last

my.model <- {attend ~ ordered_month + ordered_day_of_week + bobblehead}

# fit the model to the training set

train.model.fit <- lm(my.model, data = dodgers.train)

# summary of model fit to the training set

print(summary(train.model.fit))

# training set predictions from the model fit to the training set

dodgers.train$predict_attend <- predict(train.model.fit)

# test set predictions from the model fit to the training set

dodgers.test$predict_attend <- predict(train.model.fit,

newdata = dodgers.test)

Chapter 7. Promoting Brands and Products 115

# compute the proportion of response variance

# accounted for when predicting out-of-sample

cat("\n","Proportion of Test Set Variance Accounted for: ",

round((with(dodgers.test,cor(attend,predict_attend)^2)),

digits=3),"\n",sep="")

# merge the training and test sets for plotting

dodgers.plotting.frame <- rbind(dodgers.train,dodgers.test)

# generate predictive modeling visual for management

group.labels <- c("No Bobbleheads","Bobbleheads")

group.symbols <- c(21,24)

group.colors <- c("black","black")

group.fill <- c("black","red")

xyplot(predict_attend/1000 ~ attend/1000 | training_test,

data = dodgers.plotting.frame, groups = bobblehead, cex = 2,

pch = group.symbols, col = group.colors, fill = group.fill,

layout = c(2, 1), xlim = c(20,65), ylim = c(20,65),

aspect=1, type = c("p","g"),

panel=function(x,y, ...)

{panel.xyplot(x,y,...)

panel.segments(25,25,60,60,col="black",cex=2)

},

strip=function(...) strip.default(..., style=1),

xlab = "Actual Attendance (thousands)",

ylab = "Predicted Attendance (thousands)",

key = list(space = "top",

text = list(rev(group.labels),col = rev(group.colors)),

points = list(pch = rev(group.symbols),

col = rev(group.colors),

fill = rev(group.fill))))

# use the full data set to obtain an estimate of the increase in

# attendance due to bobbleheads, controlling for other factors

my.model.fit <- lm(my.model, data = dodgers) # use all available data

print(summary(my.model.fit))

# tests statistical significance of the bobblehead promotion

# type I anova computes sums of squares for sequential tests

print(anova(my.model.fit))

cat("\n","Estimated Effect of Bobblehead Promotion on Attendance: ",

round(my.model.fit$coefficients[length(my.model.fit$coefficients)],

digits = 0),"\n",sep="")

# standard graphics provide diagnostic plots

plot(my.model.fit)

# additional model diagnostics drawn from the car package

library(car)

residualPlots(my.model.fit)

marginalModelPlots(my.model.fit)

print(outlierTest(my.model.fit))

116 Sports Analytics and Data Science

Exhibit 7.2. Shaking Our Bobbleheads Yes and No (Python)

# Predictive Model for Los Angeles Dodgers Promotion and Attendance (Python)

# prepare for Python version 3x features and functions

from __future__ import division, print_function

from future_builtins import ascii, filter, hex, map, oct, zip

# import packages for analysis and modeling

import pandas as pd # data frame operations

from pandas.tools.rplot import RPlot, TrellisGrid, GeomPoint,\

ScaleRandomColour # trellis/lattice plotting

import numpy as np # arrays and math functions

from scipy.stats import uniform # for training-and-test split

import statsmodels.api as sm # statistical models (including regression)

import statsmodels.formula.api as smf # R-like model specification

import matplotlib.pyplot as plt # 2D plotting

# read in Dodgers bobbleheads data and create data frame

dodgers = pd.read_csv("dodgers.csv")

# examine the structure of the data frame

print("\nContents of dodgers data frame ---------------")

# attendance in thousands for plotting

dodgers[’attend_000’] = dodgers[’attend’]/1000

# print the first five rows of the data frame

print(pd.DataFrame.head(dodgers))

mondays = dodgers[dodgers[’day_of_week’] == ’Monday’]

tuesdays = dodgers[dodgers[’day_of_week’] == ’Tuesday’]

wednesdays = dodgers[dodgers[’day_of_week’] == ’Wednesday’]

thursdays = dodgers[dodgers[’day_of_week’] == ’Thursday’]

fridays = dodgers[dodgers[’day_of_week’] == ’Friday’]

saturdays = dodgers[dodgers[’day_of_week’] == ’Saturday’]

sundays = dodgers[dodgers[’day_of_week’] == ’Sunday’]

# convert days’ attendance into list of vectors for box plot

data = [mondays[’attend_000’], tuesdays[’attend_000’],

wednesdays[’attend_000’], thursdays[’attend_000’],

fridays[’attend_000’], saturdays[’attend_000’],

sundays[’attend_000’]]

ordered_day_names = [’Mon’, ’Tue’, ’Wed’, ’Thur’, ’Fri’, ’Sat’, ’Sun’]

# exploratory data analysis: box plot for day of the week

fig, axis = plt.subplots()

axis.set_xlabel(’Day of Week’)

axis.set_ylabel(’Attendance (thousands)’)

day_plot = plt.boxplot(data, sym=’o’, vert=1, whis=1.5)

plt.setp(day_plot[’boxes’], color = ’black’)

plt.setp(day_plot[’whiskers’], color = ’black’)

plt.setp(day_plot[’fliers’], color = ’black’, marker = ’o’)

axis.set_xticklabels(ordered_day_names)

plt.show()

Chapter 7. Promoting Brands and Products 117

plt.savefig(’fig_advert_promo_dodgers_eda_day_of_week_Python.pdf’,

bbox_inches = ’tight’, dpi=None, facecolor=’w’, edgecolor=’b’,

orientation=’portrait’, papertype=None, format=None,

transparent=True, pad_inches=0.25, frameon=None)

april = dodgers[dodgers[’month’] == ’APR’]

may = dodgers[dodgers[’month’] == ’MAY’]

june = dodgers[dodgers[’month’] == ’JUN’]

july = dodgers[dodgers[’month’] == ’JUL’]

august = dodgers[dodgers[’month’] == ’AUG’]

september = dodgers[dodgers[’month’] == ’SEP’]

october = dodgers[dodgers[’month’] == ’OCT’]

data = [april[’attend_000’], may[’attend_000’],

june[’attend_000’], july[’attend_000’],

august[’attend_000’], september[’attend_000’],

october[’attend_000’]]

ordered_month_names = [’April’, ’May’, ’June’, ’July’, ’Aug’, ’Sept’, ’Oct’]

fig, axis = plt.subplots()

axis.set_xlabel(’Month’)

axis.set_ylabel(’Attendance (thousands)’)

day_plot = plt.boxplot(data, sym=’o’, vert=1, whis=1.5)

plt.setp(day_plot[’boxes’], color = ’black’)

plt.setp(day_plot[’whiskers’], color = ’black’)

plt.setp(day_plot[’fliers’], color = ’black’, marker = ’o’)

axis.set_xticklabels(ordered_month_names)

plt.show()

plt.savefig(’fig_advert_promo_dodgers_eda_month_Python.pdf’,

bbox_inches = ’tight’, dpi=None, facecolor=’w’, edgecolor=’b’,

orientation=’portrait’, papertype=None, format=None,

transparent=True, pad_inches=0.25, frameon=None)

# trellis/lattice plot attendance by temp, conditioning on skies

# and day_night with bobblehead NO/YES shown in distinct colors

plt.figure()

plot = RPlot(dodgers, x = ’temp’, y = ’attend_000’)

plot.add(TrellisGrid([’day_night’, ’skies’]))

plot.add(GeomPoint(colour = ScaleRandomColour(’bobblehead’)))

plot.render(plt.gcf())

plt.show()

plt.savefig(’fig_advert_promo_dodgers_eda_many.pdf’,

bbox_inches = ’tight’, dpi=None, facecolor=’w’, edgecolor=’b’,

orientation=’portrait’, papertype=None, format=None,

transparent=True, pad_inches=0.25, frameon=None)

# map day_of_week to ordered_day_of_week

day_to_ordered_day = {’Monday’ : ’1Monday’,

’Tuesday’ : ’2Tuesday’,

’Wednesday’ : ’3Wednesday’,

’Thursday’ : ’4Thursday’,

’Friday’ : ’5Friday’,

’Saturday’ : ’6Saturday’,

’Sunday’ : ’7Sunday’}

dodgers[’ordered_day_of_week’] = dodgers[’day_of_week’].map(day_to_ordered_day)

118 Sports Analytics and Data Science

# map month to ordered_month

month_to_ordered_month = {’APR’ : ’1April’,

’MAY’ : ’2May’,

’JUN’ : ’3June’,

’JUL’ : ’4July’,

’AUG’ : ’5Aug’,

’SEP’ : ’6Sept’,

’OCT’ : ’7Oct’}

dodgers[’ordered_month’] = dodgers[’month’].map(month_to_ordered_month)

# employ training-and-test regimen for model validation

np.random.seed(1234)

dodgers[’runiform’] = uniform.rvs(loc = 0, scale = 1, size = len(dodgers))

dodgers_train = dodgers[dodgers[’runiform’] >= 0.33]

dodgers_test = dodgers[dodgers[’runiform’] < 0.33]

# check training data frame

print(’\ndodgers_train data frame (rows, columns): ’,dodgers_train.shape)

print(dodgers_train.head())

# check test data frame

print(’\ndodgers_test data frame (rows, columns): ’,dodgers_test.shape)

print(dodgers_test.head())

# specify a simple model with bobblehead entered last

my_model = str(’attend ~ ordered_month + ordered_day_of_week + bobblehead’)

# fit the model to the training set

train_model_fit = smf.ols(my_model, data = dodgers_train).fit()

# summary of model fit to the training set

print(train_model_fit.summary())

# training set predictions from the model fit to the training set

dodgers_train[’predict_attend’] = train_model_fit.fittedvalues

# test set predictions from the model fit to the training set

dodgers_test[’predict_attend’] = train_model_fit.predict(dodgers_test)

# compute the proportion of response variance

# accounted for when predicting out-of-sample

print(’\nProportion of Test Set Variance Accounted for: ’,\

round(np.power(dodgers_test[’attend’].\

corr(dodgers_test[’predict_attend’]),2),3))

# use the full data set to obtain an estimate of the increase in

# attendance due to bobbleheads, controlling for other factors

my_model_fit = smf.ols(my_model, data = dodgers).fit()

print(my_model_fit.summary())

print(’\nEstimated Effect of Bobblehead Promotion on Attendance: ’,\

round(my_model_fit.params[13],0))

8 Growing Revenues

Roy: “I think of the golf swing as a poem. The critical opening phrase of this poem will always be the grip. The hands unite to form a single unit by the simple overlap of the . . . little finger.” Molly: “Right.” Roy: “Lowly and slowly the club head is led back, pulled into position not by the hands, but by the body, which turns away from the targets, shift- ing weight to the right side without shifting balance. Tempo is everything, perfection unattainable. As the body coils down at the top of the swing, there is a slight hesitation, a nod to the gods . . . . It’s alive, this swing, and a sculpture. And down through contact, striking the ball crisply with character. . . . And the unfinished business of Roy McAvoy.” Molly: “Why unfinished?” Roy: “I have a short follow-through. It has an unfinished look.” Molly: “Why?” Roy: “Well some say that’s the easiest way to play in the winds of west Texas, and some say it’s because I never finished anything in my life. You can decide. But the point is every finishing position is unique. . . . That’s what the golf swing is all about. It’s about gaining control of your life and letting go at the same time. . . . There’s only one other acceptable theory about how to hit a golf ball.” Molly: “Oh, boy. I’m afraid to ask. Well, what’s the other theory?” Roy: “Grip it and rip it.”

—KEVIN COSTNER AS ROY MCAVOY AND RENE RUSSO AS DR. MOLLY GRISWOLD IN Tin Cup (1996)

119

120 Sports Analytics and Data Science

Professional team sports is called “the winning business” because there is often a relationship between winning and revenues. Sports consumers like winners. Winning means higher ticket sales. Winning means going into the playoffs and collecting revenue from additional games. Winning means it is easier to garner governmental support for facilities, recruit players, and find business partners, advertisers, and corporate sponsors. Winning is part of the revenue growth story, but not the whole story.

Rein, Shields, and Grossman (2015) lament “the winning fallacy” of sports organizations—the idea that winning is essential to sports business success. It is not. There are notable examples of teams that have been perennial losers, while beloved by their fans and successful as businesses. Witness the Boston Red Sox and Chicago Cubs throughout much of their history (Goodwin 1997; Will 2014). It is possible for teams to have brand equity, loyal fans, and full stadia without winning championships. Leagues also have expanded playoff schedules so more teams are winners.

Equally or perhaps more important than winning are marketing strategy and tactics. As in any business, there is work to do finding new customers and retaining current customers, identifying and targeting market segments, building brand loyalty, developing products, and defining effective pricing plans. Data science can contribute to all of these endeavors.

No business can long survive without finding new customers, and the pro- cess of finding new customers begins by learning as much as we can about current customers and groups of customers. We identify the types of cus- tomers who are most likely to buy as well as variables that may be used to find those customers.

A market segment is a group of consumers that is different from other groups of consumers in ways that matter to marketing managers. We can identify segments by geographic, demographic, psychographic, and behav- ioral characteristics. Most useful for target marketing are characteristics that are accessible and easily measured.

When properly executed, market segmentation can guide marketing strat- egy and tactics. What consumers like, what they buy, where they buy, and how much they buy may differ across segments. Some consumers are responsive to advertisements and promotions. Some are more price- conscious than others. By using knowledge of a consumer’s market seg-

Chapter 8. Growing Revenues 121

ment, marketing managers can make informed decisions about marketing actions. They can use market segments in product development, advertis- ing, promotion, pricing, and target marketing.

To be useful to marketing management, market segments must be discov- erable and reachable. We must be able to identify a consumer’s segment from available data, find our way to that consumer, and take appropriate marketing action. This is the core of sales and marketing—converting a consumer with little knowledge of a product into a buyer of the product.

Variables that go into the segmentation should be easily available or ac- cessible. We avoid variables that are difficult to measure. And we prefer publicly available data. Common segmentation variables reflect geograph- ical location, age, income, and behavioral or lifestyle variables. We look for data that we can gather without survey sampling.

Data for market segmentation are many and varied. Geographic data re- fer to where people live, such as the region of the country, state, city, street location, or census area. Behavioral data include occupational information, how consumers travel, where they shop, what they read, and to which com- munity groups they belong. Demographic data include variables such as gender, age, education, occupation, and level of income. Psychographic data include psychological factors, attitudes, interests, personality charac- teristics, and lifestyle factors. Of special importance in sports consumer segmentation is information about sports participation.

Age is a common segmentation variable. Many marketing managers think in terms of generations by date of birth. It is common to distinguish among members of the silent generation (birth range 1925–1945), baby boomers (1946–1964), Generation Xers (1965–1978) , and Millennials (also called Gen- eration Y, 1979–1994)). Consumers in generational segments are under- stood to have diverse needs, attitudes, and behaviors. Generational differ- ences can affect consumer response to marketing messages, products, pro- motions, and pricing. Millennials, for example, can be expected to be less price-sensitive and more technologically savvy (Kotler and Keller 2012).

Marketing managers often design products and tailor marketing messages for individual segments or combinations of segments. Knowing that Mil- lennials are technology-savvy, for example, may prompt managers to ad- vertise products on computers and mobile devices to reach that segment.

122 Sports Analytics and Data Science

Or they may emphasize online sales promotion as opposed to brick-and- mortar promotion.

Traditional methods of cluster analysis are widely used in market segmen- tation. They represent multivariate techniques for grouping consumers based on their similarity to one another. Distance metrics or measures of agreement between consumers guide the segmentation process. Clus- ter analysis involves finding groups in data. Cluster analysis takes many consumer-related variables and uses them to represent differences between consumers. When two consumers have similar values for such variables as age, marital status, job type, and education, they are seen as being sim- ilar. When two consumers have very different values on these variables, they are seen as dissimilar. Cluster analysis looks at the differences among consumers—their distances from one another—to identify groups of con- sumers or market segments.

In most cases, we would perform many cluster analyses, providing a set of clustering solutions. We can begin by seeing what happens when we divide the entire set of consumers into just two groups or clusters. Then we can try three clusters, then four, and so on. The number of clusters is an important feature of a clustering solution. If there are too many clusters, the clustering solution may be difficult to utilize in product marketing.

It is common to look for solutions involving ten or fewer clusters. We also seek solutions for which all clusters or segments are of sufficient size to warrant marketing attention. We note the proportion of consumers in each cluster when evaluating solutions. Clusters that are very small may be of little interest to management. The fewer consumers in a cluster, the lower the potential sales revenue.

Selecting a clustering solution among the many possible solutions we ob- tain from cluster analysis algorithms is as much art as science. There are numerous factors to consider in the context of market segmentation. We look for segments that are easy to interpret in terms of descriptive statistics. After segments have been identified, we can return to the full database of customer or client information to see if there are relationships between seg- ment membership and sales order history and/or responsiveness to sales and marketing activities.

Chapter 8. Growing Revenues 123

Mass marketing treats all customers as one group. One-to-one marketing focuses on one customer at a time. Target marketing to selected groups of customers or market segments lies between mass marketing and one-to- one marketing. Target marketing involves directing marketing activities to those customers who are most likely to buy.

Market segmentation and target marketing often go hand-in-hand. But there are people in marketing who are philosophically opposed to using segments for targeting. Instead of targeting market segments, these re- searchers promote a one-to-one marketing approach that targets each in- dividual as an individual.

Targeting involves identifying customers who are most likely to buy prod- ucts and directing marketing efforts toward those customers. The cus- tomers are given more attention in terms of pre-sales activities and post- sales support. Targeting implies selection. Some customers are identified as more valuable than others and these more highly valued customers are given special attention. By becoming skilled at targeting, a company can improve its profitability, increasing revenues and decreasing costs.

Targeting is best executed by organizations that keep detailed records for individuals. These are companies that offer loyalty programs or use a cus- tomer relationship management system. Sales transactions need to be as- sociated with specific customers and stored in a database. Where revenues (cash inflows) and expenses (cash outflows) are recorded, we can carry out discounted cash-flow analysis and compute the return on investment for each customer.

A target is a customer who is worth pursuing. A target is a profitable customer—sales revenues from the target exceed costs of sales and support. Another way to say this is that a target is a customer with positive lifetime value. Over the course of a company’s relationship with the customer, more money comes into the business than goes out of the business.

In target marketing, we need to identify factors that are useful and deter- mine how to use those factors in modeling techniques. A response variable is something we want to predict, such as sales dollars, volume, or whether a consumer will buy a product. Customer lifetime value is a composite response variable, computed from many transactions with each customer, and these transactions include observations of sales and costs.

124 Sports Analytics and Data Science

Explanatory variables are used to predict response variables. Explanatory variables can be continuous (having meaningful magnitude) or categorical (without meaningful magnitude). Statistical models show the relationship between explanatory variables and response variables.

Regression and classification can both be used in target marketing. When the response variable (the variable to be predicted) is continuous or has meaningful magnitude, we use regression to make the prediction. Exam- ples of response variables with meaningful magnitude are sales dollars, sales volume, cost of sales, cost of support, and customer lifetime value.

When the response variable is categorical (a variable without meaningful magnitude), we use classification. Examples of response variables with- out meaningful magnitude are whether a customer buys, whether a cus- tomer stays with the company or leaves to buy from another company, and whether the customer recommends a company’s products to another cus- tomer.

To develop a classification model for targeting, we proceed in much the same way as with regression, except the response variable is now a cate- gory or class. For each customer, a logistic regression model can provide a predicted probability of response. We classify responses using a cut-off value for the probability of response. If the cut-off were set at 0.50, for ex- ample, then we would target the customer if the predicted probability of response is greater than 0.50, and not target otherwise. Or we could target all customers who have a predicted probability of response of 0.40, or 0.30, and so on. The value of the cut-off will vary from one problem to the next.

When we engage in target marketing, we review data from current cus- tomers, particularly sales transaction data. We also assess the costs of sales and support for current customers. We can think of each customer as an investment, and compute the return on investment for each customer. If the expected lifetime value of a customer is positive, then it makes sense to retain that customer.

Customer lifetime value analysis draws on concepts from financial man- agement. We evaluate investments in terms of cash in-flows and out-flows over time. Before we pursue a prospective customer, we want to know that discounted cash in-flows (sales) will exceed discounted cash out-flows

Chapter 8. Growing Revenues 125

(costs). It makes sense to retain a current customer when discounted future cash flows are positive.

Customer lifetime value is computed from our experience with each cus- tomer. For the cash in-flows, we note a customer’s purchasing history as recorded in sales transactions. For the cash out-flows, we note past sales and support costs as recorded in customer relationship management systems. Customer lifetime value analysis is best executed when detailed records are maintained for customers.

Data for valuing customers may be organized as panel or longitudinal data. Rows correspond to customers and columns correspond to time periods. Data from past transactions may be incomplete, and future cash-flows are unknown. So, we use predictive models to estimate cash-flows. We draw on available data to impute missing observations from the past, and we use observations from the past to forecast observations in the future.

Direct marketers are the quintessential target marketers. Their work in- volves contacting prospective and former customers directly through tele- phone, mail, e-mail, and online channels. Direct marketers collect and maintain information about past contacts, mailings, in-coming and out- going communications, and business transactions. And they do this on a customer-by-customer basis. These data are used to guide sales promotions and direct marketing programs. Direct mailings and outgoing communica- tions include product brochures and announcements, as well as coupons and information about product prices, bundles, and promotions.

Each direct marketing promotion may be evaluated in terms of its contri- bution to the profit of the firm. There are costs associated with mailings and online activities. There are revenues coming from people who order. The hit rate or proportion of people who respond to a direct mail or online offer is a critical number to watch because it determines the success or fail- ure of the promotion. Direct marketing promotions, properly constructed, represent field experiments. Rarely is it wise to mail to an entire list at once.

When conducting a direct marketing experiment, we can divide the list into sections and vary the direct mail offer or advertising copy across sections. The conditions that yield the highest profit on the test mailings set the stage for subsequent mailings. Numerous treatment conditions can be examined for each direct marketing promotion.

126 Sports Analytics and Data Science

Direct and database marketers build models for predicting who will buy in response to marketing promotions. Traditional models, or what are known as RFM models, consider the recency (date of most recent purchase), fre- quency (number of purchases), and monetary value (sales revenue) of pre- vious purchases. More complicated models utilize a variety of explana- tory variables relating to recency, frequency, monetary value, and customer demographics.

Pricing research presents special challenges. There are many questions to answer. What are consumers willing to pay for a product or service? What do they expect to pay? How will prices across a set of competitive or substi- tute products affect consumer choice? What prices will generate the highest contribution to profit?

In setting prices, sports businesses need to consider what are called the three C’s of pricing: costs, consumers, and the competition. “Consumers” in this context refers to willingness to pay and demand, which we cover here. And “competition” refers to substitute products, not sports competition in games. To consider an application in sports management, we can look at willingness to pay for tickets.

Ticket prices deserve special mention due to their importance in contribut- ing to team revenue. Do costs, particularly player costs, drive ticket prices? Probably not. Fort and Winfree (2013) dispel the notion that player salary demands cause ticket prices to rise. Rather, it is consumer demand that en- genders both higher ticket prices and higher player salaries. Many teams experience sellouts on a regular bases, suggesting that they could set higher ticket prices. Instead of asking why ticket prices are high, we should be ask- ing why they are not higher.

To do a good job of defining ticket prices, we need to understand consumer demand. In other words, pricing research and demand estimation go hand in hand. As we have seen earlier, price can be included as an attribute in conjoint and choice studies, providing a mechanism for estimating con- sumer willingness to pay and the consumer demand curve. If a sports team can understand consumer willingness to pay, it will be better able to set prices for tickets, concessions, and branded merchandise.

Much work in the area of microeconomics and econometrics concerns es- timation of the parameters of demand and the price elasticity of demand.

Chapter 8. Growing Revenues 127

From economics we understand that the price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price. With elasticity less than 1.0, a large change in price results in a small change in quantity demanded, as we would expect for necessities or goods and services essential to life. With elasticity greater than 1.0, a small change in price results in a large change in quantity demanded. This is typical of luxury goods and services, including entertainment and sports.

Defining price elasticity is easy, but estimating elasticity is not so easy be- cause markets and the variables that affect market prices are constantly changing. Economic researchers focus on aggregate consumer behavior, demand functions, and price elasticity, whereas marketing researchers fo- cus on consumer heterogeneity and marketing mix factors that affect de- mand. How much of a product is demanded and purchased varies with consumer preferences and with the consumer’s situation in life, defined by the time available to shop and the money available to spend. The term price sensitivity refers to consumer individual differences in demand. And some marketing theorists use the term reference price to describe a hypothetical internal standard that a consumer uses in judging the prices of products.

Specialized pricing research methods include monadic tests in which a prod- uct or product description, including price, is placed in context with a likely set of competitive products, and the consumer respondent is asked if she would purchase the product. Across many respondents at many price points, monadic tests may provide meaningful estimates of price sensitivity, help- ing to find the price that will generate the highest contribution to profit.

Setting ticket prices for sporting events is a complicated process because stadia have numerous classes of seating and associated classes of tickets. With an understanding of willingness to pay and knowledge of stadium seating capacity across various classes of tickets, we could use mathemat- ical programming to maximize (or minimize) an objective. Mathematical programming requires an objective. What is the objective?

Do teams set ticket prices in order to maximize ticket revenue? Curiously, the answer to this question is no. Many teams set ticket prices lower than the revenue-maximizing price. There are many reasons for this, as Fort and Winfree (2013) point out.

128 Sports Analytics and Data Science

Prices lower than willingness to pay are associated with economic consumer surplus, which in turn generates good will among fans. Season tickets are heavily discounted to attract purchase. Lower prices ensure that more fans will go to games, resulting in higher concession and merchandise sales. In-stadium advertising is easier to sell when advertisers are assured that games will be sellouts. Lower ticket prices attract new fans—their trial pur- chases may be followed by repeat purchases. Furthermore, a team’s rep- utation depends not only on winning but also on having large and active crowds at the stadium.

Sports ticket pricing, airline, and hotel ticket pricing share in having capac- ity constraints. The objective in airline or hotel ticket pricing is revenue maximization alone. There is no requirement to fill all the seats or hotel rooms. Sports teams, on the other hand, have multiple objectives. They want to achieve the highest possible revenue while filling as many seats as possible. To define a tractable, single-goal mathematical programming model, we could simplify the problem, setting the objective of maximizing ticket revenue while filling all the seats.

Suppose we were working for the Dallas Cowboys. AT&T Stadium, home of the Dallas Cowboys, has many classes of seats, with prices between $80 for limited visibility seats to more than $36 thousand for the best luxury suites. Are these prices optimal, given an objective of maximizing ticket revenue while filling all the seats? We can use mathematical programming to answer this question. Perhaps the Cowboys should raise prices at the low end and/or lower prices at the high end.

When developing plans for revenue growth and pricing, it is useful to con- sider a business in relation to its suppliers and buyers. We draw a picture showing potential new entrants as well as substitute products. In figure 8.1 we show a strategic analysis of the Golden State Warriors using the five- forces model developed by Porter (1980).

Chapter 8. Growing Revenues 129

Figure 8.1. Competitive Analysis for an NBA Team: Golden State Warriors

Professional Basketball

Team Rivalry among existing teams

Potential Entrants

BuyersSuppliers

Substitutes

Bargaining power of suppliers strong

Limited supply of star basketball talent with many other teams bidding Facilities in transition Oakland Arena limited New arena planned

Considerable threat from substitute products

Bargaining power of buyers limited

Many potential partners, advertisers, and sponsors

Opportunities for expanded media coverage and

growth of the fan base

Minimal threat of entry of new organizations of this type

Team protected by the NBA

Alternative sporting events, some overlapping the NBA season, including professional football Oakland Raiders and San Francisco 49ers Many entertainment alternatives in the area Media-based sports, including fantasy sports, are substitutes with uncertain effects

130 Sports Analytics and Data Science

The Golden State Warriors compete with other teams for national attention and brand loyalty. But like other NBA teams they are cooperators in the league, protected from the thread of new entrants in the form of profes- sional basketball teams in the San Francisco Bay area.

The most difficult part of this business is managing resources: players and facilities. The team competes in a tough labor market. Star players are in short supply and in great demand from other NBA teams. NBA faces a tough negotiator in the National Basketball Players Association (NBPA). The current player agreement extends through the 2020–21 season, but ei- ther side can opt out in 2017 (Streeter 2015).

The team has a loyal fan base and considerable opportunities for growth. Winning the NBA finals in 2015 had a strong positive effect on fans. There are opportunities for revenue growth through media, business partners, ad- vertisers, and sponsors. These opportunities should grow after the team moves into a newer, larger arena planned at a San Francisco site. In-stadium revenues can grow by employing methods for increased fan engagement, such as those used by the San Francisco Giants (Schlough 2015).

Media growth has been exceptional. NBA commissioner, Adam Silver, has looked to media as a way to expand the reach of member teams internation- ally. In social media, the NBA has taken the lead among US-based leagues, with a reported 759 million worldwide users following the league or ex- pressing positive feelings (social media “likes”) for NBA teams (Keating 2015). Revenues from television should grow as a seven-year, $24 billion deal with ESPN and the Turner Broadcasting System takes effect in 2016 (Streeter 2015)

There is threat from substitute products, including professional sports teams when seasons overlap. There are also many entertainment options in the Bay area. The Golden State Warriors, like other professional sports teams, may have uncertainties about fantasy sports. Perhaps participation in fan- tasy sports will translate into increased involvement with the team and its players. Fans see their favorite fantasy players on the court. On the other hand, fantasy sports consumes part of a fan’s discretionary income, leaving less to spend on tickets and merchandise. It can also be argued that fantasy sports do little to build fan affiliation with teams because fantasy games concern players as individuals, independent of their true teams.

Chapter 8. Growing Revenues 131

The benefits of market segmentation are described in marketing manage- ment references (Dickson 1997; Kotler and Keller 2012). Sternthal and Ty- bout (2001) and Cespedes, Dougherty, and Skinner (2013) review manage- ment issues in segmentation and targeting. Frank, Massey, and Wind (1972), Neal (2000), and Wedel and Kamakura (2000) discuss the objectives and methods of market segmentation.

Reviews of traditional direct marketing are provided by Wunderman (1996), and Nash (2000, 1995). Hughes (2000) discusses strategies associated with database marketing and online direct marketing. Direct and database mar- keting is a rich area of application in marketing data science. Anand and Büchner (2002) discuss applications in cross-selling, finding prospects for additional products from an existing customer list. Blattberg, Kim, and Neslin (2008) provide a comprehensive review of modeling methods in di- rect and database marketing, including extensive discussion of RFM mod- els, lift charts, and alternative methods for setting probability cut-offs.

Bayesians use the term consumer heterogeneity to refer to individual differ- ences across customers. The thinking is that describing consumers in terms of their positions along underlying attribute parameters is more informa- tive than describing them as being members of segments. Bayesian meth- ods in marketing, reviewed by Rossi, Allenby, and McCulloch (2005), have been implemented in R packages by Rossi (2014) and Sermas (2014).

Introductions to pricing theory and research may be found in books about microeconomics (Pindyck and Rubinfeld 2004; Hirshleifer, Glazer, and Hir- shleifer 2005; Varian 2005) and econometrics (Pindyck and Rubinfeld 2000; Greene 2002). Discussion of pricing research methods may be found in Lyon (2000, 2002), Feldman (2002), and Orme (2006). Marder (1997) reviews monadic pricing methods. Nagle and Hogan (2005) and Krishnamurthi (2001) present reviews of pricing strategy and management issues. Em- pirical research about reference prices is summarized by Kalyanaram and Winer (1995). Revenue growth and yield management through mathemati- cal programming are well understood for airlines and hotels (Phillips 2005; Karaesmen, van Ryzin, Talluri, and Vulcano 2008). Barlow (2000) shows that similar methods may be employed to fill seats in sports stadia.

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9 Managing Finances

Billy: “I can’t compete against $120 million on a payroll with $38 million.” Steve: “We’re not going to compete with these teams that have big budgets. We’re gonna work within the constraints that we have, and you’re gonna go out and do the best job that you can recruiting new players. We’re not going to pay $17 million for players.” Billy: “I’m not asking you for 10, 20, 30 million dollars. I’m just asking for a little bit of help. Just get me a little bit closer, and I will get you that championship team. I mean, this is why I am here. This is why you hired me. And I gotta ask you what are we doing here . . . ” Steve: “Billy, you know, I . . . ” Billy: “. . . if it’s not to win a championship.” Steve: “I want to win just as much as . . . ” Billy: “That’s my bar. My bar is here. [Holds his hand high.] My bar is to take this team to the championship.” Steve: “Billy, we’re a small-market team, and you’re a small-market GM. I’m asking you to be okay not spending money that I don’t have. And I’m asking you to take a deep breath, shake off the loss, get back in a room with your guys and figure out how to find replacements for the guys we lost with the money that we do have.”

—BRAD PITT AS BILLY BEANE AND STEVE DAKOTA AS STEVE IN Moneyball (2011)

133

134 Sports Analytics and Data Science

A Moneyball ethos guides many professional sports teams. In a player draft or free-agent bidding situation, a team’s objective is to select the best player or combination of players subject to budgetary or salary-cap constraints. “Best” may be defined as being able to contribute the most to the team in additional runs or points across future games. The team’s planning hori- zon could be the remainder of the season and playoffs or future seasons. Player contract costs vary from one player to the next, especially among free agents.

There are many options to consider when adding new players to a team. We need to identify the set of possible players and estimate each player’s potential contribution to the team in runs or points scored, or in games won across the team’s planning horizon. There are constraints on the number of players on a team, so bringing on a new player means dropping one of the team’s current players. There are constraints regarding player positions. If a professional basketball team acquires a free-agent guard, for example, it may well drop another guard from its player roster. There are costs as- sociated with each player being acquired and each player being dropped. Furthermore, player contract terms may specify that dropped players con- tinue to earn all or a portion of their salaries.

In theory, maximizing output subject to constraints may be addressed by mathematical programming. In practice, player draft and free-agent ac- quisitions represent challenging problems in operations research and data science. Costs are difficult to specify with any degree of confidence. This is a labor marketplace with many teams bidding for the same players. Fur- thermore, a player’s contribution to a team is better estimated as a posterior probability distribution than as a single number, making the problem one of stochastic programming, which we return to later in this chapter.

Let us begin our consideration of costs by looking at cost-volume-profit analysis from management accounting, illustrated in figure 9.1. This is a common method for assessing costs and benefits associated with alterna- tive business practices. Although cost-volume-profit analysis would be dif- ficult to apply to player or stadium costs, we can use it to assess particular aspects of sports business, such as ticket, concession, or merchandise sales.

Chapter 9. Managing Finances 135

Figure 9.1. Cost-Volume-Profit Analysis

$ $

Q Q

R ev

en ue

li ne

p Q

Va ria

bl e

co st

c Q

Fixed cost F

To ta

l c os

t c Q +

F

To ta

l c os

t c Q +

F

Q*

pQ*

Suppose we consider hot dogs sold at baseball games, in particular, the Dodger Dog sold at Dodger Stadium. Supplied by the company Farmer John R©, the Dodger Dog is sold at a particular price at Dodger Stadium, call it p. For the purposes of our analysis, we consider the unit cost of ingredients and wrappings to be c. These costs are known as variable costs because they vary with the number of hot dogs sold.

Fixed costs do not vary with the number of units produced and sold. Typ- ical fixed costs include start-up costs, licenses, contracting costs, manage- ment overhead, and advertising. Areas within each level of Dodger Sta- dium are designated for concessions and these areas are staffed by food workers—fixed costs F.

Variable costs vary with the number of units produced and sold—they vary with quantity Q, the quantity of hot dogs produced and sold. Then total variable cost is given by cQ. Adding variable and fixed costs gives total cost: cQ + F. Total revenue is unit price p times quantity sold Q, and profit is total revenue minus total cost. Using π to represent profit, we have the formula π = pQ − (cQ − F).

136 Sports Analytics and Data Science

Figure 9.2. Higher Profits Through Increased Sales

$ $

Q Q

R ev

en ue

li ne

p Q

Va ria

bl e

co st

c Q

Fixed cost F

To ta

l c os

t c Q +

F

To ta

l c os

t c Q +

F

QQ1 2Q*

pQ*

No change in cost structure

Increase Sales

The figure for cost-volume-profit analysis, reproduced with shaded areas in figure 9.2, shows fixed costs as a horizontal line. We represent variable costs as a straight line with slope c and vertical intercept zero. And we draw total cost as a straight line parallel to the variable cost line with a vertical intercept F. From the figure, we can see that total costs equal total revenues at the breakeven quantity Q*, with associated breakeven sales pQ*.

To make money on hot dog sales, the team must sell more than Q* Dodger Dogs. If the team sells Q1, its profit will be represented by the lighter shaded area in the figure between the revenue line and the total cost line. One path to higher profits is to increase sales volume from Q1 to Q2. This would add to profits, with the amount added shown by the darker shaded area in figure 9.2.

Two other paths to increased profit, represented in figures 9.3 and 9.4, are to lower fixed costs or to run a more efficient operation. Thinking of Dodger Dog sales, the team could lower fixed costs by using fewer employees or less stadium area for concessions. This would lower the vertical axis inter- cept of both the fixed and total cost lines. Variable costs are affected by unit costs or the ingredients and wrappings that come with each Dodger Dog. Lowering unit variable cost reduces the slope of the variable and total cost lines.

Chapter 9. Managing Finances 137

Figure 9.3. Higher Profits Through Lower Fixed Costs

$ $

Q Q R

ev en

ue li

ne p

Q

Va ria

bl e

co st

c Q

Fixed cost F

To ta

l c os

t c Q +

F

To ta

l c os

t c Q +

F

Q*

pQ*

Lower fixed costs = Lower total cost

Lower total cost = Lower breakeven point

Figure 9.4. Higher Profits Through Increased Efficiency

$ $

Q Q

R ev

en ue

li ne

p Q

Va ria

ble co

st cQ

Fixed cost F

To tal

co st

cQ +

F To

tal co

st cQ

+ F

Q*

pQ*

Increased efficiency = Lower variable cost = Lower total cost

Lower total cost = Lower breakeven point

138 Sports Analytics and Data Science

Cost-volume-profit analysis provides a convenient mechanism for showing three distinct paths to higher profit: (1) increase sales volume, (2) reduce fixed costs, or (3) become more efficient, lowering variable costs. Cost- volume-profit analysis, sometimes referred to as breakeven analysis, as- sumes linear functions for sales revenue and costs. The quantities c and F are given, providing the slope and intercept of the total cost line. There is the quantity p, providing the slope of the revenue line. This implies that a single price p is being charged for each item sold.

Cost-volume-profit analysis is useful in assessing short-term product and service problems in which costs and prices are constant across all items being sold. As we have seen earlier, professional sports teams may use variable or dynamic pricing methods, rather than use a single price p. Fur- thermore, many decisions made by professional sports teams are long-term decisions.

Decisions about stadium upgrades, information systems, and long-term player contracts are investment decisions, affecting a team’s expenses and revenues for many years. We use methods of financial analysis, such as discounted cash flow analysis, to evaluate investment decisions.

Consider the Los Angeles Dodgers’ decision to establish a long-term con- tract with left-handed ace Clayton Kershaw, which made him the highest paid player in professional sports. The term of the contract was seven years at $215 million, with an opt-out after five years. As Knight (2015) points out, with this contract Kershaw joined Michael Jordan as the only American athlete to make an average of at least $30 million a season over a multiyear deal.

For Kershaw to be a good investment for the Dodgers, the team must an- ticipate substantial increases in annual revenues coming from media, ticket sales, sponsorships, and other sources. There is the expectation that Ker- shaw’s presence on the team will generate additional wins, and additional wins are associated with additional revenues. Kershaw’s wins above re- placement player (WARP) was estimated as 3.7, 5.7, and 6.1 across the 2012, 2013, and 2014 seasons (Miller and Wojciechowski 2015). In 2014, with con- tract in hand, Kershaw won both the National League Cy Young award and the National League Most Valuable Player award, the first player to do so since Bob Gibson in 1968.

Chapter 9. Managing Finances 139

Table 9.1. Discounted Cash Flow Analysis of a Player Contract: The Case of Clayton Kershaw

Discounted Year of Cash Out Cash In Cash In-Out Cash In-Out

Contract Season ($ millions) ($ millions) ($ millions) ($ millions)

0 Signing 18 0 -18 -18.000 1 2014 4 30 26 23.636 2 2015 30 31 1 0.826 3 2016 32 32 0 0.000 4 2017 33 33 0 0.000 5 2018 33 34 1 0.621 6 2019 32 35 3 1.693 7 2020 33 36 3 1.539

Net Present Value Cost of Capital (%): 10 after 5 Years: 7.084

after 7 Years: 10.317

Source for Kershaw contract terms: Stephen (2014).

Most businesses evaluate capital investments and their associated annual expenses or costs by discounted cash flow analysis.1 Table 9.1 shows a dis- counted cash flow analysis for the Dodgers’ investment in Clayton Ker- shaw, assuming a 10 percent cost of capital (applied at the end of years for ease of calculation). Cash inflows and outflows are in nominal dollars. These are discounted by the cost of capital in all but the initial year of the in- vestment. The 2014 cash out includes Kershaw’s $18 million signing bonus, which is not discounted, with his $4 million salary, which is discounted. We might imagine that the Dodgers had translated Kershaw’s contribution to wins into dollars of additional revenue. Revenues in table 9.1 are guesses or plugs to make net present values positive.

1 Annual expenses represent cash outflows, and annual revenues represent case inflows. Both flows are discounted for the term of the contract using the cost of capital for the organization. To justify capital investments, the sum of the discounted cash flows must be positive. The sum of the discounted cash flows is called the net present value of the investment. Discounting is used to adjust for the time value of money. Recall the idea that money today is worth more than money in the future. If we want money today, we have to pay for it. What is the price? The price of money is the interest rate or cost of capital. Lenders want to realize a return on the money they lend. Sometimes we adjust for inflation or deflation. Sometimes we adjust for the interest rate. And when a firm evaluates alternative investment projects, it adjusts for its cost of capital, which is a linear combination of interest rate and dividend rate paid to creditors and stockholders, respectively. Let r be the rate we are working with—the discount rate. Then an amount X to be received at the end of N periods has present value Y as follows:

Y = X

(1 + r)N

140 Sports Analytics and Data Science

Discounted cash flow analysis is the foundation of investment analysis. Investment projects should have positive net present value when evalu- ated across their potential lifetimes. When comparing projects, we use net present value, choosing the project with the highest net present value.

When comparing investment projects, some financial managers like to use return on investment (ROI). To compute ROI, we assume knowledge of cash inflows and outflows and compute the discount rate that would yield a net present value of zero. This discount rate corresponds to the ROI. To compare projects on ROI, it is important to ensure that the projects have the same duration or investment horizon.

Some managers like to think in terms of payback period or the length of time it takes for the discounted cash inflows of a project to exceed the discounted cash outflows. It is not a good idea to compare projects on the basis of payback period. It encourages managers to be short-sighted when making investment decisions. Net present value is preferred to ROI and payback period when evaluating investment decisions.

We can use discounted cash flow analysis in assessing the investment value of sports franchises. A potential investor would consider the asking price for a team, anticipated revenues and expenses (thinking of these as cash in- flows and outflows), and an investment horizon. The investor needs to in- clude capital appreciation in the analysis because team values change dra- matically across time.

The Brooklyn Nets were purchased for $365 million in 2010. The franchise was valued at $1.5 billion in January 2015, sixth in the NBA. Gate receipts in 2014 were $64 million, and total revenues were $212 million. But with player salaries at $115 million, the team lost almost $100 million in 2014. The Brooklyn Nets were the only NBA team with an operating income loss in 2014 (Badenhausen, Ozanian, and Settimi 2015a; Forbes 2015).

Investing in the Brooklyn Nets can be analyzed using discounted cash flow analysis. Revenues are likely to rise due to inflation and the possibility of increased ticket prices, but we are unsure about our ability to control costs. We expect capital appreciation, given what we have seen in recent years with NBA teams. Suppose our investment horizon is five years. Discounted cash flow analyses are illustrated in table 9.2.

Chapter 9. Managing Finances 141

Table 9.2. Would you like to buy the Brooklyn Nets?

Outcome A: $2 Billion Sales Price after Five Years, No Cost Control Discounted

Index Season Cash In Cash Out Cash In-Out Cash In-Out of Year or Event ($ millions) ($ millions) ($ millions) ($ millions)

0 Purchase 0 1,500 -1,500 -1,500 1 2015/16 220 320 -100 -95 2 2016/17 230 330 -100 -91 3 2017/18 240 340 -100 -86 4 2018/19 250 350 -100 -82 5 2019/20 260 360 -100 -78 5 Sale 2,000 0 2,000 1,567

Discount Rate (%): 5 Net Present Value -366

Outcome B: $2 Billion Sales Price after Five Years, Cost Control Discounted

Index Season Cash In Cash Out Cash In-Out Cash In-Out of Year or Event ($ millions) ($ millions) ($ millions) ($ millions)

0 Purchase 0 1,500 -1,500 -1,500 1 2015/16 220 250 -30 -29 2 2016/17 230 250 -20 -18 3 2017/18 240 250 -10 -9 4 2018/19 250 250 0 0 5 2019/20 260 250 10 8 5 Sale 2,000 0 2,000 1,567

Discount Rate (%): 5 Net Present Value 20

Outcome C: $2.5 Billion Sales Price after Five Years, Cost Control Discounted

Index Season Cash In Cash Out Cash In-Out Cash In-Out of Year or Event ($ millions) ($ millions) ($ millions) ($ millions)

0 Purchase 0 1,500 -1,500 -1,500 1 2015/16 220 250 -30 -29 2 2016/17 230 250 -20 -18 3 2017/18 240 250 -10 -9 4 2018/19 250 250 0 0 5 2019/20 260 250 10 8 5 Sale 2,500 0 2,500 1,959

Discount Rate (%): 5 Net Present Value 411

142 Sports Analytics and Data Science

We are not sure we want to invest in the Brooklyn Nets. In five years the sales price might be $2 billion. Perhaps there is a bridge in the mix, and the sales price is $2.5 million. Should we invest in the Nets or put our money in the stock market?

Decisions do not lead to perfectly predictable outcomes. We have uncer- tainty about outcomes. As rational decision makers, we can take the net present values across the three outcomes and multiply by their probabili- ties of occurrence. Summing these products, we obtain the expected value of the investment, a probability-weighted combination of net present val- ues.

To continue with the analysis, we compare this expected value of an invest- ment in the Brooklyn Nets with the expected value of an investment in the stock market across the same investment horizon. Decision analysis is a way of dealing with uncertainty. Decision analysis considers decision op- tions, possible outcomes, and probabilities of outcomes. A rational decision maker, economists tell us, will choose the option with the highest expected value. A summary of decision analysis may be displayed in a decision tree, as shown in figure 9.5.

Are sports teams a good investment? We can try to answer this question by reviewing sales prices for professional sports teams over time. In Major League Baseball, for example, sports franchises have been a good invest- ment over the history of the sport, offering higher returns (capital gains) than investments in comparably sized businesses outside of sports. Perfor- mance results have been mixed, however, with selected decades (1970s and 1990s) showing negative or zero returns (Fort 2006).

Fort (2011) presents methods for the valuation of sports franchises. See Weil et al. (2005) for an introduction to accounting principles and Higgins (2015) or Brealey, Myers, and Allen (2013) for discussion of financial anal- ysis methods, including discounted cash flow analysis. Hirshleifer, Glazer, and Hirshleifer (2005) show how discounted cash flow analysis may be un- derstood within the context of economics and the time-value of money. Raiffa (1968) introduces methods of decision analysis which have a wide range of applications in business, public policy and everyday life (Stokey and Zeckhauser 1978; Thaler 1994; Thaler and Sunstein 2009).

Chapter 9. Managing Finances 143

Figure 9.5. Decision Analysis: Investing in a Sports Franchise (Or Not)

Decision: Buy the Brooklyn Nets Probability x Net Present Net Present

Value Value Possible Outcomes ($ millions) Probability ($ millions)

Outcome A: $2 Billion Sale, No Cost Control -366 0.20 -73 Outcome B: $2 Billion Sale, Cost Control 20 0.50 10 Outcome C: $2.5 Billion Sale, Cost Control 411 0.30 123

Expected Value 60

Decision: Invest in the Stock Market Probability x Net Present Net Present

Value Value Possible Outcomes ($ millions) Probability ($ millions)

Market Up: Make $100 Million on $1.5 Billion 100 0.60 60 Market Even (Earnings Rate = Inflation Rate) 0 0.20 0 Market Down: Lose $100 Million on $1.5 Billion -100 0.20 -20

Expected Value 40

Buy Brooklyn Nets

Invest in Stock Market

A: Lose $366 million

B: Gain $20 million

C: Gain $411million

Gain $100 million

Lose $100 million

No Gain or Loss

Outcomes

Expected Values of Choices

Choices

$ 60 million

$ 40 million

P(A) = 0.20

P(B) = 0.50

P(C ) =

0.30

P(Up) = 0.60

P(Even) = 0.20

P(D ow

n) = 0.2

0

144 Sports Analytics and Data Science

Decision analysis shows a way to deal with uncertainty. If we trust our estimates of gains and losses across discrete outcomes and if we trust prob- abilities assigned to those outcomes, we are well on our way to a rational choice. The calculations are easy. What is not so easy is the estimation of gains, losses, and probabilities.

Regarding the estimation of probabilities, there are additional methods and models to employ. Following Bayesian thinking, probability estimation may be carried out in a rational manner, going from prior, subjective prob- ability distributions to posterior distributions. This is another calculation, sometimes easy, sometimes not so easy. Bayesian statistics shows how to measure uncertainty. As we continue to collect data, updating our priors, we become less and less dependent on subjective probability estimates.

As indicated earlier, many sports management decisions can be formulated as constrained optimization problems. We maximize revenues or minimize costs, subject to constraints. With perfect information or precise measures in hand, all would be well. We would input data for parameters and let the programs find an optimal solution. This is the deterministic world of mathematical programming, as reviewed in appendix A (page 200).

But the life of a sports analyst or data scientist is not so easy. Consider the problem posed at the beginning of this chapter—selecting the best combina- tion of players subject to the budgetary constraint of a salary cap. We might simplify the problem by assigning a single contract cost to each player, fix- ing some of the parameters required for mathematical programming or, to be precise, integer programming with binary decision variables. But what should we do about player contributions to the team?

However we measure players’ contributions to a team, those measures have uncertainty. We need a way to deal with that uncertainty. One approach would be to solve the integer programming problem numerous times, each with a different set of values for player contribution.

We could consider three values for player contribution: best value, expected value, and worst value. We run the integer program three times, choosing the optimal combination of players in each run. Then we identify common players across the three solutions, if indeed there are common players. We call this the best case/worst-case approach.

Chapter 9. Managing Finances 145

A similar approach, which we might call the brute-force approach, would draw a single value from each player’s distribution and use that value as input to the model. Each run of the model would have a randomly selected value for each player, fixing the input data for the parameters. We run the integer program thousands of times and count the frequency with which each player is included in the solutions. The brute-force approach is similar to a sensitivity analysis in which we vary input parameters across many runs and see what happens to the solution.

A third approach, stochastic programming, represents mathematical pro- gramming with uncertain input data. Rather than specify parameters as fixed input data, we use probability distributions. For example, we might begin by assuming that a player’s contribution to wins above replacement has an exponential distribution, continuous on the open interval of positive real numbers.

Stochastic programming also gives us a way of specifying player costs with uncertainty. Using stochastic programming, we can obtain a single opti- mal set of players for the team, accounting for uncertainties inherent in the player selection problem.

The rationale for stochastic programming is presented by Conejo, Carrión, and Morales (2010). A mathematical introduction to stochastic program- ming methods is provided by Birge and Louveaux (2011). Gershkov and Moldavanu (2014) develop stochastic programming theory for capacity- constrained dynamic pricing.

Hart, Laird, Watson, and Woodruff (2012), Watson and Woodruff (2012), Sirona (2014), and Hart and Woodruff (2015) review a Python-based al- gebraic modeling system for mathematical and stochastic programming. Algebraic modeling systems allow analysts to construct abstract models, defining parameters prior to providing input data for those parameters. Such systems are most useful in sensitivity testing and stochastic program- ming. And with an open-source, Python-based system, analysts can inter- rogate and manipulate model parameters and their distributions, integrat- ing stochastic programming and Bayesian estimation methods.

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10 Playing What-if Games

Maggie: “Mr. Dunn?” Dunn: “I owe you money?” Maggie: “No, Sir.” Dunn: “I know your Mamma?” Maggie: “I don’t rightly know, Sir.” Dunn: “What do you want?” Maggie: “I was on the other card.

I won my fight, too—Maggie Fitzgerald.” Dunn: “Well, Maggie Fitzgerald, what do you want?” Maggie: “Did you happen to see it?” Dunn: “Nope.” Maggie: “I did pretty good.

Thought you might be interested in training me.” Dunn: “I don’t train girls.” Maggie: “Maybe you should.

People seen me fight say I’m pretty tough.”

—HILARY SWANK AS MAGGIE FITZGERALD, AND CLINT EASTWOOD AS FRANKIE DUNN

IN Million Dollar Baby (2004)

147

148 Sports Analytics and Data Science

Playing what-if games means running simulations. To illustrate the pro- cess, we can use simulations to pick winning teams. Suppose we consider the 2007 baseball season and use selected inter-league games as an example. We note that there are games scheduled between the Mets and Yankees at Yankee Stadium for Friday, Saturday, and Sunday, June 15, 16, and 17, 2007. Just prior to June 15 we ask these questions: How many runs can the Mets be expected to score against the Yankees when playing at Yankee Stadium? How many runs can the Yankees be expected to score? And, consequently, which team is expected to win these three games?

To predict straight-up runs scored in the future, we start with runs scored in the past. We select Mets’ and Yankees’ data for the current season, ignor- ing team statistics from previous seasons and the 2007 preseason. June 15 would be the first meeting of the Mets and Yankees at Yankee Stadium in the regular 2007 season, so we need to use runs scored against other teams. For the Mets, we can select all Mets’ regular season away games between opening day in St. Louis with the Cardinals on May 1 to an away game on June 13 with the Los Angeles Dodgers. And for the Yankees, we can select all Yankees home games prior to June 15, which begin with the home opener with the Devil Rays on April 2 to a home game with the Diamond- backs on June 14.

Table 10.1 provides a complete list of Mets’ games and scores between April 1 and June 15, and table 10.2 provides a complete list of Yankees’ games and scores for the same period. We can see that the Mets have been scoring more runs than their opponents in away games, but fewer in home games. The Yankees, on the other hand, have been scoring more runs than their opponents both home and away.

Overall, Yankees’ games appear to have more scoring than Mets’ games. This is understandable because American League games have a designated hitter. All but three Yankees’ games were played in American League parks. The three games that the Yankees played in a National League park prior to June 15, 2007 happened to be at Shea Stadium against the Mets:

May 18 Yankees 2 Mets 3

May 19 Yankees 7 Mets 10

May 20 Yankees 6 Mets 2

Chapter 10. Playing What-if Games 149

Table 10.1. New York Mets’ Early Season Games in 2007

Away Games (n = 31) Home Games (n = 33)

Runs Scored Runs Scored

Home Home Away Away Date Team Mets Team Date Team Team Mets

4/1/07 STL 6 1 4/9/07 PHI 5 11 4/3/07 STL 4 1 4/11/07 PHI 5 2 4/4/07 STL 10 0 4/12/07 PHI 3 5 4/6/07 ATL 11 1 4/13/07 WSH 2 3 4/7/07 ATL 3 5 4/14/07 WSH 6 2 4/8/07 ATL 2 3 4/20/07 ATL 7 3 4/17/07 PHI 8 1 4/21/07 ATL 2 7 4/18/07 FLA 9 2 4/22/07 ATL 9 6 4/19/07 FLA 11 3 4/23/07 COL 1 6 4/27/07 WSH 3 4 4/24/07 COL 1 2 4/28/07 WSH 6 2 4/25/07 COL 11 5 4/29/07 WSH 1 0 4/30/07 FLA 9 6 5/3/07 ARI 9 4 5/1/07 FLA 5 2 5/4/07 ARI 5 3 5/2/07 FLA 3 6 5/5/07 ARI 6 2 5/11/07 MIL 4 5 5/6/07 ARI 1 3 5/12/07 MIL 12 3 5/7/07 SF 4 9 5/13/07 MIL 1 9 5/8/07 SF 4 1 5/14/07 CHC 4 5 5/9/07 SF 5 3 5/15/07 CHC 10 1 5/22/07 ATL 1 8 5/16/07 CHC 1 8 5/23/07 ATL 3 0 5/17/07 CHC 5 6 5/24/07 ATL 1 2 5/18/07 NYY 2 3 5/25/07 FLA 6 2 5/19/07 NYY 7 10 5/26/07 FLA 7 2 5/20/07 NYY 6 2 5/27/07 FLA 6 4 5/29/07 SF 4 5 6/8/07 DET 3 0 5/30/07 SF 3 0 6/9/07 DET 7 8 5/31/07 SF 2 4 6/10/07 DET 7 15 6/1/07 ARI 5 1 6/11/07 LAD 3 5 6/2/07 ARI 1 7 6/12/07 LAD 1 4 6/3/07 ARI 4 1 6/13/07 LAD 1 9 6/5/07 PHI 4 2

6/6/07 PHI 4 2 6/7/07 PHI 6 3

Average Runs 4.97 3.45 Average Runs 4.67 4.33

150 Sports Analytics and Data Science

Table 10.2. New York Yankees’ Early Season Games in 2007

Away Games (n = 31) Home Games (n = 33)

Runs Scored Runs Scored

Home Home Away Away Date Team Yankees Team Date Team Team Yankees

4/9/07 MIN 8 2 4/2/07 TB 5 9 4/10/07 MIN 10 1 4/5/07 TB 7 6 4/11/07 MIN 1 5 4/6/07 BAL 6 4 4/13/07 OAK 4 5 4/7/07 BAL 7 10 4/14/07 OAK 4 3 4/8/07 BAL 6 4 4/15/07 OAK 4 5 4/17/07 CLE 3 10 4/20/07 BOS 6 7 4/18/07 CLE 2 9 4/21/07 BOS 5 7 4/19/07 CLE 6 8 4/22/07 BOS 6 7 4/26/07 TOR 6 0 4/23/07 TB 8 10 4/27/07 BOS 11 4 4/24/07 TB 4 6 4/28/07 BOS 1 3 5/1/07 TEX 10 1 4/29/07 BOS 7 4 5/3/07 TEX 4 3 5/4/07 SEA 15 11 5/3/07 TEX 5 2 5/5/07 SEA 1 8 5/11/07 SEA 0 3 5/6/07 SEA 0 5 5/12/07 SEA 7 2 5/7/07 SEA 3 2 5/13/07 SEA 1 2 5/8/07 TEX 2 8 5/16/07 CWS 3 5 5/9/07 TEX 2 6 5/16/07 CWS 8 1 5/10/07 TEX 14 2 5/17/07 CWS 1 4 5/21/07 BOS 2 6 5/18/07 NYM 2 3 5/22/07 BOS 7 3 5/19/07 NYM 7 10 5/23/07 BOS 3 8 5/20/07 NYM 6 2 5/25/07 LAA 10 6 5/28/07 TOR 2 7 5/26/07 LAA 3 1 5/29/07 TOR 2 3 5/27/07 LAA 4 3 5/30/07 TOR 10 5 6/8/07 PIT 4 5 6/1/07 BOS 9 5 6/9/07 PIT 3 9 6/2/07 BOS 6 11 6/10/07 PIT 6 13 6/3/07 BOS 6 5 6/12/07 ARI 1 4 6/4/07 CWS 4 6 6/13/07 ARI 2 7 6/5/07 CWS 7 3 6/14/07 ARI 1 7 6/6/07 CWS 5 1 6/7/07 CWS 10 3

Average Runs 5.30 4.39 Average Runs 4.84 5.97

Chapter 10. Playing What-if Games 151

One might be tempted to use the results of these three games to predict the outcome of the games on June 15, 16, and 17. But three games do not provide sufficient data from which to draw trustworthy inferences. Fur- thermore, the upcoming Yankees-Mets games will be played at Yankee Sta- dium with the designated hitter rule in force, a fact that we would like to accommodate (at least in part) through our simulation.

Game-day simulation uses data from real games in the past to generate data about hypothetical games, past and future. Many sports fans are familiar with simulation from fantasy sports. A fantasy baseball game can have Babe Ruth hitting against Bob Gibson or Honus Wagner hitting against Sandy Koufax. Simulations are executed by computer. They utilize base- ball statistics from the history of the game and its players. Randomness is introduced by random number generators, so that playing the same game again and again provides a distinct outcome each time.

Taking the lead from fantasy sports, we can create fantasy games with an objective to estimate the probability that one team will beat another. For ex- ample, suppose we use a simple game-day simulation to pick the winning team in the June Mets-Yankees’ series. Drawing from the away runs-scored distribution of the Mets and the home runs-scored distribution of the Yan- kees on each playing of our fantasy game (each iteration of the simulation), we observe the runs scored by the Mets and the runs scored by the Yan- kees. If tied, we discard the observation. If the Mets’ score is higher than the Yankees’ score, we count a win for the Mets. If the Yankees’ score is higher than the Mets’ score, we count a win for the Yankees. Dividing the number of times the Mets win by the number of times we play the game without a tie provides an estimate of the probability of the Mets winning. Dividing the number of times the Yankees win by the number of times we play the game without a tie gives an estimate of the the probability of the Yankees winning, which is one minus the probability of the Mets winning.

The game-day simulation we are describing is an empirical simulation be- cause it is based on empirical distributions of runs scored by the two teams. The simulation uses only past runs scored and an identification of the Mets and Yankees as the teams. Figure 10.1 illustrates the results of such a simu- lation.

152 Sports Analytics and Data Science

Figure 10.1. Game-day Simulation (Offense Only)

6 4 10 11 3 2 8 9 11 3 6 1 9 5 6 1 4 4 5 1 3 1 6 7 6 3 7 7 3 1 1

9 6 4 10 4 10 9 8 0 4 3 4 11 8 5 2 8 6 2 6 3 8 6 1 3 5 9 13 4 7 7

Runs Scored by Mets Away

Runs Scored by Yankees at HomeFantasy Games

Results from 50,000 fantasy games without ties: 19,945 Mets' wins 0.40 probability of winning 30,055 Yankees' wins 0.60 probability of winning

Yankees Win

Mets Win

Discard Tie

random draw

random draw

random draw

random draw

random draw

random draw

random draw

random draw

random draw

random draw

random draw

random draw

3

6

Yankees Win

1 6

Yankees Win

1 2

6

0

9

Mets Win

11 7

5

Chapter 10. Playing What-if Games 153

We see that one way to pick a winning team is to simulate play between teams. We should not expect too much from this simple game-day simu- lation. Knowing visiting and home teams, where the game is played, and past team scores is only the beginning. Our simulation ignores the fact that the Mets play most of their games in National League parks without a designated hitter and the Yankees play most of their games in American League parks with a designated hitter. Furthermore, this first simulation is focused solely on offense, considering runs scored by each team with no recognition of runs allowed. It gives a picture of offense without defense. Based only on runs scored, the Yankees look like they could beat the Mets.

To get a better picture of how the Mets and Yankees stack up against each other, we juxtapose the teams’ offensive and defensive performance data. For games played at Yankee Stadium, we set the Mets’ away offense against the Yankees’ home defense and the Yankees’ home offense against the Mets away defense. See figure 10.2.

A balanced simulation would consider both offense and defense, as shown in figure 10.3, with offense being runs scored and defense being runs al- lowed (runs scored by the other team). Here we take random drawings from the empirical distributions of runs scored and allowed by opposing teams to estimate expected runs scored by each team. Our approach in this example is to average opposing team offensive and defensive numbers. Taking both offense and defense into consideration, the Mets and Yankees appear to be more evenly matched, with the Mets’ probability of winning 0.52 and the Yankees’ probability of winning 0.48.

What actually happened in these three interleague games? Friday evening, June 15, 2007 the Mets beat the Yankees 2 to 0. The following day the Yan- kees beat the Mets 11 to 8. And on Sunday, June 17, the Yankees won again, beating the Mets 8 to 2.

When working with the number of runs scored (a count), we use probabil- ity distributions such as the Poisson and negative binomial distributions. Using a Poisson distribution to represent runs scored, zero-run games are rare events, especially for teams scoring an average of three or more runs per game.

154 Sports Analytics and Data Science

Figure 10.2. Mets’ Away and Yankees’ Home Data (Offense and Defense)

0 2 4 6 8 10 12 14

Runs Scored

Fr eq

ue nc

y 0

2 4

6 8

Mets' Offense Away Mean = 4.97

(n = 31)

0 2 4 6 8 10 12 14

Runs Allowed

Fr eq

ue nc

y 0

2 4

6 8

Yankees' Defense Home Mean = 4.84

(n = 31)

0 2 4 6 8 10 12 14

Runs Scored

Fr eq

ue nc

y 0

2 4

6 8

Yankees' Offense Home Mean = 5.97

(n = 31)

0 2 4 6 8 10 12 14

Runs Allowed

Fr eq

ue nc

y 0

2 4

6 8

Mets' Defense Away Mean = 3.45

(n = 31)

Data drawn from Mets and Yankees games April 1–June 14, 2007.

Chapter 10. Playing What-if Games 155

Figure 10.3. Balanced Game-day Simulation (Offense and Defense)

Fantasy Games

Results from 50,000 fantasy games without ties: 26,011 Mets' wins 0.52 probability of winning 23,989 Yankees' wins 0.48 probability of winning

random draws 3 61

Offense

Runs Scored by Yankees at Home (Mean = 5.97)

Runs Allowed by Mets Away (Mean = 3.45)

Defense Yankees' Scoring Components

Runs Scored by Mets Away (Mean = 4.97)

Runs Allowed by Yankees at Home (Mean = 4.84)

Offense Defense Mets' Scoring Components

2 Yankees Win

2 4

random draws

7 random draws 3 1

Discard Tie

5 5

random draws

random draws 11 51 3

Mets Win

6 4

random draws

random draws 2 62 0

Yankees Win

2 3

random draws

9

156 Sports Analytics and Data Science

Baseball scores of more than twenty runs are rare events for teams scoring fewer than seven runs a game on average. The Poisson distribution reflects this fact.1

For the 2007 baseball season, taking runs scored across all teams and all games between April 1 and July 8 (prior to the All Star Game), we ob- tain 2,598 observations and an average or mean runs scored of 4.68. The frequency distribution of these runs-scored observations is shown in the upper left-hand panel of figure 10.4. This figure also shows the relative fre- quency distribution and theoretical probabilities for a Poisson distribution with mean 4.68 and for a negative binomial distribution with mean 4.68 and shape parameter 4.00. Notice that for these runs-scored data the neg- ative binomial appears to provide a better fit or match. This is especially apparent at the low end of the distribution.

Mean runs-scored and shape (k = 4) are the defining parameters of a neg- ative binomial probability distribution. The negative binomial distribution represents a good model for runs-scored distributions when the rate or probability of scoring varies from one game to the next, as it would for a group of teams or a team that shows considerable variability in its per- formance across time. The negative binomial distribution has been shown to be useful for modeling scores in various sports (Reep, Pollard, and Ben- jamin 1971; Pollard 1973). Again, we refer to Feller (1968) for probability theory and use the computer to do the work. Using a negative binomial distribution to represent runs scored, shutouts are not so rare as with the Poisson distribution. Higher scores are also more common with the nega- tive binomial than with the Poisson distribution.

1 Keller (1994) showed that the Poisson probability distribution can be used as a model for base- ball scores. The Poisson model works best when the rate or probability of run scoring does not vary substantially from game to game, which might make sense when working with a single team using a stable lineup from day to day. The word Poisson, pronounced “poy san,” refers to Siméon D. Poisson (1781–1840), who published the first derivation of the distribution in 1837. The Poisson probability distribution is given by the formula:

P(x) = e−λ λx

x! where e is the exponential constant and λ (Greek letter lambda) is its one parameter, giving both the mean and variance of the distribution. With no runs scored, the probability is P(0) = e−λ . For one run scored, P(1) = P(0)λ. And generalizing, for x runs scored, P(x) = P(x − 1) λx . Those interested in the mathematics behind probability distributions as well as other topics in probability theory may refer to Feller (1968).

Chapter 10. Playing What-if Games 157

Figure 10.4. Actual and Theoretical Runs-scored Distributions

0 5 10 15 20

0. 00

0. 05

0. 10

0. 15

0. 20

Runs Scored

N eg

at iv

e B

in om

ia l P

ro ba

bi lit

y

Negative Binomial Mean = 4.68 Shape Parameter = 4.00

0 2 4 6 8 10 12 14 16 18 20

Runs Scored

Fr eq

ue nc

y 0

10 0

20 0

30 0

(n = 2,598 observations)

0 5 10 15 20

0. 00

0. 05

0. 10

0. 15

0. 20

Runs Scored

R el

at iv

e Fr

eq ue

nc y

Mean Runs Scored = 4.68

0 5 10 15 20

0. 00

0. 05

0. 10

0. 15

0. 20

Runs Scored

P oi

ss on

P ro

ba bi

lit y

Poisson Mean = 4.68

158 Sports Analytics and Data Science

Another way to execute a game-day simulation is to use theoretical proba- bility distributions. For example, we could simulate Mets-Yankees’ games as paired random drawings from a theoretical probability distribution, with the stipulation that drawings with ties be discarded. That is, we draw ran- dom pairs of observations from the Mets’ away and Yankees’ home distri- butions, executing a balanced simulation of offensive and defensive perfor- mance with probability models for runs scored. We often use the negative binomial distribution to represent runs scored in baseball.2

We show a Poisson model for how the Mets and Yankees stack up against each other in figure 10.5. The corresponding negative binomial model is shown in figure 10.6. With the Poisson model, executing the Mets-Yankees simulation for 50,000 games without ties, we observe the Mets beating the Yankees in 26,863 games, obtaining an estimated probability of 0.54.

Moving away from the Poisson model and using a negative binomial model with shape parameter k set to 4, we observe the Mets beating the Yankees in 26,202 of 50,000 games without ties, obtaining an estimated probability of 0.52. The Poisson estimate is close to the estimate from the balanced empiri- cal runs-scored simulation, and the negative binomial estimate, rounded to two significant digits, is the same as the estimate from the empirical simula- tion. Both simulations predict the Yankees winning about two out of three games.

2 The negative binomial distribution may be thought of as the reverse or flip-side of the binomial. While the binomial distribution gives the number of successes in n trials, the negative binomial gives the number of trials x until we observe some number of success. The negative binomial may be derived as a mixture of Poisson distributions and is sometimes called the compound Poisson distribution. It is defined by two parameters, the mean µ and the shape parameter k. The probability of observing x runs in a game is given by the formula

p(x) = (

1 + µ

k

)−k (k + x − 1)! x!(k − 1)!

( µ u + k

)x For zero runs scored, we obtain a much simpler expression:

p(0) = (

1 + µ

k

)−k The negative binomial distribution is especially useful for working with counts for which the variance is larger than the mean, a situation called overdispersion. The shape or dispersion parameter k may be estimated by comparing the mean and variance of the observed counts. Our research with baseball runs scored suggests that a shape parameter k between 3 and 5 works well for the number of runs scored by a group of major league baseball teams. For the examples in this chapter we set k to 4, which was determined to be a good fit to the actual runs-scored data.

Chapter 10. Playing What-if Games 159

Figure 10.5. Poisson Model for Mets vs. Yankees at Yankee Stadium

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Scored

P ro

ba bi

lit y

Mets' Offense Away Mean = 4.97

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Allowed

P ro

ba bi

lit y

Yankees' Defense Home Mean = 4.84

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Scored

P ro

ba bi

lit y

Yankees' Offense Home Mean = 5.97

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Allowed

P ro

ba bi

lit y

Mets' Defense Away Mean = 3.45

Poisson means estimated from Mets and Yankees games April 1–June 14, 2007.

160 Sports Analytics and Data Science

Figure 10.6. Negative Binomial Model for Mets vs. Yankees at Yankee Stadium

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Scored

P ro

ba bi

lit y

Mets' Offense Away Mean = 4.97

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Allowed

P ro

ba bi

lit y

Yankees' Defense Home Mean = 4.84

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Scored

P ro

ba bi

lit y

Yankees' Offense Home Mean = 5.97

0 5 10 15

0. 00

0. 05

0. 10

0. 15

0. 20

0. 25

Runs Allowed

P ro

ba bi

lit y

Mets' Defense Away Mean = 3.45

Negative binomial means estimated from Mets and Yankees games April 1–June 14, 2007.

The negative binomial shape parameter k set to 4.

Chapter 10. Playing What-if Games 161

When we use game-day simulator to estimate a team’s probability of win- ning, we are employing a model-dependent approach to predictive mod- eling. We generate data from a model and note how well they conform to real or empirical data. The Poisson and negative binomial distributions conform well, so we use them to build models. We can use them to estimate the probability that one team will beat another and to pick a winning team. The simulator is model-dependent, but the inputs to the simulator come from predictive models fit to observed data.

Figure 10.7 shows results from a probability simulator for home and away teams scoring between one and nine runs each, again using a negative bi- nomial probability model with shape parameter k set to 4. This probability heat map is the result of running (9×8)2 or 36 game-day simulations, with each simulation consisting of 100,000 games.

Precise mathematical calculations and well-designed simulations are the easy part of predictive inference in sports. We have algorithms and com- puter programs to do the work. What is not so easy is obtaining the runs- scored estimates for input to the programs.

Do not underestimate the difficulty of predicting which team will win the next game. Predictive analytics is a precarious enterprise. It is a process of extrapolating and forecasting. In sports, it takes a very good model to do a better job than the bookmakers, to win against the spread and cover betting fees in the process. Accurate models for predicting the outcome of sporting events may be elusive. Nonetheless, it is comforting to know that we have a plan for finding accurate models if indeed they do exist.

A game day simulation is a statistical simulation, thinking of the game as a single complete event. It is useful to anyone interested in predicting game outcomes, including coaches, managers, owners, and sports betters. By changing the composition of a team, an owner can influence a team’s scor- ing, a opponent’s scoring, and the outcome of a game. The input to the model and the simulator consists of data for a newly constructed or hypo- thetical team. We predict average runs scored for the teams and run the game-day simulation.

162 Sports Analytics and Data Science

Figure 10.7. Probability of Home Team Winning (Negative Binomial Model)

Visiting Team Runs Expected

H om

e Te

am R

un s

E xp

ec te

d

1

2

3

4

5

6

7

8

9

1 2 3 4 5 6 7 8 9

0.272 0.163 0.104 0.071 0.049 0.035 0.026 0.019

0.727 0.345 0.243 0.176 0.129 0.097 0.075 0.059

0.838 0.656 0.380 0.292 0.225 0.175 0.140 0.113

0.898 0.757 0.620 0.403 0.324 0.260 0.214 0.177

0.931 0.823 0.705 0.597 0.417 0.347 0.291 0.248

0.953 0.870 0.773 0.674 0.582 0.426 0.367 0.315

0.966 0.903 0.822 0.737 0.653 0.572 0.437 0.382

0.974 0.925 0.859 0.786 0.708 0.633 0.562 0.444

0.981 0.941 0.886 0.821 0.752 0.683 0.617 0.556

0.0

0.2

0.4

0.6

0.8

1.0

The negative binomial shape parameter k set to 4.

Chapter 10. Playing What-if Games 163

What we show in Mets/Yankees simulation considers a game as a sin- gle, complete event. Suppose we break a game into its component parts, play-by-play events, model each event individually, and then observe sim- ulated outcomes from a sequence of events. This is the idea behind methods known as discrete event simulation.

Every play in a game has alternative outcomes, setting the stage for the next play. Plays occur in sequence until time runs out in a time-limited game, such as football, basketball, or soccer, or until a winning score is ob- tained in an untimed game, such as baseball or tennis. Games may include overtime periods or extra innings, and tied games are permitted in some circumstances. The contingencies of each game define the structure of the discrete event simulation.

We can think of discrete event simulation as a micro-model. We define the characteristics of players and their interactions with one another. In base- ball, for example, we note possible outcomes when a particular pitcher faces a particular hitter. These outcomes have a multinomial probability distri- bution. For each simulation run, one of those outcomes is observed, setting the stage for the next pitcher/hitter interaction.

Methods of discrete event simulation can be especially useful in providing advice to coaches and managers regarding game-day decisions. Alternative game-day, in-game strategies may be explored by running the simulation thousands of times under each alternative strategy. A coach or manager can observe the range of scoring outcomes and select the outcome that provides the highest probability of winning.

Of course, every coach or manager has an opposing coach or manager equally capable of exploring alternative strategies. As we model this battle of coaching minds, marrying discrete event simulation with the mathemat- ics of game theory, our computer programs take on additional complexity.

With agent-based models, we anticipate the future of sports analytics and data science. Individual players differ from one another in athleticism, playing technique, positioning on the field, and objectives of play as de- fined by managerial in-game strategies. Agent-based models present a po- tentially rich platform for modeling complexity, most useful in exploring alternative in-game strategies.

164 Sports Analytics and Data Science

Figure 10.8. Strategic Modeling Techniques in Sports

Mathematics and Probability Theory

Discrete Event Simulation

Agent-Based Simulation

Prove

Demonstrate

Explore

Known solutions follow from assumptions

Flexible real-world solutions that vary with generated distributions

Predicted outcomes for strategic alternatives

add randomness random number generators for probability distributions

add agents players di�er in athleticism, technique, �eld positioning, and in-game objectives

Chapter 10. Playing What-if Games 165

Figure 10.8 provides an overview of strategic modeling techniques, begin- ning with mathematical models and ending with agent-based models. With mathematical models, known solutions follow from mathematics and prob- ability theory—they are proven to be correct. Mathematical models provide the foundation of in-game strategic analysis as we have seen with run ex- pectancy and state-to-state transition probabilities in baseball.

Discrete event simulations, as demonstrated with the Mets-Yankees exam- ple, compute the likelihood of events by repeatedly sampling from proba- bility distributions. Agent-based modeling builds on discrete event simu- lation. Acknowledging the fact that individual players differ from one an- other in athleticism, playing technique, positioning on the field, and objec- tives of play, we have an opportunity to explore alternative in-game strate- gies and fine-tune those strategies.

Discussions of agent-based models and complexity go hand-in-hand. This is because agent-based models are most useful when the entire system is less well understood than its individual components. So rather than build a complex systems model, we build many small models. Agent-based mod- els also have a role to play when underlying processes are coincidental rather than sequential. This is precisely the type of world we experience in sport with many players moving simultaneously across playing fields.

Simulations and the methods of data science are data-driven rather than expert- or rule-driven. And, being data-driven, we can test their accuracy before we use them to make decisions about players, teams, and sports business marketing or operations.

To move from the academic world into sports—to be viewed as more than a modeler’s playground—agent-based models need to do things that are use- ful and understood by people outside the modeling community. Validation of agent-based models presents challenges. Will it be sufficient to see the simulation acting as an actual game? And how shall we judge the degree of similarity between a simulation and an actual game?

For reading in probability, refer to the Mosteller, Rourke, and Thomas (1970), the classic references of Feller (1968, 1971), and (for fun) a book of problems by Mosteller (1965). A Bayesian perspective is presented by Robert (2007), Albert (2009), and Hoff (2009).

166 Sports Analytics and Data Science

Ross (2014) provides an introduction to probability modeling. Generat- ing probability distributions and simulation programming in R are dis- cussed by Robert and Casella (2009), Suess and Trumbo (2010), Chihara and Hesterberg (2011), Grolemund (2014), and Jones, Maillardet, and Robinson (2014). Law (2014) discusses the domain of simulation modeling, including discrete event simulation and agent-based modeling.

Much work with agent-based models has been biologically inspired, mod- eling the behavior of individual organisms to see what happens in a com- munity (Resnick 1998; Mitchell 2009). For discussion of complexity theory and agent-based modeling, see North and Macal (2007), Miller and Page (2007), and Šalamon (2011).

An R program for the baseball probability simulator is shown in exhibit 10.1. It draws on a graphics package developed by Sarkar (2014). A com- parable Python program is shown in exhibit 10.2

Chapter 10. Playing What-if Games 167

Exhibit 10.1. Team Winning Probabilities by Simulation (R)

# Game-day Simulator for Baseball (R)

library(lattice) # graphics package for probability matrix visual

simulator <- function(home_mean,away_mean,niterations) {

# input runs scored means, output probability of winning for home team

set.seed(1234) # set to obtain reproducible results

away_game_score <- numeric(niterations)

home.game.score <- numeric(niterations)

home_win <- numeric(niterations)

i <- 1

while (i < niterations + 1) {

away_game_score[i] <- rnbinom(1,mu=away_mean, size = 4)

home.game.score[i] <- rnbinom(1,mu=home_mean, size = 4)

if(away_game_score[i] > home.game.score[i]) home_win[i] <- 1

if(away_game_score[i] > home.game.score[i] ||

away_game_score[i] < home.game.score[i]) i <- i + 1

}

n_home_win <- sum(home_win)

n_home_win/niterations # return probability of away team winning

}

niterations <- 100000 # use smaller number for testing

# probability matrix for results... home team is rows, away team is columns

probmat <- matrix(data = NA, nrow = 9, ncol = 9,

dimnames = list(c(as.character(1:9)), c(as.character(1:9))))

for (index_home in 1:9)

for (index_away in 1:9)

if (index_home != index_away) {

probmat[index_home,index_away] <-

simulator(index_home, index_away, niterations)

}

pdf(file = "fig_sports_analytics_prob_matrix.pdf", width = 8.5, height = 8.5)

x <- rep(1:nrow(probmat),times=ncol(probmat))

y <- NULL

for (i in 1:ncol(probmat)) y <- c(y,rep(i,times=nrow(probmat)))

probtext <- sprintf("%0.3f", as.numeric(probmat)) # fixed format 0.XXX

text_data_frame <- data.frame(x, y, probtext)

text_data_frame$probtext <- as.character(text_data_frame$probtext)

text_data_frame$probtext <- ifelse((text_data_frame$probtext == "NA"),

NA,text_data_frame$probtext) # define diagonal cells as missing

text_data_frame <- na.omit(text_data_frame) # diagonal cells

print(levelplot(probmat, cuts = 25, tick.number = 9,

col.regions=colorRampPalette(c("violet", "white", "light blue")),

xlab = "Visiting Team Runs Expected",

ylab = "Home Team Runs Expected",

panel = function(...) {

panel.levelplot(...)

panel.text(text_data_frame$x, text_data_frame$y,

labels = text_data_frame$probtext)

}))

dev.off()

168 Sports Analytics and Data Science

Exhibit 10.2. Team Winning Probabilities by Simulation (Python)

# Game-day Simulator for Baseball (Python)

from __future__ import division, print_function

import numpy as np

from scipy.stats import nbinom

def simulator(home_mean, away_mean, niterations):

# estimates probability of home team win

seed(1234) # set to obtain reproducible results

home_game_score = [0] * niterations

away_game_score = [0] * niterations

home_win = [0] * niterations

i = 0

while (i < niterations):

home_game_score[i] = \

nbinom.rvs(n = 4.0, p = 4.0/(4.0 + home_mean), size = 1)[0]

away_game_score[i] = \

nbinom.rvs(n = 4.0, p = 4.0/(4.0 + away_mean), size = 1)[0]

if (home_game_score[i] > away_game_score[i]):

home_win[i] = 1

if ((away_game_score[i] > home_game_score[i]) or \

(away_game_score[i] < home_game_score[i])):

i = i + 1

n_home_win = sum(home_win)

return n_home_win / niterations

niterations = 100000 # use smaller number for testing

# probability matrix for results... home team rows, away team columns

probmat = array([[0.0] * 9] * 9)

# matrix representation of home and away team runs for table

homemat = array([[9] * 9, [8] * 9, [7] * 9, [6] * 9, [5] * 9,\

[4] * 9, [3] * 9, [2] *9, [1] * 9])

awayrow = array([1, 2, 3, 4, 5, 6, 7, 8, 9])

awaymat = array([awayrow] * 9)

# generate table of probabilities

for index_home in range(9):

for index_away in range(9):

if (homemat[index_home,index_away] != awaymat[index_home,index_away]):

print(index_home, index_away)

probmat[index_home, index_away] = \

simulator(float(homemat[index_home, index_away]), \

float(awaymat[index_home, index_away]), niterations)

print(probmat)

11 Working with Sports Data

Ben: “You know what’s really great about baseball?”

Lindsey: “Hmm?”

Ben: “You can’t fake it. Anything else in life, you don’t have to be great in—business, music, art—I mean, you can get lucky.”

Lindsey: “Really?”

Ben: “Yeah, you can fool everyone for a while, you know. It’s like—not— not baseball. You can either hit a curve ball or you can’t. That’s the way it works, you know?”

Lindsey: “Hmm.”

Ben: “You know, you could have a lucky day, sure, but you can’t have a lucky career. It’s a little like math. It’s orderly. Win or lose, it’s fair. It all adds up. It’s, like, not as confusing or as ambiguous as, uh—” Lindsey: “Life?” Ben: “Yeah, it’s, it’s safe.”

—JIMMY FALLON AS BEN, AND DREW BARRYMORE AS LINDSEY IN Fever Pitch (2005)

169

170 Sports Analytics and Data Science

Information technology has undergone great change in recent years. To- day’s desktop and laptop computers have more power than mainframe computers of the past. Databases and analytics information systems are dis- tributed across many computers in clusters or clouds. We carry the smallest of computers in our pockets. Watches, wearables, and data collection de- vices abound. Microprocessor chips and sensors contribute to the glut of data in what is sometimes called the Internet of Things.

Sports teams have special requirements for working with physiological and athletic performance measurements. There are wearables, including wrist bands, patches, chest straps, and smart watches. Devices can monitor heart rate, body mass, activity levels, and physiological load. These devices may be used for training and lifestyle measurement. And when permitted by professional sports leagues, wearables may be used in games. Collected data, organized as longitudinal observations for each individual player, provide important information for fitness and conditioning staff, trainers, medical personnel, and coaches.

Professional sports leagues are working with commercial firms to collect in-game data relating to player and ball positions on the fields and courts of play. Major League Baseball tracks every pitch and every player on the field at a rate of thirty times per second. There are data for assessing fielding ability, including fielder distance covered, top speed, and route-to-the-ball efficiency. Fielder arm strength is assessed by noting the speed of balls thrown. Stealing bases may be better understood by looking at the distance of a runner’s lead, top running speed, and time to the base being stolen. Batting is being assessed by noting exit velocity from the bat, launch angle, and hang time of balls hit. For pitchers, there are data being collected for position on the rubber, pitch release points, pitch speed, position of the ball within the strike zone, and spin of the ball (Gries 2015).

Commercial firms working with the National Basketball Association offer video and annotated videos, computer-vision-aided observations and in- person observations for all games. Spatial data provide player and ball po- sitions twenty-five times per second. The National Football League is using radio frequency identification (RFID) technology in conjunction with video to track player and ball positions in games. Time-stamped spatial data offer considerable opportunities for spatio-temporal modeling and analysis.

Chapter 11. Working with Sports Data 171

Each professional sports team operates in the public arena. A team needs to know what people are saying about their team, their competitors, and the league. A team wants to know what fans are thinking and saying on talk radio and television. A team wants to follow sports commentators, writers, and analysts. A team wants to see what its players are posting on Twitter, Facebook, and other social media sites. It is difficult for public relations and marketing communications personnel to keep track of the many sources of information and media channels in today’s world of 24/7 communication.

With these many devices and data sources and the networks that connect them, data are flowing into sports teams at unprecedented rates. Profes- sional sports teams are struggling to keep pace. Automated, real-time data collection and analysis are needed.

Today’s world of data science brings together statisticians fluent in R and information technology professionals fluent in Python. These communi- ties have much to learn from each other. For the practicing sports analyst and data scientist, there are considerable advantages to being technically inclined. It pays to be multilingual, with some understanding of R and Python.

Designed by Ross Ihaka and Robert Gentleman, R first appeared in 1993. R provides specialized tools for modeling and data visualization. It rep- resents an extensible, object-oriented, open-source scripting language for programming with data. It is well established in the statistical community and has syntax, data structures, and methods similar to its precursors, S and S-Plus. Contributors to the language have provided more than five thousand packages, most focused on traditional statistics, machine learn- ing, and data visualization. R is the most widely used language in data science, but it is not a general-purpose programming language.

Guido van Rossum, a fan of Monty Python, released version 1.0 of Python in 1994. This general-purpose language has grown in popularity in the en- suing years. Many systems programmers have moved from Perl to Python, and Python has a strong following among mathematicians and scientists. Many universities use Python as a way to introduce basic concepts of object- oriented programming. An active open-source community has contributed more than fifty-seven thousand Python packages.

172 Sports Analytics and Data Science

We benefit from Python’s capabilities as a general-purpose programming language. Sometimes referred to as a “glue language,” Python provides a rich open-source environment for scientific programming and research. For computer-intensive applications, it gives us the ability to call on compiled routines from C, C++, and Fortran. We can also use Cython to convert Python code into optimized C.

Some problems are more easily solved with Python, others with R. For modeling techniques or graphics not currently implemented in Python, we can execute R programs from Python. We draw on R packages for tradi- tional statistics, time series analysis, multivariate methods, statistical graph- ics, and handling missing data. There are times as well when we move beyond Python and R to consider additional programming environments.

Java provides an object-oriented framework for building systems that run on many computer platforms. The Java Virtual Machine makes this possi- ble. But Java is not the best choice for fast development or prototyping— Scala is better suited for that. And Scala can call on routines built on the Java Virtual Machine.

Compiled C and C++ programs may be good performers, but C and C++ are difficult languages in which to program. A new language called Go of- fers the high performance of a compiled language and the programming convenience of a scripting language such as Python or R. The Go language is also well suited for working within a multi-node, multiprocessor envi- ronment or cloud. If we were tasked with building a high-performance agent-based simulation from scratch, for example, we might turn to Go with its support for concurrency.

Technology solutions are best understood in layers—an information tech- nology or software stack. Applications written in R or Python build on lower-level languages and databases, which depend on operating systems and software utilities.

Consider an information hierarchy or stack defining a real-time analytics system. One such system, an open-source system, is Apache Spark, which may be accessed by Python. Spark itself is built on the Scala language, which in turn is built on the Java Virtual Machine. Spark may be im- plemented within various software stacks and works with a number of database and distributed file systems, including Hadoop.

Chapter 11. Working with Sports Data 173

Figure 11.1. Software Stack for a Document Search and Selection System

Linux Operating System, C, C++, and Fortran Compilers, and Apache Software Foundation Utilities

Java Virtual Machine

RPython Apache Lucene

Elasticsearch

Application Programs for Information Retrieval and Analysis

Elasticsearch, an open-source, near-real-time indexing, search, and selec- tion system, is especially useful for finding information in large document collections. Elasticsearch builds on Lucene, which in turn builds on the Java Virtual Machine. It provides its own distributed file system and appli- cation programming interface. As with Spark, Python client programs may be used to interact within the Elasticsearch stack, as shown in figure 11.1.

Data science goes beyond the methods of traditional statistics, incorporat- ing flexible data-adaptive methods. Data science addresses unstructured and semi-structured text as well as numerical data. Data science employs NoSQL document stores as well as spreadsheets and relational databases. And increasingly, data science provides methods for data exploration and discovery that help businesses benefit from large information stores. In a data-intensive, data-driven world, searching and selecting data have be- come as important as sampling.

Gathering and making use of information is what sports analysts and data scientists do every day. They understand information technology as well as statistical modeling. They work with data. They understand databases as well as box scores. They know about object-oriented programming and play-by-play logs.

174 Sports Analytics and Data Science

Figure 11.2. The Information Supply Chain of Professional Team Sports

RESPONDENT SERVICES

RESEARCH TOOLS

EXTERNAL SOURCES

RESEARCH PROVIDER SOURCES

INTERNAL SOURCES

TEAM

Tools for data collection and analysis

Access to samples and panels

Open-source software and systems Technology, services, and tools from application services providers (ASPs), Internet services providers (ISPs), system integrators, and suppliers of statistical and machine learning packages

Player health, fitness, and athletic performance data Data generated through fan and ticket-holder use of team websites, support e-mail and fan groups, as well as data from business transactions

Customized software implementation of team methods and models Analytics information systems, decision support, management reporting Automated and partially automated systems for statistical analysis, data mining, text analytics, and data visualization

Web-browser and Internet access to remote resources

League and commercial sources of game event and performance data Governmental, commercial, and public-domain data sources, including census demographics, business, economic, and financial market data

Public-domain sources from social media Sampling and recruitment services, development and maintenance of panels of research participants, both consumers and business buyers

Database systems and tools for information retrieval

Adapted from Miller (2015a).

Data scientists in professional team sports are knowledge workers and re- searchers. They rely on an information supply chain, as illustrated in figure 11.2. They utilize data sources, both internal and external, in serving the information needs of management, both on the coaching and player perfor- mance side and on the business side.

A big part of the data scientist’s job is finding information from the World Wide Web. The web represents a critical data source for sports teams, as it does for all organizations. The web holds the promise of unlimited information and connection. It is a huge data repository, a path to the world’s knowledge, and the research medium through which we develop new knowledge.

Chapter 11. Working with Sports Data 175

The web’s network foundation, the Internet, grew out of earlier wide-area networks, such as ARPANET and Usenet, serving the defense establish- ment, universities, and technical research centers. ARPANET was initially established for defense purposes, but became a wide-area network for many university researchers as well. Usenet linked many computers together in a simple telephone dial-up mode, permitting e-mail and file transfers. Standards-based networking protocols made Internet communications pos- sible. Lower-level protocols defined how data could be transferred reliably over communication links. Higher-level protocols were developed for com- munication applications, such as telnet for terminal-to-computer communi- cation and ftp for file transfers.

The World Wide Web arose from the marriage of hypertext and network- ing technologies. The idea for the World Wide Web was presented in 1989, while ideas behind hypertext date back to the 1960s. Hypertext—text with links to other text—represented a technology for developing dynamic doc- uments, with the user determining the path between sections of text within documents. Hypertext markup language (HTML), originally designed as a text-only system, references files for graphics, audio, and video as well.

On the World Wide Web, hypertext links include uniform resource locators (URLs), which can refer to remote files and web pages on the network or to local files and web pages on the user’s computer. Extensible markup language (XML) and JavaScript Object Notation (JSON) provide standards for information interchange.

We live in new world of research. Secondary research dominates primary research. Traditional scientific research, with formally stated hypotheses followed by data collection, followed by tests of hypotheses, no longer rules the day. Instead, businesses collect data—mountains of data—often with- out any idea of how they will use those data.

Firms such as Google, Microsoft, and Yahoo! crawl the entire web, building indexes for their search engines. Professional sports teams lack the com- puter resources of Google, Microsoft, and Yahoo!, but they are quite capa- ble of conducting focused crawls to meet particular needs. Sports organiza- tions also have the ability to develop business- and team-focused document stores, gathering data from application programming interfaces (APIs) to social media.

176 Sports Analytics and Data Science

The World Wide Web is a huge data repository that changes with each mo- ment. To address sports business problems, we must find our way to the right links, extracting relevant data, and analyzing them in ways that make sense.

We want data that are meaningful. We want data that are representative of a larger domain or population. And we want data that are relevant to the problem at hand. Finding our way to these data often presents a challenge, but this is an important part of data science.

Web crawling is faster than web surfing. It is automated. A crawler or spider does more than gather data from one web page. Like an actual spider in its web, a World Wide Web crawler or spider traverses links with ease. It follows web links from one web page to another, gathering information from many sources.

A focused crawl has a starting point or points, usually a list of relevant web addresses obtained from initial web surfing. A focused crawl has a stopping point. We can restrict the range of the crawl to named domains, stop the crawl after a specified number of pages have been downloaded, set selection rules for pages being downloaded, and/or limit the total number of pages to be downloaded.

A focused crawl has a defined purpose. We retain those web pages that meet specific criteria. With the crawl well in hand, the task turns to scraping or extracting the specific information we want from web pages. Each web page includes HTML tags, defining a hierarchy of nodes (or tree structure). We call this tree the Document Object Model (DOM). We gather data from the the DOM, such as text within paragraph tags.

Figure 11.3 shows a framework for automated data acquisition on the web that is consistent with Python web crawling and scraping software devel- oped by Hoffman et al. (2014). First we crawl, then we scrape, then we parse. This is the work of web-based secondary research. Next, we select an appropriate wrapping for text and associated metadata, JSON or XML perhaps. We build a document store or text corpus for subsequent analysis.

Chapter 11. Working with Sports Data 177

Figure 11.3. Automated Data Acquisition by Crawling, Scraping, and Parsing

Web data collection and data preparation create a document collection or text corpus for further analysis.

Web

Exporter

Crawler Scraper Parser

Requests Web Pages

Documents

Files

Document Store

178 Sports Analytics and Data Science

Suppose we were working for the commissioner of a major sports league who is concerned about injuries affecting the game. We want to learn as much as we can about the science of health and exercise physiology re- lating to injuries, so we search the web for answers. We want to consult experts in the areas of medicine and sports, so we search the web for con- tacts. Concerned that news about injuries (some career-ending and some with ramifications long after the end of an athlete’s career) affects public opinion about the sport, we review postings to social media. We want to know if rule changes have had the beneficial effect of reducing injuries. We consult various sources regarding this problem, including published stud- ies in medical journals and magazines. Our initial path to these sources is the web.

Crawling and scraping work well for data collection. Modeling and analy- sis begin with data, and the web is a massive store of data. Learning how to extract relevant data in an efficient manner is an essential skill of sports an- alytics and data science. After extracting text data from a web page, we can parse those data using regular expressions. Page formatting codes, unneces- sary spaces, and punctuation can be removed from each document before that document is passed to the next step in text analysis.

Professional sports organizations see opportunities for communicating with fans through social media. Many of a team’s key stakeholders, including high-visibility players, utilize social media, generating short text messages, personal statements, and blog posts.

Social network data sets from Twitter and Facebook are large but accessible. Obtaining these data involves using the various application programming interfaces (APIs) offered by social media providers. We illustrate the pro- cess of obtaining social media data in figure 11.4.

Social media provide two classes of data relevant to professional team sports. First, there are the connections among social media participants, which lead to social network analysis, and then there are the raw data of social media, text and images submitted by participants, which afford opportunities for sentiment analysis or opinion mining.

Chapter 11. Working with Sports Data 179

Figure 11.4. Automated Data Acquisition with an Application Programming Interface (API)

Server

Client

Document Store

Web

Client-side programs interact with server-side applications to obtain data within a defined structure, such as JavaScript Object Notation (JSON).

{“id”: 12345, “longitude”: 33.5339475, “latitude”: -116.7040751, “name”, “Maria”, “source”: “social_media”, “message”: “What’s up?”, “friend”: “Max”, “reply”, false }

Files or databases provide persistent storage of data.

Representational state transfer (REST) data exchange between client and server.

Service provider (Twitter, Facebook, LinkedIn, Google . . . ) makes data available through the API.

Client registers as developer/user of the API, agreeing to follow rules set forth by the service provider.

JSON provides a flexible data interchange format, supporting various data types. It is plain text, simple, concise, and easy to read.There are no mark-up characters.

180 Sports Analytics and Data Science

Figure 11.5. Gathering and Organizing Data for Analysis

Web pages Blogs E-mail Social media Twitter Facebook LinkedIn Google+

Tables Spreadsheets Documents JSON XML Databases Relational NoSQL

Select and search data sources.

Crawl, scrape, and parse data. Utilize APIs.

Unstructured and Semi-structured Data

Structured Data for Analysis

Web

Persistent Storage

How shall we deal with text data from the web and social media? At the very least we need to store them and index them so we can find them. Learning how to find relevant data in an efficient manner is an essential skill, and data collection and preparation can be the most time-consuming aspect of sports analytics and data science. Figure 11.5 provides a summary of the process as it relates to data gathered from the web.

There have always been more data than we have time to analyze. What is new today is the ease of collecting data and the low cost of storing data. Data come from many sources. There are unstructured text data from on- line systems. There are pixels from sensors and cameras. There are data from wearables, mobile phones, tablets, and computers worldwide. Game events are located in space with field-of-play coordinates or geocoded by latitude and longitude and with timestamps showing date and time to the nearest milisecond. We need flexible, scalable, distributed systems to ac- commodate these data.

Chapter 11. Working with Sports Data 181

Doing data science means being able to gather data from the full range of database systems, relational and non-relational, commercial and open source. Relational databases have a row-and-column table structure, simi- lar to a spreadsheet. We access and manipulate these data using structured query language (SQL). Because they are transaction-oriented with enforced data integrity, relational databases provide the foundation for sales order processing and financial accounting systems.

It is easy to understand why non-relational (NoSQL) databases have re- ceived so much attention. Non-relational databases focus on availability and scalability. They may employ key-value, column-oriented, document- oriented, or graph structures.

We employ database query and analysis tools, gathering information across distributed systems, collating information, creating contingency tables, and computing indices of relationship across variables of interest. We use infor- mation technology and database systems as far as they can take us, and then we do more, applying what we know about sports analytics and data science.

We acknowledge an unwritten code in data science. We try to select data that are representative of all data (the population). We do not change data to conform to what we would like to see or expect to see. A two of clubs that destroys the meld is part of the natural variability in the game and must be played with the other cards. We play the hand that is dealt. The hallmarks of science are an appreciation of variability, an understanding of sources of error, and a respect for data. Data science is science.

Raw data are unstructured, messy, and sometimes missing. But to work well in models, data should be organized, clean, and complete. We are often asked to make a model out of a mess. Management needs answers, and the data are replete with miscoded and missing observations, outliers and values of dubious origin. We use our best judgement in preparing data for analysis, recognizing that many decisions we make are subjective and difficult to justify.

Missing data present problems in applied research because many modeling algorithms require complete data sets. With large numbers of explanatory variables, most cases have missing data on at least one of the variables. List- wise deletion of cases with missing data is not an option. Filling in missing

182 Sports Analytics and Data Science

data fields with a single value, such as the mean, median, or mode, would distort the distribution of a variable, as well as its relationship with other variables. Filling in missing data fields with values randomly selected from the data adds noise, making it more difficult to discover relationships with other variables. Multiple imputation is preferred by statisticians.

Doing data science with R means looking for task views posted with the Comprehensive R Archive Network (CRAN). We go to RForge and GitHub. We read package vignettes and papers in The R Journal and the Journal of Statistical Software. The R programming environment consists of more than five thousand packages, many of them focused on modeling methods. Use- ful general references for learning R include Matloff (2011), Lander (2014), and Wickham (2015). Venables and Ripley (2002), although written with S/SPlus in mind, remains a critical reference in the statistical programming community.

Doing data science with Python means gathering programs and documen- tation from GitHub and staying in touch with organizations like PyCon, SciPy and PyData. At the time of this writing, the Python programming environment consists of more than fifty-seven thousand packages. There are large communities of open-source developers working on scientific pro- gramming packages like NumPy, SciPy, and SciKit-Learn. There is the Python Software Foundation, which supports code development and edu- cation. Useful general references for learning Python include Chun (2007), Beazley (2009), Beazley and Jones (2013), Lubanovic (2015), Slatkin (2015), and Sweigart (2015).

Ellis (2015) introduces ideas behind real-time analytics. Spark real-time analytics is discussed by Karau et al. (2015). See Chiusano and Bjarnason (2015) for an overview of Scala and Summerfield (2012) for an introduction to the Go language. Clojure is a modern Lisp-like language that works with the Java Virtual Machine (Fogus and Houser 2014). Scala, Go, and Clojure support concurrency, allowing several computations to execute at the same time, a desirable property for distributed, high-throughput applications. Sports teams need to manage information in ways that allow efficient in- formation retrieval at a later time. This is the task of automated search and document selection. Elasticsearch provides an integrated document stor- age and information retrieval system. To learn more about Elasticsearch,

Chapter 11. Working with Sports Data 183

we can refer to Gheorghe, Hinman, and Russo (2015) and Gromley and Tong (2015). Information retrieval as a general topic is reviewed in Ceri et al. (2013). See Morville and Callender (2010) and Russell-Rose and Tyler- Tate (2013) for guidance regarding the design of search applications.

For the history of the World Wide Web, we can refer to its inventor, Tim Berners-Lee (2000). Further information about today’s web may be ob- tained from the World Wide Web Consortium at www.w3.org. To learn more about crawling and scraping and automated data acquisition from the web, refer to Chakrabarti (2003) and Liu (2011).

Russell (2014) provides Python scripts for accessing social media APIs, and Mitchell (2015) provides Python examples of web crawling and scraping and working with APIs. Nolan and Lang (2014) present R scripts for gath- ering data from the web and working with those data. Miller (2015d) intro- duces web and network data science with Python and R examples.

Garcia-Molina, Ullman, and Widom (2009) and Connolly and Begg (2015) review database systems with a focus on the relational model. Worsley and Drake (2002) and Obe and Hsu (2012) review PostgreSQL. White (2011), Chodorow (2013), and Robinson, Webber, and Eifrem (2013) review selected non-relational systems. Copeland (2013) and Hoberman (2014) provide MongoDB document database examples. Dean and Ghemawat (2004) and Rajaraman and Ullman (2012) discuss map-reduce operations for working with the Hadoop distributed file system.

Osborne (2013) provides an overview of data preparation issues, and the edited volume by McCallum (2013) provides much needed advice about what to do with messy data. Missing data methods are discussed in various sources (Rubin 1987; Little and Rubin 1987; Schafer 1997; Lumley 2010; Sni- jders and Bosker 2012), with methods implemented in R packages from Gel- man et al. (2014), Honaker, King, and Blackwell (2014), and Lumley (2014).

Many organizations are moving from internally-owned, centralized com- puting systems toward cloud-based services. When designing analytics in- formation systems and document stores, flexibility and scalability are key. Distributed file systems and databases are preferred to single-server sys- tems. Systems need to grow with the data. Bahga and Madisetti (2014) use Python examples to illustrate cloud computing. Most server systems utilize the Linux operating system. See Ward (2015) for an overview of Linux.

184 Sports Analytics and Data Science

Open-source software and systems have been the focus throughout this chapter and this book. By using open-source software and systems, pro- fessional sports teams are better able to maintain ownership of their infor- mation technology and to protect their intellectual property. Professional sports teams would be well advised to avoid long-term commitments to commercial suppliers of software and systems. It is best to remain flexible and not to tie an organization into a single analytics platform or database system. Utilize open-source, standards-based systems whenever possible. An added benefit to open-source systems, of course, is that they are less expensive than commercial solutions.

Commercial consulting and support services are available for most popular open-source systems. This is true for database systems like PostgreSQL and MongoDB. It is true for the Elasticsearch document store. As well, there are numerous commercial firms specializing in development and support of software built on Python and R platforms. Going with open-source systems does not mean “going it alone.”

Popular open-source languages and programming environments are also preferred because it is easy to find information technology professionals who already know these languages and environments. When hiring sports analysts and data scientists, teams can look for people who love program- ming and are willing to learn new things. Database systems and analytics technology change quickly, and it is important to keep pace with current developments. Professional sports teams want people who understand data processing software and systems, as well as data analysis methods and models.

One research firm estimated a sports analytics market size of $125 million in 2014, with expected growth to $4.7 billion by 2021 (WinterGreen Research 2015). While seven years is a long forecasting horizon, especially for tech- nology markets, we do expect substantial growth in sports analytics and data science. And growth implies investment in analytics information sys- tems and people.

Discounted cash flow analysis, the basis of investment analysis reviewed in chapter 9, applies equally well to investments in analytics. Analytics projects should have positive net present value when evaluated across their expected lifetimes.

Chapter 11. Working with Sports Data 185

Exhibit 11.1 shows how to crawl and scrape a single website using a Python framework developed by Hoffman et al. (2014) and networking utilities from Lefkowitz et al. (2014). The program executes a focused crawl of www.toutbay.com, a data science services site maintained by the author. The program crawls the entire site, extracting text within paragraph tags and storing results in a plain text file.

The focus of exhibit 11.2 (page 189) is social media data acquisition. Many have expressed concerns about football injuries (Dwyre 2015), so we see what people have been saying about this topic. We utilize the Twitter REST API, drawing on well-documented code examples from Russell (2014). The word “REST” stands for “representational state transfer,” which means that we make requests for data using HTTP operators such as the GET operator. A uniform resource locator (URL) points to the web address for the Twit- ter service. Formatted text data are returned. We can request data down- loads in JSON, a preferred text data interchange format for working on the web. An alternative to the approach taken here would be to use the Twitter Streaming API.1

1 To use programs that access social media data from Twitter, the programmer sets up a personal Twitter account and then obtains user credentials at http://twitter.com/apps/new/. The program- mer employs these user credentials with each request posted to the API. This process applies to both the Twitter REST API and Streaming API. See Russell (2014) and Mitchell (2015) for further discussion of methods for working with Twitter.

186 Sports Analytics and Data Science

Exhibit 11.1. Simple One-Site Web Crawler and Scraper (Python)

# Simple One-Site Web Crawler and Scraper (Python)

#

# prepare for Python version 3x features and functions

from __future__ import division, print_function

# scrapy documentation at http://doc.scrapy.org/

# workspace directory set to outer folder/directory wnds_chapter_3b

# the operating system commands in this example are Mac OS X

import scrapy # object-oriented framework for crawling and scraping

import os # operating system commands

# function for walking and printing directory structure

def list_all(current_directory):

for root, dirs, files in os.walk(current_directory):

level = root.replace(current_directory, ’’).count(os.sep)

indent = ’ ’ * 4 * (level)

print(’{}{}/’.format(indent, os.path.basename(root)))

subindent = ’ ’ * 4 * (level + 1)

for f in files:

print(’{}{}’.format(subindent, f))

# initial directory should have this form (except for items beginning with .):

# sads_exhibit_11_1

# run_one_site_crawler.py

# scrapy.cfg

# scrapy_application/

# __init__.py

# items.py

# pipelines.py

# settings.py

# spiders

# __init__.py

# one_site_crawler.py

# examine the directory structure

current_directory = os.getcwd()

list_all(current_directory)

# list the avaliable spiders, showing names to be used for crawling

os.system(’scrapy list’)

# decide upon the desired format for exporting output: csv, JSON, or XML

# run the scraper exporting results as a JSON text file items.jsonlines

# this file provides text information with linefeeds to provide

# text output that is easily readable in a plain text editor

os.system(’scrapy crawl TOUTBAY -o items.jsonlines’)

Chapter 11. Working with Sports Data 187

# output formats commented out (choose the one needed for further parsing work)

# run the scraper exporting results as a comma-delimited text file items.csv

# os.system(’scrapy crawl TOUTBAY -o items.csv’)

# run the scraper exporting results as a JSON text file items.json

# os.system(’scrapy crawl TOUTBAY -o items.json’)

# run the scraper exporting results as a dictionary XML text file items.xml

# os.system(’scrapy crawl TOUTBAY -o items.xml’)

# ----------------------------

# MyItem class defined by

# items.py

# ----------------------------

# location in directory structure:

# sads_exhibit_11_1/scrapy_application/items.py

# establishes data fields for scraped items

import scrapy # object-oriented framework for crawling and scraping

class MyItem(scrapy.item.Item):

# define the data fields for the item (just one field used here)

paragraph = scrapy.item.Field() # paragraph content

# ----------------------------

# MyPipeline class defined by

# pipelines.py

# ----------------------------

# location in directory structure:

# sads_exhibit_11_1/scrapy_application/pipelines.py

class MyPipeline(object):

def process_item(self, item, spider):

return item

# ----------------------------

# settings for scrapy.cfg

# settings.py

# ----------------------------

# location in directory structure:

# sads_exhibit_11_1/scrapy_application/settings.py

BOT_NAME = ’MyBot’

BOT_VERSION = ’1.0’

SPIDER_MODULES = [’scrapy_application.spiders’]

NEWSPIDER_MODULE = ’scrapy_application.spiders’

USER_AGENT = ’%s/%s’ % (BOT_NAME, BOT_VERSION)

188 Sports Analytics and Data Science

COOKIES_ENABLED = False

DOWNLOAD_DELAY = 2

RETRY_ENABLED = False

DOWNLOAD_TIMEOUT = 15

REDIRECT_ENABLED = False

DEPTH_LIMIT = 50

# ----------------------------

# spider class defined by

# script one_site_crawler.py

# ----------------------------

# location in directory structure:

# sads_exhibit_11_1/scrapy_application/spiders/one_site_crawler.py

# prepare for Python version 3x features and functions

from __future__ import division, print_function

# each spider class gives code for crawing and scraping

import scrapy # object-oriented framework for crawling and scraping

from scrapy_application.items import MyItem # item class

from scrapy.spiders import CrawlSpider, Rule

from scrapy.linkextractors import LinkExtractor

# spider subclass inherits from BaseSpider

# this spider is designed to crawl just one website

class MySpider(CrawlSpider):

name = "TOUTBAY" # unique identifier for the spider

allowed_domains = [’toutbay.com’] # limits the crawl to this domain list

start_urls = [’http://www.toutbay.com’] # first url to crawl in domain

# define the parsing method for the spider

def parse(self, response):

html_scraper = scrapy.selector.HtmlXPathSelector(response)

divs = html_scraper.select(’//div’) # identify all <div> nodes

# XPath syntax to grab all the text in paragraphs in the <div> nodes

results = [] # initialize list

this_item = MyItem() # use this item class

this_item[’paragraph’] = divs.select(’.//p’).extract()

results.append(this_item) # add to the results list

return results

Chapter 11. Working with Sports Data 189

Exhibit 11.2. Gathering Opinion Data from Twitter: Football Injuries (Python)

# Gathering Opinion Data from Twitter: Football Injuries (Python)

# prepare for Python version 3x features and functions

from __future__ import division, print_function

import twitter # work with Twitter APIs

import json # methods for working with JSON data

windows_system = False # set to True if this is a Windows computer

if windows_system:

line_termination = ’\r\n’ # Windows line termination

if (windows_system == False):

line_termination = ’\n’ # Unix/Linus/Mac line termination

# name used for JSON file storage

json_filename = ’my_tweet_file.json’

# name for text file for review of results

full_text_filename = ’my_tweet_review_file.txt’

# name for text from tweets

partial_text_filename = ’my_tweet_text_file.txt’

# See Russell (2014) and Twitter site for documentation

# https://dev.twitter.com/rest/public

# Go to http://twitter.com/apps/new to provide an application name

# to Twitter and to obtain OAuth credentials to obtain API data

# -------------------------------------

# Twitter authorization a la Russell (2014) section 9.1

# Insert credentials in place of the "blah blah blah" strings

# Sample usage of oauth() function

# twitter_api = oauth_login()

def oauth_login():

CONSUMER_KEY = ’blah’

CONSUMER_SECRET = ’blah blah’

OAUTH_TOKEN = ’blah blah blah’

OAUTH_TOKEN_SECRET = ’blah blah blah blah’

auth = twitter.oauth.OAuth(OAUTH_TOKEN, OAUTH_TOKEN_SECRET,

CONSUMER_KEY, CONSUMER_SECRET)

twitter_api = twitter.Twitter(auth=auth)

return twitter_api

# -------------------------------------

# searching the REST API a la Russell (2014) section 9.4

def twitter_search(twitter_api, q, max_results=200, **kw):

# See https://dev.twitter.com/docs/api/1.1/get/search/tweets and

# https://dev.twitter.com/docs/using-search for details on advanced

190 Sports Analytics and Data Science

# search criteria that may be useful for keyword arguments

# See https://dev.twitter.com/docs/api/1.1/get/search/tweets

search_results = twitter_api.search.tweets(q=q, count=100, **kw)

statuses = search_results[’statuses’]

# Iterate through batches of results by following the cursor until we

# reach the desired number of results, keeping in mind that OAuth users

# can "only" make 180 search queries per 15-minute interval. See

# https://dev.twitter.com/docs/rate-limiting/1.1/limits

# for details. A reasonable number of results is ~1000, although

# that number of results may not exist for all queries.

# Enforce a reasonable limit

max_results = min(1000, max_results)

for _ in range(10): # 10*100 = 1000

try:

next_results = search_results[’search_metadata’][’next_results’]

except KeyError, e: # No more results when next_results doesn’t exist

break

# Create a dictionary from next_results, which has the following form:

# ?max_id=313519052523986943&q=NCAA&include_entities=1

kwargs = dict([ kv.split(’=’)

for kv in next_results[1:].split("&") ])

search_results = twitter_api.search.tweets(**kwargs)

statuses += search_results[’statuses’]

if len(statuses) > max_results:

break

return statuses

# -------------------------------------

# use the predefined functions from Russell to conduct the search

# here we see what people are saying about football injuries

twitter_api = oauth_login()

print(twitter_api) # verify the connection

q = "football injuries" # one of many possible search strings

results = twitter_search(twitter_api, q, max_results = 200) # limit to 200 tweets

# examping the results object... should be list of dictionary objects

print(’\n\ntype of results:’, type(results))

print(’\nnumber of results:’, len(results))

print(’\ntype of results elements:’, type(results[0]))

Chapter 11. Working with Sports Data 191

# -------------------------------------

# working with JSON files composed of multiple JSON objects

# results is a list of dictionary items obtained from twitter

# these functions assume that each dictionary item

# is written as a JSON object on a separate line

item_count = 0 # initialize count of objects dumped to file

with open(json_filename, ’w’) as outfile:

for dict_item in results:

json.dump(dict_item, outfile, encoding = ’utf-8’)

item_count = item_count + 1

if item_count < len(results):

outfile.write(line_termination) # new line between items

# -------------------------------------

# working with text file for reviewing multiple JSON objects

# this text file will show the full contents of each tweet

# results is a list of dictionary items obtained from twitter

# these functions assume that each dictionary item

# is written as group of lines printed with indentation

item_count = 0 # initialize count of objects dumped to file

with open(full_text_filename, ’w’) as outfile:

for dict_item in results:

outfile.write(’Item index: ’ + str(item_count) +\

’ -----------------------------------------’ + line_termination)

# indent for pretty printing

outfile.write(json.dumps(dict_item, indent = 4))

item_count = item_count + 1

if item_count < len(results):

outfile.write(line_termination) # new line between items

# -------------------------------------

# working with text file for reviewing text from multiple JSON objects

# this text file will show only the text from each tweet

# results is a list of dictionary items obtained from twitter

# these functions assume that the text of each tweet

# is written to a separate line in the output text file

item_count = 0 # initialize count of objects dumped to file

with open(partial_text_filename, ’w’) as outfile:

for dict_item in results:

outfile.write(json.dumps(dict_item[’text’]))

item_count = item_count + 1

if item_count < len(results):

outfile.write(line_termination) # new line between text items

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12 Competing on Analytics

“. . . in either game, life or football, the margin for error is so small. I mean, one-half a step too late or too early, and you don’t quite make it. One- half second too slow, too fast, and you don’t quite catch it. The inches we need are everywhere around us. They’re in every break of the game, every minute, every second. On this team we fight for that inch.”

—AL PACINO AS COACH TONY D’AMATO IN Any Given Sunday (1999)

An alert runner on second base sees a pitch in the dirt and breaks for third. The ball hits the catcher’s chest protector and bounces a couple feet in front of the catcher. Surprised by the runner’s aggressiveness, the catcher rushes his throw to third, a throw that bounces off the third baseman’s glove and rolls into left field. The throwing error allows the runner to come home, scoring what might be called a manufactured run.

Small differences make all the difference in sports. It may be hard to docu- ment fully the manufactured runs and points attributed to sports analytics. The extra inches in football, assists and blocked shots in basketball, head- ers into soccer goals, or hockey face-offs won or lost by milliseconds—these represent the difference between winning and losing. And small differences justify investments in information technology and data science.

193

194 Sports Analytics and Data Science

While detractors of sports analytics might imagine a dystopian future of data- and analytics-driven sports, most people in the know see higher lev- els of competition resulting from the intelligent use of analytics. Improved measures aid player evaluation. Performance data and models guide player selection and game-day strategies. Medical data and models help players avoid injuries and recover from injuries more quickly. Coaches and man- agers who know what to expect from their decisions make better rosters and player assignments. They make informed choices about player posi- tioning, competitive strategy, and in-game tactics.

Davenport and Harris (2007) used the term “competing on analytics” to describe an emerging ethos in business. In a data-intensive world, a world driven by information technology and communications, it makes sense to use data and models to guide business decisions. Nowhere in their book do Davenport and Harris suggest that models replace decision-makers. Rather their argument is that business managers do a better job of defining strategy and tactics when they are guided by analytics.

Those who would pit the opinions of scouts against the predictions of mod- els are framing the question incorrectly. The question is not, “Should teams use scouts or sports analytics?” Scouts are not going away—they play an essential role in all sports, as do trainers and coaches. The question is, “Will scouts do a better job after being informed by analytics?” And the answer to this question is a resounding yes.

Our work with models and methods shows that sports analytics is more than a matter of defining new metrics. We must think more broadly, con- sidering the extent to which performance measures may be used to make predictions about the future. Predictive inference is at the core of selecting the right players for teams and helping players perform at their best.

We have argued that sports analytics, as it is commonly understood, is not sufficient. Teams are bombarded by data from sporting events and social media. They need to utilize information technology and the tools of data science if they are to remain competitive. To win the game with methods and models, teams need to utilize information systems that serve the needs of the entire organization—players, trainers, coaches, and business man- agers alike. The good news is that information systems designed for sports performance analytics are also applicable to sports management analytics.

Chapter 12. Competing on Analytics 195

General managers who understand the competitive advantage of analyt- ics ensure that analytics information systems are in place to serve the data needs of player health and performance, team management, and business operations. These general managers ensure that there are appropriate staff members to do the work of analytics.

To compete on analytics effectively, to have competitive advantage, pro- fessional sports teams need to do more than hire one or two statisticians or economists. Teams need information technology professionals, database administrators, and data scientists, people who can work with data and program computers. Teams benefit by organizing in ways that promote creativity and learning from data. Decision-making should be informed by data, recognizing the limitations of measures and predictive models.

Doing sports analytics and data science means finding people who under- stand methods and models and can communicate with management. These are people who understand both the performance and management sides of sports.

The number of analysts and data scientists in professional sports will grow in the coming years. Sports is “the winning business,” and sports teams do what they can to win. This means finding the most talented analysts and data scientists as well as the most talented players. It also means paying team members what they are worth.

Each sports team has a playbook to guide game-day decisions. That play- book is team-proprietary, a set of trade secrets shared only among coaches and players on the team. A similar strategy would seem to make sense regarding data science methods and models. Analytics competitive advan- tage emanates from the analysts and data scientists the team is able to hire and retain. Competitive advantage grows with the development of inno- vative methods and models. Recommendations derived from data science methods and models contribute to the team’s playbook.

Front offices may be well advised to let all good ideas in, while keeping many good ideas to themselves. Letting good ideas in means drawing on the literature of data science and using open-source software and systems. Keeping good ideas to themselves means protecting proprietary measure- ments, methods, and models.

196 Sports Analytics and Data Science

It was Thursday, June 18, 2015, and the Los Angeles Dodgers were play- ing an inter-league game with the Texas Rangers. It was a home game at Dodger Stadium with no score in the bottom of the ninth inning.

Rangers’ reliever Keone Kela walked Yasmani Grandal and Andre Ethier to begin the inning. Enrique “Kiki” Hernandez was running for Grandal when Alberto Callaspo grounded into a 3-6-3 double play. “Kiki” went to third on the play. Jimmy Rollins, an excellent bunter with acceptable speed, but batting only 0.198 at the time, came to the plate. Dodgers manager Don Mattingly had many options to consider.

I may be a data scientist, sufficiently informed about event probabilities and expected runs. I may have a good idea of what a manager should call with two outs and a runner on third. But I am also a baseball fan.

On June 18, 2015, what I really wanted was to see “Kiki” Hernandez steal home. Whatever the probability of success, I wanted to be entertained.

As it turned out, a most improbable thing happened. “Kiki” jumped off third, faking a move to home plate. This disturbed the pitcher Kela, who committed a balk. “Kiki” was awarded home, and the Dodgers won the game—it was a walk-off balk (Carr 2015).

Using analytics to provide competitive advantage in no way reduces the ex- citement or joy of sports. Players and teams must still compete in matches and games. They fight for every inch, whether guided by analytics or not. As long as there is sport, there is the challenge, uncertainty, and joy of win- ning. And every once in a great while we see a player take a page from the Jackie Robinson playbook and steal home.

A Data Science Methods

This book is different from other sports analytics books because it views sports analytics in the broader context of data science. Data scientists speak the language of business—accounting, finance, marketing, and manage- ment. They know about information technology, including data structures, algorithms, and object-oriented programming. They understand statistical modeling, machine learning, mathematical programming, and simulation methods. These are the things that data scientists do:

Information search and selection. We begin by reviewing the re- search literature in the field, learning what others have done in the past. Then we search for relevant data sources and select sources for analysis and modeling. Preparing text and data. Text is unstructured or partially structured data that must be prepared for analysis. We extract features from text. We define measures. Quantitative data are often messy or missing. They may require transformation prior to analysis. Data preparation consumes much of a data scientist’s time. Looking at data. We do exploratory data analysis, data visualization for the purpose of discovery. We look for groups in data. We find outliers. We identify common dimensions, patterns, and trends. Predicting how much. We are often asked to predict how many units or dollars of product will be sold, the price of financial securities or real estate. Regression techniques are useful for making these predic- tions.

197

198 Sports Analytics and Data Science

Predicting yes or no. Many business problems are classification prob- lems. We use classification methods to predict whether or not a per- son will buy a product, default on a loan, or access a web page. Testing it out. We examine models with diagnostic graphics. We see how well a model developed on one data set works on other data sets. We employ a training-and-test regimen with data partitioning, cross-validation, or bootstrap methods. Playing what-if. We manipulate key variables to see what happens to our predictions. We play what-if games in simulated marketplaces. We employ sensitivity or stress testing of mathematical programming models. We see how values of input variables affect outcomes, pay- offs, and predictions. We assess uncertainty about forecasts. Explaining it all. Data and models help us understand the world. We turn what we have learned into an explanation that others can understand. We present project results in a clear and concise manner.

Prediction is distinct from explanation. We may not know why models work, but we need to know when they work and when to show others how they work. We identify the most critical components of models and focus on the things that make a difference.1

Data scientists are methodological eclectics, drawing from many scientific disciplines and translating the results of empirical research into words and pictures that management can understand. These presentations benefit from well-constructed data visualizations. In communicating with management, data scientists need to go beyond formulas, numbers, definitions of terms, and the magic of algorithms. Data scientists convert the results of predictive models into simple, straightforward language that others can understand.

Data scientists are knowledge workers par excellence. They are communi- cators playing a critical role in today’s data-intensive world. Data scientists turn data into models and models into plans for action.

The approach we have taken in this and other books in the Modeling Tech- niques series has been to employ both classical and Bayesian methods. And

1 Statisticians distinguish between explanatory and predictive models. Explanatory models are de- signed to test causal theories. Predictive models are designed to predict new or future observations. See Geisser (1993), Breiman (2001), and Shmueli (2010).

Appendix A. Data Science Methods 199

sometimes we dispense with traditional statistics entirely and rely on ma- chine learning algorithms.

Within the statistical literature, Seymour Geisser introduced an approach best described as Bayesian predictive inference (Geisser 1993). In emphasizing the success of predictions in data science, we are in agreement with Geisser. But our approach is purely empirical and in no way dependent on classical or Bayesian thinking. We do what works, following a simple premise:

The value of a model lies in the quality of its predictions.

We learn from statistics that we should quantify our uncertainty. On the one hand, we have confidence intervals, point estimates with associated stan- dard errors, significance tests, and p-values—that is the classical way. On the other hand, we have posterior probability distributions, probability in- tervals, prediction intervals, Bayes factors, and subjective (perhaps diffuse) priors—the path of Bayesian statistics.

The role of data science in business has been discussed by many (Daven- port and Harris 2007; Laursen and Thorlund 2010; Davenport, Harris, and Morison 2010; Franks 2012; Siegel 2013; Maisel and Cokins 2014; Provost and Fawcett 2014). In-depth reviews of methods include those of Izenman (2008), Hastie, Tibshirani, and Friedman (2009), and Murphy (2012).

Doing data science means implementing flexible, scalable, extensible sys- tems for data preparation, analysis, visualization, and modeling. We are empowered by the growth of open source. Whatever the modeling tech- nique or application, there is likely a relevant package, module, or library that someone has written or is thinking of writing. Doing data science with open-source tools is discussed in Conway and White (2012), Putler and Krider (2012), James et al. (2013), Kuhn and Johnson (2013), Lantz (2013), and Ledoiter (2013). Additional discussion of data science, predictive mod- eling techniques, and open-source tools is provided in other books in the Modeling Techniques series (Miller 2015a, 2015b, 2015c, and 2015d).

This appendix provides an overview of data science methods, citing rel- evant sources for further reading. Topics include mathematical program- ming, classical and Bayesian statistics, regression and classification, ma- chine learning, data visualization, text analytics, and time series analysis. The final section shows how data science relates to other disciplines.

200 Sports Analytics and Data Science

A.1 Mathematical Programming

We use the term mathematical programming to refer to problems that involve constrained optimization. The word “programming” in this context means “planning,” as in “resource planning.” It does not mean computer pro- gramming, although we certainly use computer programs to solve con- strained optimization problems. We specify constrained optimization in what is known as standard form. The objective or goal is to maximize the quantity z, which is a sum of n non-negative decision variables xj:

Maximize z = ∑ j

cj xj (j = 1, 2, . . . , n)

subject to ∑ j

aij xj ≤ bi (i = 1, 2, . . . , m)

where xj ≥ 0

There is one and only one objective in this standard form, and the equation is linear in the parameters cj. In standard form, we maximize the objective. But it is easy enough to set minimization as the objective by maximizing the negative of z. Many problems involve minimizing costs, which explains why we use the letter c for the fixed parameters in the objective function. Using standard form, we write less-than-or-equal-to inequality constraints on the decision variables. The form of the m constraint inequalities is linear with fixed parameters aij and bi.

Figure A.1 provides an overview of mathematical programming modeling methods. The nature of the decision variables and the number of con- straints define the type of mathematical programming problem. When all of the decision variables are continuous, we have a linear programming problem. When all of the decision variables are integer, we say we have a pure integer programming problem. And when there is a mixture of contin- uous and integer decision variables, we have a mixed integer programming problem. We sometimes solve integer programming problems by pretend- ing that the decision variables are continuous and using linear program- ming. This provides what is known as “relaxation” of linear programming. Most mathematical programming problems involve many constraints. A knapsack or backpack problem is a special type of integer programming problem involving only one constraint.

Appendix A. Data Science Methods 201

Figure A.1. Mathematical Programming Modeling Methods

Mixed Integer Programming

Linear Programming

Pure Integer Programming

LP Relaxation of Integer Problem

Integer Knapsack Problem

Binary Integer Programming (Multidimensional Knapsack Problem)

Standard Knapsack Problem

all continuous variables all integer variables

all binary variables

only one constraint

only one constraint

all binary variables

integer variables modeled as continuous

Adapted from. Chen, Batson, and Dang (2010).

202 Sports Analytics and Data Science

The solution to a mathematical programming problem is the set of decision variable values xj. Some problems have a single, exact solution, satisfying the objective, and most problems have approximately optimal or very good solutions.

There are myriad applications of mathematical programming in sports. We need to pick players for teams and determine when and where to use play- ers. Choices are subject to constraints such as salary caps, the number of players on a rosters, and the number of players in the lineup. Many prob- lems in sports management analytics involve allocating scarce resources, maximizing revenue, or minimizing costs subject to constraints.

Mathematical programming models are deterministic, with known, fixed parameters in the objective function and constraints. But for practical pur- poses, it is unreasonable to assume that parameters are known and fixed. Nonetheless, here are four ways of using constrained optimization methods when we have uncertainty about cost and constraint parameters:

Guided Decision-Making. Employ mathematical programming as a method for understanding the logic or nature of a decision problem and treat the solution as one of many possible answers to the problem. Best-case/Worst-case Approach. Set best-case and worst-case values for the parameters and obtain multiple solutions. Sensitivity Analysis. Let parameter values vary in a systematic way, and observe the degree to which the solution changes. Stochastic Programming. Estimate probability distributions for the parameters and employ stochastic programming to find solutions.

For an introduction to the mathematics of linear programming, see Hadley (1962), Chvátal (1983), or Walker (2012). Stokey and Zeckhauser (1978) provide a non-mathematical introduction for decision makers. Chen, Bat- son, and Dang (2010) present an overview of mixed integer programming. Bradley, Hax, and Magnanti (1977) and Williams (2013) review business applications of mathematical programming. Wright (2009) reviews appli- cations in sport. Braun and Murdoch (2007) show how to use R to solve linear programming problems. Hart, Laird, Watson, and Woodruff (2012), Sirona (2014), and Hart and Woodruff (2015) review a Python-based alge- braic modeling system for mathematical programming.

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A.2 Classical and Bayesian Statistics

How shall we draw inferences from data? Formal scientific method sug- gests that we construct theories and test those theories with sample data. The process involves drawing statistical inferences as point estimates, in- terval estimates, or tests of hypotheses about the population. Whatever the form of inference, we need sample data relating to questions of interest. For valid use of statistical methods we desire a random sample from the population.

Which statistics do we trust? Statistics are functions of sample data, and we have more faith in statistics when samples are representative of the popula- tion. Large random samples, small standard errors, and narrow confidence intervals are preferred.

Classical and Bayesian statistics represent alternative approaches to infer- ence, alternative ways of measuring uncertainty about the world. Classi- cal hypothesis testing involves making null hypotheses about population parameters and then rejecting or not rejecting those hypotheses based on sample data. Typical null hypotheses (as the word null would imply) state that there is no difference between proportions or group means, or no rela- tionship between variables. Null hypotheses may also refer to parameters in models involving many variables.

To test a null hypothesis, we compute a special statistic called a test statistic along with its associated p-value. Assuming that the null hypothesis is true, we can derive the theoretical distribution of the test statistic. We obtain a p-value by referring the sample test statistic to this theoretical distribution. The p-value, itself a sample statistic, gives the probability of rejecting the null hypothesis under the assumption that it is true.

Let us assume that the conditions for valid inference have been satisfied. Then, when we observe a very low p-value (0.05, 0.01, or 0.001, for in- stance), we know that one of two things must be true: either (1) an event of very low probability has occurred under the assumption that the null hy- pothesis is true or (2) the null hypothesis is false. A low p-value leads us to reject the null hypothesis, and we say the research results are statistically significant. Some results are statistically significant and meaningful. Others are statistically significant and picayune.

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For applied research in the classical tradition, we look for statistics with low p-values. We define null hypotheses as straw men with the intention of rejecting them. When looking for differences between groups, we set up a null hypothesis that there are no differences between groups. In study- ing relationships between variables, we create null hypotheses of indepen- dence between variables and then collect data to reject those hypotheses. When we collect sufficient data, testing procedures have statistical power.

Variability is both our enemy and our friend. It is our enemy when it arises from unexplained sources or from sampling variability—the values of statistics vary from one sample to the next. But variability is also our friend because, without variability, we would be unable to see relationships between variables.2

While the classical approach treats parameters as fixed, unknown quanti- ties to be estimated, the Bayesian approach treats parameters as random variables. In other words, we can think of parameters as having probability distributions representing our uncertainty about the world.

The Bayesian approach takes its name from Bayes’ theorem, a famous the- orem in statistics. In addition to making assumptions about population distributions, random samples, and sampling distributions, we can make assumptions about population parameters. In taking a Bayesian approach, our job is first to express our degree of uncertainty about the world in the form of a probability distribution and then to reduce that uncertainty by collecting relevant sample data.

How do we express our uncertainty about parameters? We specify prior probability distributions for those parameters. Then we use sample data and Bayes’ theorem to derive posterior probability distributions for those same parameters. The Bayesian obtains conditional probability estimates from posterior distributions.

Many argue that Bayesian statistics provides a logically consistent approach to empirical research. Forget the null hypothesis and focus on the research question of interest—the scientific hypothesis. There is no need to talk

2 To see the importance of variability in the discovery of relationships, we can begin with a scatter plot of two variables with a high correlation. Then we restrict the range of one of the variables. More often than not, the resulting scatter plot within the window of the restricted range will exhibit a lower correlation.

Appendix A. Data Science Methods 205

about confidence intervals when we can describe uncertainty with a prob- ability interval. There is no need to make decisions about null hypotheses when we can view all scientific and business problems from a decision- theoretic point of view (Robert 2007). A Bayesian probabilistic perspective can be applied to machine learning and traditional statistical models (Mur- phy 2012).

It may be a challenge to derive mathematical formulas for posterior proba- bility distributions. Indeed, for many research problems, it is impossible to derive formulas for posterior distributions. This does not stop us from us- ing Bayesian methods, however, because computer programs can generate or estimate posterior distributions. Markov chain Monte Carlo simulation is at the heart of Bayesian practice (Tanner 1996; Albert 2009; Robert and Casella 2009; Suess and Trumbo 2010).

Bayesian statistics is alive and well today because it helps us solve real- world problems (McGrayne 2011; Flam 2014). In the popular press, Silver (2012) makes a strong argument for taking a Bayesian approach to predic- tive models. As Efron (1986) points out, however, there are good reasons why everyone is not a Bayesian.

There are many works from which to learn about classical inference (Fisher 1970; Fisher 1971; Snedecor and Cochran 1989; Hinkley, Reid, and Snell 1991; Stuart, Ord, and Arnold 2010; O’Hagan 2010; Wasserman 2010). There are also many good sources for learning about Bayesian methods (Geisser 1993; Gelman, Carlin, Stern, and Rubin 1995; Carlin and Louis 1996; Robert 2007).

When asked if the difference between two groups could have arisen by chance, we might prefer a classical approach. We estimate a p-value as a conditional probability, given a null hypothesis of no difference between the groups. But when asked to estimate the probability that the share price of Apple stock will be above $100 at the beginning of the next calendar year, we may prefer a Bayesian approach. Which is better, classical or Bayesian? It does not matter. We need both. Which is better, Python or R? It does not matter. We need both.

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A.3 Regression and Classification

Much of the work of data science involves a search for meaningful relation- ships between variables. We look for relationships between pairs of contin- uous variables using scatter plots and correlation coefficients. We look for relationships between categorical variables using contingency tables and the methods of categorical data analysis. We use multivariate methods and multi-way contingency tables to examine relationships among many vari- ables. And we build predictive models.

There are two main types of predictive models: regression and classification. Regression is prediction of a response of meaningful magnitude. Classifica- tion involves prediction of a class or category. In the language of machine learning, these are methods of supervised learning.

The most common form of regression is least-squares regression, also called ordinary least-squares regression, linear regression, or multiple regression. When we use ordinary least-squares regression, we estimate regression co- efficients so that they minimize the sum of the squared residuals, where residuals are differences between the observed and predicted response val- ues. For regression problems, we think of the response as taking any value along the real number line, although in practice the response may take a limited number of distinct values. The important thing for regression is that the response values have meaningful magnitude.

Poisson regression is useful for counts. The response has meaningful mag- nitude but takes discrete (whole number) values with a minimum value of zero. Log-linear models for frequencies, grouped frequencies, and contin- gency tables for cross-classified observations fall within this domain.

For models of events, duration, and survival, as in survival analysis, we must often accommodate censoring, in which some observations are measured precisely and others are not. With left censoring, all we know about impre- cisely measured observations is that they are less than some value. With right censoring, all we know about imprecisely measured observations is that they are greater than some value.

A good example of a duration or survival model in marketing is customer lifetime estimation. We know the lifetime or tenure of a customer only after

Appendix A. Data Science Methods 207

that person stops being our customer. For current customers, lifetime is imprecisely measured—it is right censored.

Most traditional modeling techniques involve linear models or linear equa- tions. The response or transformed response is on the left-hand side of the linear model. The linear predictor is on the right-hand side. The linear pre- dictor involves explanatory variables and is linear in its parameters. That is, it involves the addition of coefficients or the multiplication of coefficients by the explanatory variables. The coefficients we fit to linear models repre- sent estimates of population parameters.

Generalized linear models, as their name would imply, are generalizations of the classical linear regression model. They include models for choices and counts, including logistic regression, multinomial logit models, log- linear models, ordinal logistic models, Poisson regression, and survival data models. To introduce the theory behind these important models, we begin by reviewing the classical linear regression model.

We can write the classical linear regression model in matrix notation as

y = Xb + e

y is an n × 1 vector of responses. X is an n × p matrix, with p being the number of parameters being estimated. Often the first column of X is a column of ones for the constant or intercept term in the model; additional columns are for parameters associated with explanatory variables. b is a p × 1 vector of parameter estimates. That is to say that Xb is linear pre- dictor in matrix notation. The error vector e represents independent and identically distributed errors; it is common to assume a Gaussian or normal distribution with mean zero.

The assumptions of the classical linear regression model give rise to clas- sical methods of statistical inference, including tests of regression param- eters and analyses of variance. These methods apply equally well to ob- servational and experimental studies. Parameters in the classical linear re- gression model are estimated by ordinary least squares. There are many variations on the theme, including generalized least squares and a variety of econometric models for time-series regression, panel (longitudinal) data models, and hierarchical models in general. There are also Bayesian alter- natives for most classical models. For now, we focus on classical inference

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and the simplest error structure—independent, identically distributed (iid) errors.

Let y be one element from the response vector, corresponding to one obser- vation from the sample, and let x be its corresponding row from the matrix X. Because the mean or expected value of the errors is zero, we observe that

E[y] = µ = xb

That is, µ, the mean of the response, is equal to the linear predictor. Gener- alized linear models build from this fact. If we were to write in functional notation g(µ) = xb, then, for the Gaussian distribution of classical linear regression, g is the identity function: g(µ) = µ.

Suppose g(µ) were the logit transformation. We would have the logistic regression model:

g(µ) = log (

µ

(1 − µ)

) = xb

Knowing that the exponential function is the inverse of the natural loga- rithm, we solve for µ as

µ = exb

1 + exb

For every observation in the sample, the expected value of the binary re- sponse is a proportion. It represents the probability that one of two events will occur. It has a value between zero and one. In generalized linear model parlance, g is called the link function. It links the mean of the response to the linear predictor.

In most of the choice studies in this book, each observation is a binary re- sponse. Customers choose to stay with their current telephone service or switch to another service. Commuters choose to drive their cars or take the train. Probability theorists think of binary responses as Bernoulli trials with the proportion or probability µ representing the mean of the response. For n observations in a sample, we have mean nµ and variance µ(1−µ)n . The distribution is binomial.3

3 In many statistical treatments of this subject, π, rather than µ is used to represent the mean of the response. We use µ here to provide a consistent symbol across the class of generalized linear models.

Appendix A. Data Science Methods 209

Table A.1. Three Generalized Linear Models

Distribution Link Function Variance Function

Gaussian (normal) µ 1

Poisson log(µ) µ

Binomial log (

µ (1−µ)

) µ(1−µ)

n

Table A.1 provides an overview of the most important generalized linear models for work in business and economics. Classical linear regression has an identity link. Logistic regression uses the logit link. Poisson regression and log-linear models use a log link. We work Gaussian (normal), binomial, and Poisson distributions, which are in the exponential family of distribu- tions. Generalized linear models have linear predictors of the form Xb. This is what makes them linear models—they involve functions of explanatory variables that are linear in their parameters.

Generalized linear models help us model what are obvious nonlinear re- lationships between explanatory variables and responses. Except for the special case of the Gaussian or normal model, which has an identity link, the link function is nonlinear. Also, unlike the normal model, there is often a relationship between the mean and variance of the underlying distribu- tion.

The binomial distribution builds on individual binary responses. Customers order or do not order, respond to a direct marketing mailing or not. Cus- tomers choose to stay with their current telephone service or switch to an- other service. This type of problem lends itself to logistic regression and the use of the logit link. Note that the multinomial logit model is a natu- ral extension of logistic regression. Multinomial logit models are useful in the analysis of multinomial response variables. A customer chooses Coke, Pepsi, or RC Cola. A commuter drives, takes the train or bus, or walks to work.

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When we record choices over a period of time or across a group of indi- viduals, we get counts or frequencies. Counts arranged in multi-way con- tingency tables comprise the raw data of categorical data analysis. We also use the Poisson distribution and the log link for categorical data analysis and log-linear modeling. As we have seen from our discussion of the logit transformation, the log function converts a variable defined on the domain of positive real numbers into a variable defined on the range of all real num- bers. This is why it works for counts.

The Poisson distribution is discrete on the domain of non-negative integers. It is used for modeling counts, as in Poisson regression. The insurance com- pany counts the number of claims over the past year. A retailer counts the number of customers responding to a sales promotion or the number of stock units sold. A nurse counts the number of days a patient stays in the hospital. An auto dealer counts the number of days a car stays on the lot before it sells.

Linear regression is a special generalized linear model. It has normally dis- tributed responses and an identity link relating the expected value of re- sponses to the linear predictor. Linear regression coefficients may be esti- mated by ordinary least squares. For other members of the family of gen- eralized linear models we use maximum likelihood estimation. With the classical linear model we have analysis of variance and F-tests. With gen- eralized linear models we have analysis of deviance and likelihood ratio tests, which are asymptotic chi-square tests.

There are close connections among generalized linear models for the analy- sis of choices and counts. Alternative formulations often yield comparable results. The multinomial model looks at the distribution of counts across response categories with a fixed sum of counts (the sample size). For the Poisson model, counts are random variables, being associated with individ- ual cases, and the sum of counts is not known until observed in the sam- ple. But we can use the Poisson distribution for the analysis of multinomial data. Log-linear models make no explicit distinction between response and explanatory variables. Instead, frequency counts act as responses in the model. But, if we focus on appropriate subsets of linear predictors, treating response variables as distinct from explanatory variables, log-linear mod-

Appendix A. Data Science Methods 211

els yield results comparable to logistic regression. The Poisson distribution and the log link are used for log-linear models.

When communicating with managers, we often use R-squared or the coeffi- cient of determination as an index of goodness of fit. This is a quantity that is easy to explain to management as the proportion of response variance accounted for by the model. An alternative index that many statisticians prefer is the root-mean-square error (RMSE), which is an index of badness or lack of fit. Other indices of badness of fit, such as the percentage error in prediction, are sometimes preferred by managers.

The method of logistic regression, although called “regression,” is actually a classification method. It involves the prediction of a binary response. Or- dinal and multinomial logit models extend logistic regression to problems involving more than two classes. Linear discriminant analysis is another classification method from the domain of traditional statistics. The bench- mark study of text classification in the chapter on sentiment analysis em- ployed logistic regression and a number of machine learning algorithms for classification.

Evaluating classifier performance presents a challenge because many prob- lems are low base rate problems. Fewer than five percent of customers may respond to a direct mail campaign. Disease rates, loan default, and fraud are often low base rate events. When evaluating classifiers in the context of low base rates, we must look beyond the percentage of events correctly predicted. Based on the four-fold table known as the confusion matrix, figure A.2 provides an overview of various indices available for evaluating binary classifiers.

Summary statistics such as Kappa (Cohen 1960) and the area under the re- ceiver operating characteristic (ROC) curve are sometimes used to evaluate classifiers. Kappa depends on the probability cut-off used in classification. The area under the ROC curve does not.

The area under the ROC curve is a preferred index of classification per- formance for low-base-rate problems. The ROC curve is a plot of the true positive rate against the false positive rate. It shows the tradeoff between sensitivity and specificity and measures how well the model separates pos- itive from negative cases.

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Figure A.2. Evaluating the Predictive Accuracy of a Binary Classifier

Predicted Binary Response

Actual Binary Response

YES

YES

NO

NO

True Positive a

False Positive b

False Negative c

True Negative d

a + c aTrue

Positive = Rate

b + d bFalse Positive =

Rate

False Positive Rate

Tr ue

P os

iti ve

R at

e

The true positive rate, also called sensitivity, shows the proportion of positives (YES responses) that are correctly identified as positive. We want this to be high.

The false positive rate shows the proportion of negatives (NO responses) incorrectly identified as positive. We want this to be low.

Nu ll M

od el

Pe rfo

rm an

ce

ROC Curve

Observed predictive accuracy = proportion correctly classified O = (a + d) / (a + b + c + d)

Precision = proportion of positive predictions that are true positives = a / (a + b)

Specificity = true negative rate = proportion of negatives that are correctly classified as negatives = d / (b + d) = 1 - (false positive rate)

Kappa = accuracy relative to accuracy expected by chance = (O - E) / (1 - E)

1

0 0 1

The receiver operating characteristic (ROC) curve shows the performance of a binary classifier across the full range of decision criteria or cutoffs. Perfect performance would correspond to the point (0,1), that is, a false positive rate of 0 and a true positive rate of 1. The area under the curve provides a general index of classification performance.

a + c b + d

a + b

c + d

n = a + b + c + d

Expected accuracy by chance based upon marginal totals E = of the confusion matrix

(a + b)(a + c) + (b + d)(c + d) n2

Confusion Matrix

Appendix A. Data Science Methods 213

The area under the ROC curve provides an index of predictive accuracy independent of the probability cut-off that is being used to classify cases. Perfect prediction corresponds to an area of 1.0 (curve that touches the top- left corner). An area of 0.5 depicts random (null-model) predictive accuracy.

Useful references for linear regression include Draper and Smith (1998), Harrell (2001), Chatterjee and Hadi (2012), and Fox and Weisberg (2011). Data-adaptive regression methods and machine learning algorithms are re- viewed in Berk (2008), Izenman (2008), and Hastie, Tibshirani, and Fried- man (2009). For traditional nonlinear models, see Bates and Watts (2007).

Of special concern to data scientists is the structure of the regression model. Under what conditions should we transform the response or selected ex- planatory variables? Should interaction effects be included in the model? Regression diagnostics are data visualizations and indices we use to check on the adequacy of regression models and to suggest variable transforma- tions. Discussion may be found in Belsley, Kuh, and Welsch (1980) and Cook (1998). The base R system provides many diagnostics, and Fox and Weisberg (2011) provide additional diagnostics. Diagnostics may suggest that transformations of the response or explanatory variables are needed in order to meet model assumptions or improve predictive performance. A theory of power transformations is provided in Box and Cox (1964) and reviewed by Fox and Weisberg (2011).

When defining parametric models, we would like to include the right set of explanatory variables in the right form. Having too few variables or omit- ting key explanatory variables can result in biased predictions. Having too many variables, on the other hand, may lead to over-fitting and high out- of-sample prediction error. This bias-variance tradeoff, as it is sometimes called, is a statistical fact of life.

Shrinkage and regularized regression methods provide mechanisms for tun- ing, smoothing, or adjusting model complexity (Tibshirani 1996; Hoerl and Kennard 2000). Alternatively, we can select subsets of explanatory variables to go into predictive models. Special methods are called into play when the number of parameters being estimated is large, perhaps exceeding the number of observations (Bühlmann and van de Geer 2011). For additional discussion of the bias-variance tradeoff, regularized regression, and subset selection, see Izenman (2008) and Hastie, Tibshirani, and Friedman (2009).

214 Sports Analytics and Data Science

Graybill (1961, 2000) and Rencher and Schaalje (2008) review linear models. Generalized linear models are discussed in McCullagh and Nelder (1989) and Firth (1991). Kutner, Nachtsheim, Neter, and Li (2004) provide a com- prehensive review of linear and generalized linear models, including dis- cussion of their application in experimental design. R methods for the esti- mation of linear and generalized linear models are reviewed in Chambers and Hastie (1992) and Venables and Ripley (2002).

The standard reference for generalized linear models is McCullagh and Nelder (1989). Firth (1991) provides additional review of the underlying theory. Hastie (1992) and Venables and Ripley (2002) give modeling exam- ples with S/SPlus, most which are easily duplicated in R. Lindsey (1997) discusses a wide range of application examples. See Christensen (1997), Le (1998), and Hosmer, Lemeshow, and Sturdivant (2013) for discussion of logistic regression. Lloyd (1999) provides an overview of categorical data analysis. See Fawcett (2003) and Sing et al. (2005) for further discussion of the ROC curve. Discussion of alternative methods for evaluating classifiers is provided in Hand (1997) and Kuhn and Johnson (2013).

For Poisson regression and the analysis of multi-way contingency tables, useful references include Bishop, Fienberg, and Holland (1975), Cameron and Trivedi (1998), Fienberg (2007), Tang, He, and Tu (2012), and Agresti (2013). Reviews of survival data analysis have been provided by Andersen, Borgan, Gill, and Keiding (1993), Le (1997), Therneau and Grambsch (2000), Harrell (2001), Nelson (2003), Hosmer, Lemeshow, and May (2013), and Al- lison (2010), with programming solutions provided by Therneau (2014) and Therneau and Crowson (2014). Wassertheil-Smoller (1990) provides an ele- mentary introduction to classification procedures and the evaluation of bi- nary classifiers. For a more advanced treatment, see Hand (1997). Burnham and Anderson (2002) review model selection methods, particularly those using the Akaike information criterion or AIC (Akaike 1973).

We sometimes consider robust regression methods when there are influen- tial outliers or extreme observations. Robust methods represent an active area of research using statistical simulation tools (Fox 2002; Koller and Sta- hel 2011; Maronna, Martin, and Yohai 2006; Maechler 2014b; Koller 2014). Huet et al. (2004) and Bates and Watts (2007) review nonlinear regression, and Harrell (2001) discusses spline functions for regression problems.

Appendix A. Data Science Methods 215

A.4 Data Mining and Machine Learning

Recommender systems, collaborative filtering, association rules, optimiza- tion methods based on heuristics, as well as a myriad of methods for regres- sion, classification, and clustering fall under the rubric of machine learning.

We use the term “machine learning” to refer to the methods or algorithms that we use as an alternative to traditional statistical methods. When we apply these methods in the analysis of data, we use the term “data mining.” Rajaraman and Ullman (2012) describe data mining as the “discovery of models for data.” Regarding the data themselves, we are often referring to massive data sets.

With traditional statistics, we define the model specification prior to work- ing with the data. With traditional statistics, we often make assumptions about the population distributions from which the data have been drawn. Machine learning, on the other hand, is data-adaptive. The model specifica- tion is defined by applying algorithms to the data. With machine learning, few assumptions are made about the underlying distributions of the data.

Machine learning methods often perform better than traditional linear or logistic regression methods, but explaining why they work is not easy. Ma- chine learning models are sometimes called black box models for a reason. The underlying algorithms can yield thousands of formulas or nodal splits fit to the training data.

Extensive discussion of machine learning algorithms may be found in Duda, Hart, and Stork (2001), Izenman (2008), Hastie, Tibshirani, and Friedman (2009), Kuhn and Johnson (2013), Tan, Steinbach, and Kumar (2006), and Murphy (2012). Bacon (2002) describes their application in marketing.

Hothorn et al. (2005) review principles of benchmark study design, and Schauerhuber et al. (2008) show a benchmark study of classification meth- ods. Alfons (2014a) provides cross-validation tools for benchmark studies. Benchmark studies, also known as statistical simulations or statistical ex- periments, may be conducted with programming packages designed for this type of research (Alfons 2014b; Alfons, Templ, and Filzmoser 2014).

Duda, Hart, and Stork (2001), Tan, Steinbach, and Kumar (2006), Hastie, Tibshirani, and Friedman (2009), and Rajaraman and Ullman (2012) in- troduce clustering from a machine learning perspective. Everitt, Landau,

216 Sports Analytics and Data Science

Leese, and Stahl (2011), Kaufman and Rousseeuw (1990) review traditional clustering methods. Izenman (2008) provides a review of traditional clus- tering, self-organizing maps, fuzzy clustering, model-based clustering, and biclustering (block clustering).

Within the machine learning literature, cluster analysis is referred to as un- supervised learning to distinguish it from classification, which is supervised learning, guided by known, coded values of a response variable or class. Association rules modeling, frequent itemsets, social network analysis, link analysis, recommender systems, and many multivariate methods as we em- ploy them in data science represent unsupervised learning methods.

An important multivariate method, principal component analysis, draws on linear algebra and gives us a way to reduce the number of measures or quantitative features we use to describe domains of interest. Long a staple of measurement experts and a prerequisite of factor analysis, principal com- ponent analysis has seen recent applications in latent semantic analysis, a technology for identifying important topics across a document corpus (Blei, Ng, and Jordan 2003; Murphy 2012; Ingersoll, Morton, and Farris 2013).

When some observations in the training set have coded responses and oth- ers do not, we employ a semi-supervised learning approach. The set of coded observations for the supervised component can be small relative to the set of uncoded observations for the unsupervised component (Liu 2011).

Leisch and Gruen (2014) describe programming packages for various clus- tering algorithms. Methods developed by Kaufman and Rousseeuw (1990) have been implemented in R programs by Maechler (2014a), including sil- houette modeling and visualization techniques for determining the number of clusters. Silhouettes were introduced by Rousseeuw (1987), with addi- tional documentation and examples provided in Kaufman and Rousseeuw (1990) and Izenman (2008).

Thinking more broadly about machine learning, we see it as a subfield of artificial intelligence (Luger 2008; Russell and Norvig 2009). Machine learn- ing encompasses biologically-inspired methods, genetic algorithms, and heuristics, which may be used to address complex optimization, schedul- ing, and systems design problems. (Mitchell 1996; Engelbrecht 2007; Micha- lawicz and Fogel 2004; Brownlee 2011).

Appendix A. Data Science Methods 217

A.5 Text and Sentiment Analysis

Text analytics draws from a variety of disciplines, including linguistics, communication and language arts, experimental psychology, political dis- course analysis, journalism, computer science, and statistics. And, given the amount of text being gathered and stored by organizations, text analyt- ics is an important and growing area of predictive analytics.

We have discussed web crawling, scraping, and parsing. The output from these processes is a document collection or text corpus. This document collection or corpus is in the natural language. The two primary ways of analyzing a text corpus are the bag of words approach and natural language processing. We parse the corpus further, creating commonly formatted ex- pressions, indices, keys, and matrices that are more easily analyzed by com- puter. This additional parsing is sometimes referred to as text annotation. We extract features from the text and then use those features in subsequent analyses.

Natural language is what we speak and write every day. Natural language processing is more than a matter of collecting individual words. Natural language conveys meaning. Natural language documents contain para- graphs, paragraphs contain sentences, and sentences contain words. There are grammatical rules, with many ways to convey the same idea, along with exceptions to rules and rules about exceptions. Words used in combination and the rules of grammar comprise the linguistic foundations of text ana- lytics as shown in figure A.3.

Linguists study natural language, the words and the rules that we use to form meaningful utterances. “Generative grammar” is a general term for the rules; “morphology,” “syntax,” and “semantics” are more specific terms. Computer programs for natural language processing use linguistic rules to mimic human communication and convert natural language into structured text for further analysis.

Natural language processing is a broad area of academic study itself, and an important area of computational linguistics. The location of words in sen- tences is a key to understanding text. Words follow a sequence, with earlier words often more important than later words, and with early sentences and paragraphs often more important than later sentences and paragraphs.

218 Sports Analytics and Data Science

Figure A.3. Linguistic Foundations of Text Analytics

Lexicon (words, regular and irregular forms)

Phonology (rules for sounds)

Morphology (rules for forming complex words)

Syntax (rules for forming phrases, sentences)

Semantics (meanings expressed through language)

Voice, Hearing, Gestures (speaking, listening, communicating)

Brain, Mind (thoughts, beliefs, desires)

Pragmatics (rules for language use in context)

Source: Adapted from Pinker (1999).

Appendix A. Data Science Methods 219

Words in the title of a document are especially important to understanding the meaning of a document. Some words occur with high frequency and help to define the meaning of a document. Other words, such as the defi- nite article “the” and the indefinite articles “a” and “an,” as well as many prepositions and pronouns, occur with high frequency but have little to do with the meaning of a document. These stop words are dropped from the analysis.

The features or attributes of text are often associated with terms—collections of words that mean something special. There are collections of words relat- ing to the same concept or word stem. The words “marketer,” “marketeer,” and “marketing” build on the common word stem “market.” There are syntactic structures to consider, such as adjectives followed by nouns and nouns followed by nouns. Most important to text analytics are sequences of words that form terms. The words “New” and “York” have special mean- ing when combined to form the term “New York.” The words “financial” and “analysis” have special meaning when combined to form the term “fi- nancial analysis.” We often employ stemming, which is the identification of word stems, dropping suffixes (and sometimes prefixes) from words. More generally, we are parsing natural language text to arrive at structured text.

In English, it is customary to place the subject before the verb and the object after the verb. In English, verb tense is important. The sentence “Daniel carries the Apple computer,” can have the same meaning as the sentence “The Apple computer is carried by Daniel.” “Apple computer,” the object of the active verb “carry” is the subject of the passive verb “is carried.” Understanding that the two sentences mean the same thing is an important part of building intelligent text applications.

A key step in text analysis is the creation of a terms-by-documents matrix (sometimes called a lexical table). The rows of this data matrix correspond to words or word stems from the document collection, and the columns cor- respond to documents in the collection. The entry in each cell of a terms-by- documents matrix could be a binary indicator for the presence or absence of a term in a document, a frequency count of the number of times a term is used in a document, or a weighted frequency indicating the importance of a term in a document.

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Figure A.4 illustrates the process of creating a terms-by-documents matrix. The first document comes from Steven Pinker’s Words and Rules (1999, p. 4), the second from Richard K. Belew’s Finding Out About (2000, p. 73). Terms correspond to words or word stems that appear in the documents. In this example, each matrix entry represents the number of times a term appears in a document. We treat nouns, verbs, and adjectives similarly in the defini- tion of stems. The stem “combine” represents both the verb “combine” and the noun “combination.” Likewise, “function” represents the verb, noun, and adjective form “functional.” An alternative system might distinguish among parts of speech, permitting more sophisticated syntactic searches across documents. After being created, the terms-by-documents matrix is like an index, a mapping of document identifiers to terms (keywords or stems) and vice versa. For information retrieval systems or search engines we might also retain information regarding the specific location of terms within documents.

Typical text analytics applications have many more terms than documents, resulting in sparse rectangular terms-by-documents matrices. To obtain meaningful results for text analytics applications, analysts examine the dis- tribution of terms across the document collection. Very low frequency terms, those used in few documents, are dropped from the terms-by-documents matrix, reducing the number of rows in the matrix.

Unsupervised text analytics problems are those for which there is no re- sponse or class to be predicted. Rather, the task is to identify common pat- terns or trends in the data. As part of the task, we may define text measures describing the documents in the corpus.

A fundamental unsupervised application of text analytics is information re- trieval. Text documents are indexed, making them searchable. A popular search algorithm depends on term frequency-inverse document frequency (TF-IDF) measurement. We note the frequency of terms in each document, relative to the frequency of those terms across the entire document collec- tion. A vector of TF-IDF values represents each document. A user searching for information enters a text query, which is itself a document represented by a TF-IDF vector. Each document in the collection is matched to the query, obtaining a relevance score. The result is a ranked list of search results.

Appendix A. Data Science Methods 221

Figure A.4. Creating a Terms-by-Documents Matrix

People do not just blurt out isolated words, but rather combine them into phrases and sentences, in which the meaning of the combination can be inferred from the meanings of words and the way they are arranged. We talk not merely of roses, but of the red rose, proud rose, sad rose of all my days. We can express our feelings about bread and roses, guns and roses, the War of Roses, or days of wine and roses. We can say that lovely is the rose, roses are red, or a rose is a rose is a rose When we combine words, their arrangement is crucial: Violets are red, roses are blue, though containing all the ingredients of the familiar verse, means something very different.

The most frequently occurring words are not really about anything. Words like NOT, OF, THE, OR, TO, BUT, and BE obviously play an important functional role, as part of the syntactic structure of sentences, but it is hard to imagine users asking for documents about OF or about BUT. Define function words to be those that have only a syntactic function, for example, OF, THE, BUT, and distinguish them from content words, which are descriptive in the sense that we're interested in them for the indexing task.

Document

Term 3 0combine

0 1document

0 3function

3 0mean

14 0rose

1 1sentence

3 4word

Pinker (1999)

Pin ke

r ( 19

99 )

Belew (2000)

Be lew

(2 00

0)

Source: Adapted from Miller (2005).

222 Sports Analytics and Data Science

For supervised text analytics problems, there is a response or class of doc- uments to be predicted. We build a model on a training set and test it on a test set. Text classification problems are common. Spam filtering has long been a subject of interest as a classification problem, and many e-mail users have benefitted from the efficient algorithms that have evolved in this area. In the context of information retrieval, search engines classify documents as being relevant to the search or not. Useful modeling techniques for text classification include logistic regression, linear discriminant function anal- ysis, classification trees, and support vector machines. Various ensemble or committee methods may be employed.

Automatic text summarization is an area of research and development that can help with information management. Imagine a text processing program with the ability to read each document in a collection and summarize it in a sentence or two, perhaps quoting from the document itself. Today’s search engines are providing partial analysis of documents prior to their being displayed. They create automated summaries for fast information retrieval. They recognize common text strings associated with user requests. These applications of text analysis comprise tools of information search that we take for granted as part of our daily lives.

Programs with syntactic processing capabilities, such as IBM’s Watson, pro- vide a glimpse of what intelligent agents for text analytics are becoming. These programs perform grammatical parsing with an understanding of the roles of subject, verb, object, and modifier. They know parts of speech (nouns, verbs, adjective, adverbs). And, using identified entities represent- ing people, places, things, and organizations, they perform relationship searches.

Sentiment analysis is measurement-focused text analysis. Sometimes called opinion mining, one approach to sentiment analysis is to draw on positive and negative word sets (lexicons, dictionaries) that convey human emotion or feeling. These word sets are specific to the language being spoken and the context of application. Another approach to sentiment analysis is to work directly with text samples and human ratings of those samples, de- veloping text scoring methods specific to the task at hand.

A semi-supervised machine learning regimen can be especially useful in sentiment analysis. We work two sets of text samples. One sample, often

Appendix A. Data Science Methods 223

a small sample (because it is expensive and time-consuming to obtain hu- man ratings of text), associates a rating or score with each text document. Another much larger sample is unrated but comes from the same content domain. We learn the direction of scoring from the first sample, and we learn about the text domain (including term frequencies in context) from both samples.

The objective of sentiment analysis is to score text for affect, feelings, at- titudes, or opinions. Sentiment analysis and text measurement in gen- eral hold promise as technologies for understanding consumer opinion and markets. Just as political researchers can learn from the words of the pub- lic, press, and politicians, business researchers can learn from the words of customers and competitors. There are customer service logs, telephone transcripts, and sales call reports, along with user group, listserv, and blog postings. And we have ubiquitous social media from which to build docu- ment collections for text and sentiment analysis.

Precursors to sentiment analysis may be found in content analysis, the- matic, semantic, and network text analysis (Roberts 1997; Popping 2000; West 2001; Leetaru 2011; Krippendorff 2012). These methods have seen a wide range of applications within the social sciences, including analysis of political discourse. An early computer implementation of content analy- sis is found in the General Inquirer program (Stone et al. 1966; Stone 1997). Buvac̆ and Stone (2001) describe a version of the program that provides text measures based on word counts across numerous semantic categories.

Text measures flow from a measurement model (algorithms for scoring) and a dictionary, both defined by the researcher or analyst. A dictionary in this context is not a traditional dictionary; it is not an alphabetized list of words and their definitions. Rather, the dictionary used to construct text measures is a repository of word lists, such as synonyms and antonyms, positive and negative words, strong and weak sounding words, bipolar adjectives, parts of speech, and so on. The lists come from expert judgments about the meaning of words. A text measure assigns numbers to documents according to rules, with the rules being defined by the word lists, scoring algorithms, and modeling techniques in predictive analytics.

Sentiment analysis and text measurement in general hold promise as tech- nologies for understanding consumer opinion and markets. Just as political

224 Sports Analytics and Data Science

researchers can learn from the words of politicians, the press, and the pub- lic, data scientists can learn from the words of customers and competitors. For the data scientist interested in understanding consumer opinions about brands and products, there are substantial sources from which to draw sam- ples. We have customer service logs, telephone transcripts, and sales call reports, along with user group, listserv, and blog postings. And we have ubiquitous social media from which to build document collections for text and sentiment analysis.

The measurement story behind opinion and sentiment analysis is an impor- tant story that needs to be told. Sentiment analysis, like all measurement, is the assignment of numbers to attributes according to rules. But what do the numbers mean? To what extent are text measures reliable or valid? Face validity (or content validity) involves showing that the content of the text measure relates to the attribute being measured. We examine word sets, and we try to gain agreement (among subject matter experts, perhaps) that they measure a particular attribute or trait. Sentiment research often involves testing word sets within specific contexts and, when possible, test- ing against external criteria. To demonstrate predictive validity, we show that a text measure can be used for prediction.

Numerous studies have demonstrated the utility of Twitter-based measures in predictive models. Some researchers have predicted the success of movies prior to their being distributed to theaters nationwide (Sharda and Delen 2006; Delen, Sharda, and Kumar 2007). Most telling is work completed at HP Labs that used Twitter chat as a predictor of movie revenues (Asur and Huberman 2010). Bollen, Mao, and Zeng (2011) predicted stock market movements from Twitter sentiment measures. Taddy’s (2013b, 2014) senti- ment analysis work built on the inverse regression methods of Cook (1998, 2007). Taddy (2013a) also used Twitter data to examine political sentiment.

Some have voiced concerns about unidimensional measures of sentiment. There have been attempts to develop more extensive sentiment word sets, as well as multidimensional measures (Turney 2002; Asur and Huberman 2010). Recent developments in machine learning and quantitative linguis- tics point to sentiment measurement methods that employ natural language processing rather than relying on positive and negative word sets (Socher et al. 2011). Among the more popular measurement schemes from the psycho-

Appendix A. Data Science Methods 225

metric literature is Charles Osgood’s semantic differential (Osgood, Suci, and Tannenbaum 1957; Osgood 1962). Exemplary bipolar dimensions in- clude the positive–negative, strong–weak, and active–passive dimensions. Schemes like Osgood’s set the stage for multidimensional measures of sen- timent. We expect sentiment analysis to be an active area of research for many years. Reviews of sentiment analysis methods have been provided by Liu (2010, 2011, 2012) and Feldman (2013). Other books in the Modeling Techniques series provide examples of sentiment analysis using document collections of movie reviews Miller (2015c, 2015b, 2015d).

Ingersoll, Morton, and Farris (2013) give an introduction to the domain of text analytics for the working data scientist. Those interested in reading further can refer to Feldman and Sanger (2007), Jurafsky and Martin (2009), Weiss, Indurkhya, and Zhang (2010), and the edited volume by Srivastava and Sahami (2009).

Salton, Wong, and Yang (1975), Belew (2000), Meadow, Boyce, and Kraft (2000), and Baeza-Yates and Ribeiro-Neto (2011) review document indexing and search theory. Open-source search solutions include Elasticsearch and Solr, which build on Apache Lucene. Gromley and Tong (2015) introduce the Elasticsearch implementation of indexing and search.

Hausser (2001) gives an account of generative grammar and computational linguistics. Statistical language learning and natural language processing are discussed by Charniak (1993), Manning and Schütze (1999), and In- durkhya and Damerau (2010). Many of Steven Pinker’s works (1994, 1997, 1999) provide insight into grammar and psycholinguistics. Maybury (1997) reviews data preparation for text analytics and the related tasks of source detection, translation and conversion, information extraction, and informa- tion exploitation.

Authorship identification, a problem addressed a number of years ago in the statistical literature by Mosteller and Wallace (1984), continues to be an active area of research (Joula 2008). Merkl (2002) provides discussion of clustering techniques, which explore similarities between documents and the grouping of documents into classes. Dumais (2004) reviews latent se- mantic analysis and statistical approaches to extracting relationships among terms in a document collection.

226 Sports Analytics and Data Science

A.6 Time Series, Sales Forecasting, and Market Response Models

Sales forecasts are a critical component of business planning and a first step in the budgeting process. Models and methods that provide accurate fore- casts can greatly benefit management. They help managers understand what determines sales, including promotions, pricing, advertising, and dis- tribution. They reveal competitive position and market share.

There are many approaches to forecasting. Some rely on expert opinions or consensus. There are top-down and bottom-up forecasts, and various techniques for combining expert opinions. Other approaches depend on the analysis of past sales data.

A sales forecasting model can and should be organized by time periods useful to management. These may be days, weeks, months, or whatever intervals make sense for the problem at hand. Time dependencies can be noted in the same manner as in traditional time-series models. Autoregres- sive terms are useful in many contexts. Time-construed covariates, such as day of the week or month of the year, may be added to provide additional predictive power. And we may include promotion, pricing, and advertising variables organized in time.

An analyst can work with time series data, using past sales to predict fu- ture sales, noting overall trends and cyclical patterns in the data. Exponen- tial smoothing, moving averages, and various regression and econometric methods may be used with time series data.

Forecasting by location provides detail needed for management action. And organizing data by location contributes to a model’s predictive power. Lo- cation may itself be used as a factor in models. In addition, we can search for explanatory variables tied to location. With geographic regions, for ex- ample, we might include consumer and business demographic variables known to relate to sales.

Sales dollars per time period is the typical response variable of interest in sales forecasting studies. Alternative response variables include sales vol- ume and time-to-sale. Related studies of market share require information about other firms’ sales in the same product category.

Forecasting is a large application area deserving its own professional con- ferences and journals. An overview of business forecasting methods is pro-

Appendix A. Data Science Methods 227

vided by Armstrong (2001). Time-series, financial, and econometric mod- eling methods are especially relevant to this application area (Judge et al. 1985; Hamilton 1994; Zivot and Wang 2003).

Longitudinal data analysis or panel data analysis is an example of a hier- archical, multi-level, or mixed data method with data organized by cross- sectional units and time. Frees and Miller (2004) describe a sales forecasting method that utilizes a mixed data modeling approach, working with sales data organized by time and location.

Autoregressive integrated moving average (ARIMA) models or what are often called Box-Jenkins models (Box, Jenkins, and Reinsel 2008) represent an important class of time series models. These have been used extensively in sales forecasting and in the analysis of financial and economic time series.

When working with time series models for sales, we try to select the very best model in terms of the Akaike Information Criterion (AIC) or some other measure that combines goodness-of-fit and parsimony. We use the selected model to generate forecasts and error bands around those fore- casts. Hyndman et al. (2014) provide programs to search across large sets of candidate models, including autoregressive, moving-average, and seasonal components.

Forecasting uncertainty is estimated around the forecasted values. There is always uncertainty about the future, and the further we look into the future, the greater our uncertainty. The value of a model lies in the quality of its predictions, and sales forecasting presents challenging problems for data scientists.

When working with multiple time series, we might fit a multivariate time series or vector autoregressive (VAR) model to data. Alternatively, we could explore dynamic linear models, regressing one time series on another. We can utilize ARIMA transfer function models or state space models with re- gression components. The possibilities are as many as the modeling issues to be addressed.

There is a subtle but important distinction to be made between time se- ries models and time series regression models. When we use the term time series regression, we are referring to regression analysis in which the orga- nizing unit of analysis is time. We look at relationships among economic

228 Sports Analytics and Data Science

measures organized in time. Much economic analysis concerns time series regression. Special care must be taken to avoid what might be called spu- rious relationships, as many economic time series are correlated with one another because they depend on common underlying factors, such as pop- ulation growth or seasonality.

In time series regression, we check the residuals from our regression model to ensure that they are not correlated in time. If they are correlated in time (autocorrelated), then we use a method such as generalized least squares as an alternative to ordinary least squares. That is, we incorporate an error data model as part of our modeling process.

When we use the term time series analysis, we are not talking about time series regression. We are talking about methods that start by focusing on one economic measure at a time and its pattern across time. We look for trends, seasonality, and cycles in that individual time series. Then, after working with that single time series, we look at possible relationships with other time series. If we are concerned with forecasting or predicting the future, as we often are in data science, then we use time series analysis. Recently, there has been considerable interest in state space models for time series, which provide a convenient mechanism for incorporating regression components into dynamic time series models (Commandeur and Koopman 2007; Hyndman, Koehler, Ord, and Snyder 2008; Durbin and Koopman 2012).

There are myriad applications of time series analysis in sports business mar- keting, including marketing mix models and advertising research models. Along with sales forecasting, these fall under the general class of market response models, as reviewed by Hanssens, Parsons, and Schultz (2001). Marketing mix models look at the effects of price, promotion, and product placement in retail establishments. These are multiple time series problems.

Advertising research looks for cumulative effectiveness of advertising on brand and product awareness, as well as on sales. Exemplary reviews of advertising research methods and findings have been provided by Berndt (1991) and Lodish et al. (1995). Much of this research employs measures such as “advertising stock,” which is an accumulation of advertising im- pressions or rating points across a moving time series window of months or years. The thinking is that messages are most influential immediately

Appendix A. Data Science Methods 229

after being received, decline in influence with time, but do not decline com- pletely until many units in time later. Viewers or listeners remember ad- vertisements long after initial exposure. Due to carry-over effects from one time period to the next, assessing advertising effectiveness presents a spe- cial challenge for data scientists.

Similar to other data with which we work, sales and marketing data are organized by observational unit, time, and space. The observational unit is typically an economic agent (individual or firm) or a group of such agents as in an aggregate analysis. It is common to use geographical areas as a basis for aggregation. Alternatively, space (longitude and latitude) can be used directly in spatial data analyses. Time considerations are especially important in macroeconomic analysis, which focuses on nationwide eco- nomic measures.

Baumohl (2008) provides a review of economic measures that are com- monly thought of as leading indicators. Kennedy (2008) provides an intro- duction to the terminology of econometrics. Key references in the area of econometrics include Judge et al.(1985), Berndt (1991), Enders (2010), and Greene (2012). Reviews of time series modeling and forecasting methods are provided by Holden, Peel, and Thompson (1990) and in the edited vol- ume by Armstrong (2001).

More detailed discussion of time series methods is provided by Hamilton (1994), Makridakis, Wheelwright, and Hyndman (2005), Box, Jenkins, and Reinsel (2008), Hyndman et al. (2008), Durbin and Koopman (2012), and Hyndman and Athanasopoulos (2014). Time-series, panel (longitudinal) data, financial, and econometric modeling methods are especially relevant in demand and sales forecasting. Hierarchical and grouped time series methods are reviewed by Athanasopoulos, Ahmed, and Hyndman (2009) and Hyndman et al. (2011).

For gathering economic data with R, see Ryan (2014). Useful for program- ming with dates are R functions provided by Grolemund and Wickham (2011, 2014). Econometric and time series programs are listed in Kleiber and Zeileis (2008), Hothorn et al. (2014), Cowpertwait and Metcalfe (2009), Petris, Petrone, and Campagnoli (2009), Tsay (2013), Hyndman et al.(2014), Petris (2010), Petris and Gilks (2014), and Szymanski (2014).

230 Sports Analytics and Data Science

A.7 Social Network Analysis

Teams, apart from competing on the fields and courts, interact as businesses and cooperate in leagues. There are player trades between teams and many communications among teams. Professional sports present a potentially rich domain for social network research, thinking of teams as economic agents. Another way of using social network analysis in sports would be to consider patterns of interaction among players and coaches of a team.

A social network consists of nodes and links (vertices and edges in the lan- guage of graph theory). For example, we could think of each team as a node in a social network and each player trade as a link in that network. Then we could use social network analysis to understand better a log of trades across one or a number of seasons. To date, social network analysis is a relatively unexplored area of sports analytics.

Social network analysis has been an active area of research in psychology, sociology, anthropology, and political science for many years. The inven- tion of the sociogram and concepts of social structure may be traced back more than eighty years (Moreno 1934; Radcliffe-Brown 1940). Research top- ics include isolation and popularity, prestige, power, and influence, social cohesion, subgroups and cliques, status and roles within organizations, bal- ance and reciprocity, marketplace relationships, and measures of centrality and connectedness.

In years past, social network data collection was a painstaking process. Not so today. Social media implemented through the web have rekindled inter- est in social network analysis. Technologies of the web provide a record of what people do, where they come from, where they go, with whom they communicate, and sometimes transcripts of what they say. There are online friends and followers, tweets and retweets, text messages, e-mail, and blog postings. The data are plentiful. The challenge is to find our way to useful data and make sense of them.

Recognizing growth in the use of electronic social networks and intelligent mobile devices, organizations see opportunities for communicating with and selling to friends of friends. Businesses, nonprofits, and governmental organizations (not to mention political campaigns) are interested in learn-

Appendix A. Data Science Methods 231

ing from the data of social media. Network data sets are large but accessi- ble. The possibilities are many.

Social networks are useful for making predictions. We can expect that a our attitudes and behavior are affected by the people we know. People closest to us in “network space,” as it were, may be most influential in affecting our attitudes and behavior.

Various network measures come from mathematicians working with graph theory and from sociologists working with social networks. Network mea- sures describe relationships among nodes and structural characteristics of networks.

We use mathematical models of networks in making predictions about net- work phenomena and in studying relationships across network measures. Three types of models are of special interest: random graph, preferential attachment, and small-world network models.

The first mathematical model of interest, developed by Paul Erdös and Alfred Rényi (1959, 1960, 1961), laid the foundation for models to follow. A random graph is a set of nodes connected by links in a purely random fashion. The small-world network is especially important in representing so- cial networks (Watts and Strogatz 1998). It defines a structure in which many nodes or actors are connected to nearby neighbors and some nodes are linked to nodes that are not nearby. Small-world networks have been studied extensively in social psychology, sociology, and network science (Milgram 1967; Travers and Milgram 1969; Watts 1999; Schnettler 2009).

Measures of node importance are useful for finding sources of power, in- fluence, or importance. We might want to characterize the importance of a politician to his party, thinking of measures of centrality as indicators of political power.

We can begin by counting the links connected to the node. And for a di- rected network, we can count the number of links in and out—we measure the degree of each node, both in-degree and out-degree. The degree distribution of a network is one way to characterize the structure of a network, and the average degree or degree centrality is a way to summarize the connectedness of an entire network.

232 Sports Analytics and Data Science

While the degree centrality of a node may be computed by looking only at that single node, other measures of centrality depend on the structure of the entire network. One nodal measure is closeness centrality, which character- izes how close a node is to all other nodes in the network, where closeness is the number of hops or links between nodes. Computing closeness cen- trality can be problematic in disconnected networks, so it is used less often to measure centrality than other measures (Borgatti, Everett, and Johnson 2013). When measuring betweenness centrality, we consider the proportion of times a node lies on the shortest path between other pairs of nodes. Be- tweenness centrality reflects the degree to which a node is a broker or go- between node, affecting the traffic or flow of information across the net- work.

What if we consider a node as important if it is close to other nodes of im- portance, which are in turn close to other nodes of importance, and so on. This thinking moves us in the direction of the notion of eigenvector centrality. Much as the first principle component characterizes common variability in a set of variables, eigenvector centrality characterizes the degree to which a node is central to the set of nodes comprising the network. Eigenvector centrality is a measure of overall connectedness or importance. A node acquires higher eigenvector centrality by being connected to other well- connected nodes. Eigenvector centrality depends on the entire network and is a good summary measure of node importance.

There are power brokers within professional sports, as documented for Ma- jor League Baseball by Pessah (2015). If data scientists working for an MLB team were to trace trades among teams from the beginning of December 2014 through the end of July 2015, for example, they would learn much about the social network of teams or, more specifically, the social network of team general managers. And what data scientists learn about the social network of teams could inform future team behavior within that network. Information provides strategic advantage.

Major League Baseball posts a complete list of team transactions online, showing player injuries, transfers, assignments, and trades. Transactions from one day in December 2014 are shown in table A.2. Trades are impor- tant to sports teams, and much can be learned about teams by reviewing trades among teams.

Appendix A. Data Science Methods 233

Table A.2. Social Network Data: MLB Player Transactions, December 18, 2014

Kansas City Royals designated 2B Johnny Giavotella for assignment.

Oakland Athletics designated Fernando Rodriguez for assignment.

Cleveland Indians sent RHP Bryan Price outright to Columbus Clippers. Los Angeles Dodgers traded RF Matt Kemp, C Tim Federowicz and cash to San Diego Padres for C Yasmani Grandal, RHP Joe Wieland and RHP Zach Eflin.

Los Angeles Angels traded CF Matt Long to Los Angeles Dodgers. Milwaukee Brewers traded C Shawn Zarraga to Los Angeles Dodgers for CF Matt Long and LHP Jarret Martin.

Oakland Athletics traded C Derek Norris and RHP Seth Streich to San Diego Padres for RHP Jesse Hahn and RHP R.J. Alvarez. Arizona Diamondbacks traded LHP Eury De La Rosa to Oakland Athletics for cash. Toronto Blue Jays signed free agent RHP Rafael Cova to a minor league contract. Texas Rangers signed free agent 1B Mike McDade to a minor league contract. Chicago Cubs signed free agent RHP Jesus Camargo to a minor league contract. Detroit Tigers signed free agent 2B Brandon Douglas to a minor league contract. Kansas City Royals signed free agent RHP Kris Medlen. Pittsburgh Pirates signed free agent RHP Adam Miller to a minor league contract. Minnesota Twins signed free agent 1B Brock Peterson to a minor league contract. Seattle Mariners signed free agent RHP Mark Lowe to a minor league contract and invited him to spring training. Colorado Rockies signed free agent LF Roger Bernadina to a minor league contract and invited him to spring training. Cleveland Indians signed free agent RHP Jeff Manship to a minor league contract and invited him to spring training. Detroit Tigers signed free agent C Miguel Gonzalez to a minor league contract and invited him to spring training. Chicago Cubs signed free agent 2B Carlos Sepulveda to a minor league contract.

Source. Major League Baseball (2015b).

234 Sports Analytics and Data Science

A.8 Data Visualization

Data visualization is critical to the work of data science. Examples in this book demonstrate the importance of data visualization in discovery, diag- nostics, and design. We employ tools of exploratory data analysis (dis- covery) and statistical modeling (diagnostics). In communicating results to management, we use presentation graphics (design).

Statistical summaries fail to tell the story of data. To understand data, we must look beyond data tables, regression coefficients, and the results of sta- tistical tests. Visualization tools help us learn from data. We explore data, discover patterns in data, identify groups of observations that go together and unusual observations or outliers. We note relationships among vari- ables, sometimes detecting underlying dimensions in the data.

There is no more telling example of the importance of data visualization than a demonstration that is affectionately known as the Anscombe Quar- tet. Consider the data sets in figure A.5, developed by Anscombe (1973). Looking at the tabulated data, the casual reader will note that the fourth data set is clearly different from the others. But what about the first three data sets? Are there obvious differences in patterns of relationship between x and y?

When we regress y on x for the data sets, we see that the models provide similar statistical summaries. The mean of the response y is 7.5, the mean of the explanatory variable x is 9. The regression analyses for the four data sets are virtually identical. The fitted regression equation for each of the four sets is ŷ = 3 + 0.5x. The proportion of response variance accounted for is 0.67 for each of the four models. Python and R programs for the Anscombe Quartet are provided in exhibits A.1 and A.2 (pages 242 and 244, respectively).

We see many examples of the utility of visualization in sports analytics and data science. Events in games are revealed by play-by-play and spatial data plots. We can view team performance across entire seasons. On the sports business side, we can see relationships among products and services and explore consumer preferences in perceptual maps. We can explore relation- ships among continuous performance measures in scatter plots and rela- tionships among categorical variables in mosaic plots.

Appendix A. Data Science Methods 235

Figure A.5. Data and Plots for the Anscombe Quartet

Set I Set II Set III Set IV x1 y1 x2 y2 x3 y3 x4 y4

10 8.04 10 9.14 10 7.46 8 6.58 8 6.95 8 8.14 8 6.77 8 5.76

13 7.58 13 8.74 13 12.74 8 7.71 9 8.81 9 8.77 9 7.11 8 8.84

11 8.33 11 9.26 11 7.81 8 8.47 14 9.96 14 8.10 14 8.84 8 7.04

6 7.24 6 6.13 6 6.08 8 5.25 4 4.26 4 3.10 4 5.39 19 12.50

12 10.84 12 9.13 12 8.15 8 5.56 7 4.82 7 7.26 7 6.42 8 7.91 5 5.68 5 4.74 5 5.73 8 6.89

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236 Sports Analytics and Data Science

Figure A.6. Visualizing Many Games Across a Season: Differential Runs Plot

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Displays of events across an entire season or a portion of a season are demonstrated by differential runs plots for baseball, introduced by Miller (2008). To make a differential runs plot, we work with one team at a time. The plot shows positive or negative differential runs on the vertical axis and is indexed on the horizontal axis by games. It is often convenient to show the abbreviation for the opposing team along the horizontal axis. Indices of competitive power may be computed from these data. With solid or open circles to show home versus away games, a differential runs plot provides a picture of a team’s performance across many games.

Figure A.6 shows the differential runs plot for the Arizona Diamondbacks from April 1 through August 31, 2007. The plot shows a team with a good win/loss record but low competitive power—they win many one-run games but lose many other games by five runs or more. Streaks of win- ning games, clearly visible in this Diamondbacks’ differential runs plot, are seen as consecutive vertical lines above the zero-line. Exhibit A.3 (page 245) shows R code for generating differential runs plots.

Appendix A. Data Science Methods 237

Figure A.7. Moving Fraction Plot for Basketball: Oklahoma City Thunder (2014–2015 Season)

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Displays of winning and losing streaks across a season are illustrated by the moving fraction plot, introduced by Albert and Bennett (2001). To make a moving fraction plot, we organize box score data in temporal order, noting game outcomes with a binary variable. We then employ a moving window across the game series, computing the proportion or percentage of wins within the widow. A ribbon plot may be used to color-code winning streaks above the 50-percent line and losing streaks below the 50-percent line.

Figure A.7 shows the moving fraction plot for the Oklahoma City Thunder of the NBA. The plot shows streaks of winning and losing across the 2014– 2015 season. Exhibit A.4 (page 246) shows an R program for making this moving fraction plot. This program draws on graphics software developed by Wickham and Chang (2014) and documented by Chang (2013).

238 Sports Analytics and Data Science

Data visualization of play-by-play data reveals the effects of team scoring streaks. Long no-scoring streaks go hand-in-hand with lead changes, as we can see in figure A.8. In the Lakers-Mavericks game, we see no-scoring streaks by both teams associated with lead changes across the game. In the Lakers-Thunder game, we see one no-scoring streak in the second period, setting the stage for the Lakers taking and keeping the lead.

Exhibit A.5 (page 248) shows an R program that uses basketball play-by- play data to create game visualizations. It generates the complete set of cumulative frequency distributions for the Los Angeles Lakers’ 2008–2009 season. The program utilizes play-by-play data provided by Parker (2010) and code developed by Grolemund and Wickham (2011, 2014), Wickham and Chang (2014), and Wickham (2014).

Heer, Bostock, and Ogievetsky (2010) demonstrate contemporary visual- ization techniques for web distribution. When working with very large data sets, special methods may be needed, such as partial transparency and hexbin plots (Unwin, Theus, and Hofmann 2006; Carr, Lewin-Koh, and Maechler 2014; Lewin-Koh 2014).

R is particularly strong for data visualization. An R graphics overview is provided by Murrell (2011). R lattice graphics, discussed by Sarkar (2008, 2014), build on the conceptual structure of an earlier system called S-Plus TrellisTM (Cleveland 1993; Becker and Cleveland 1996). Wilkinson’s (2005) “grammar of graphics” approach has been implemented in the Python gg- plot package (Lamp 2014) and in the R ggplot2 package (Wickham and Chang 2014), with R programming examples provided by Chang (2013). Cairo (2013) and Zeileis, Hornik, and Murrell (2009, 2014) provide advice about colors for statistical graphics. Ihaka et al. (2014) show how to specify colors in R by hue, chroma, and luminance.

Graphics for exploratory data analysis are reviewed in classic references by Tukey (1977) and Tukey and Mosteller (1977). Regression graphics are covered by Cook (1998), Cook and Weisberg (1999), and Fox and Weis- berg (2011). Statistical graphics and data visualization are illustrated in the works of Tufte (1990, 1997, 2004, 2006), Few (2009), and Yau (2011, 2013). Wilkinson (2005) presents a review of human perception and graphics, as well as a conceptual structure for understanding statistical graphics. Cairo (2013) provides a general review of information graphics.

Appendix A. Data Science Methods 239

Figure A.8. Visualizing Basketball Play-by-Play Data

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240 Sports Analytics and Data Science

A.9 Data Science: The Eclectic Discipline

Data science draws from many academic disciplines, as we have seen in this book. To show how data science relates to other disciplines, I constructed a similarity ranking task for myself. The task comprised forty-five items— all possible pairs of ten discipline names. Figure A.9 shows my personal perceptual map of these disciplines.

Information technology is about gathering data, distributing data, taking care of data, and providing secured access to data. Information retrieval and selection are important, as are data indexing and storage. Increasingly, organizations are turning to distributed solutions, storing data and docu- ments across many computers. Data preparation is a big part of any sports analytics project. Data must be cleaned and organized prior to analysis.

Measurement is about getting to the right data, measures that are reliable and valid. It is about understanding the meaning of measures, noting that the validity of a measure is defined by that measure’s relationships with other measures. We check data quality, validate, transform, and annotate data. We make data from data, defining new measures as combinations of other measures. To do a good job of measurement, we need to understand the research context, be it sport or business.

Statistics is about doing the right things with data. We sample from popula- tions. We draw inferences from samples. We explore, looking at data visu- alizations or statistical graphics. We compute summary statistics, reducing data to their essence. We build models from data for making inferences and predictions. We learn from data.

Data science is closely related to information technology and computer sci- ence. Like operations research, data science is concerned with methods and models for making informed, sometimes optimal, business decisions. Context is important, whether working on the performance or management sides of team sports. Data scientists need to be multilingual, understanding the languages of information systems, statistics, sport, and business.

Exhibit A.6 (page 252) shows the R program for making the map of the ten disciplines, showing their relationships. The program reads the matrix of similarity judgments and uses multidimensional scaling to define the map.

Appendix A. Data Science Methods 241

Figure A.9. Data Science: The Eclectic Discipline

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242 Sports Analytics and Data Science

Exhibit A.1. Programming the Anscombe Quartet (Python)

# The Anscombe Quartet (Python)

# demonstration data from

# Anscombe, F. J. 1973, February. Graphs in statistical analysis.

# The American Statistician 27: 1721.

# prepare for Python version 3x features and functions

from __future__ import division, print_function

# import packages for Anscombe Quartet demonstration

import pandas as pd # data frame operations

import numpy as np # arrays and math functions

import statsmodels.api as sm # statistical models (including regression)

import matplotlib.pyplot as plt # 2D plotting

# define the anscombe data frame using dictionary of equal-length lists

anscombe = pd.DataFrame({’x1’ : [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],

’x2’ : [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],

’x3’ : [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5],

’x4’ : [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8],

’y1’ : [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26,10.84, 4.82, 5.68],

’y2’ : [9.14, 8.14, 8.74, 8.77, 9.26, 8.1, 6.13, 3.1, 9.13, 7.26, 4.74],

’y3’ : [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73],

’y4’ : [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.5, 5.56, 7.91, 6.89]})

# fit linear regression models by ordinary least squares

set_I_design_matrix = sm.add_constant(anscombe[’x1’])

set_I_model = sm.OLS(anscombe[’y1’], set_I_design_matrix)

print(set_I_model.fit().summary())

set_II_design_matrix = sm.add_constant(anscombe[’x2’])

set_II_model = sm.OLS(anscombe[’y2’], set_II_design_matrix)

print(set_II_model.fit().summary())

set_III_design_matrix = sm.add_constant(anscombe[’x3’])

set_III_model = sm.OLS(anscombe[’y3’], set_III_design_matrix)

print(set_III_model.fit().summary())

set_IV_design_matrix = sm.add_constant(anscombe[’x4’])

set_IV_model = sm.OLS(anscombe[’y4’], set_IV_design_matrix)

print(set_IV_model.fit().summary())

# create scatter plots

fig = plt.figure()

set_I = fig.add_subplot(2, 2, 1)

set_I.scatter(anscombe[’x1’],anscombe[’y1’])

set_I.set_title(’Set I’)

set_I.set_xlabel(’x1’)

set_I.set_ylabel(’y1’)

set_I.set_xlim(2, 20)

set_I.set_ylim(2, 14)

Appendix A. Data Science Methods 243

set_II = fig.add_subplot(2, 2, 2)

set_II.scatter(anscombe[’x2’],anscombe[’y2’])

set_II.set_title(’Set II’)

set_II.set_xlabel(’x2’)

set_II.set_ylabel(’y2’)

set_II.set_xlim(2, 20)

set_II.set_ylim(2, 14)

set_III = fig.add_subplot(2, 2, 3)

set_III.scatter(anscombe[’x3’],anscombe[’y3’])

set_III.set_title(’Set III’)

set_III.set_xlabel(’x3’)

set_III.set_ylabel(’y3’)

set_III.set_xlim(2, 20)

set_III.set_ylim(2, 14)

set_IV = fig.add_subplot(2, 2, 4)

set_IV.scatter(anscombe[’x4’],anscombe[’y4’])

set_IV.set_title(’Set IV’)

set_IV.set_xlabel(’x4’)

set_IV.set_ylabel(’y4’)

set_IV.set_xlim(2, 20)

set_IV.set_ylim(2, 14)

plt.subplots_adjust(left=0.1, right=0.925, top=0.925, bottom=0.1,

wspace = 0.3, hspace = 0.4)

plt.savefig(’fig_anscombe_Python.pdf’, bbox_inches = ’tight’, dpi=None,

facecolor=’w’, edgecolor=’b’, orientation=’portrait’, papertype=None,

format=None, transparent=True, pad_inches=0.25, frameon=None)

# Suggestions for the student:

# See if you can develop a quartet of your own,

# or perhaps just a duet, two very different data sets

# with the same fitted model.

244 Sports Analytics and Data Science

Exhibit A.2. Programming the Anscombe Quartet (R)

# The Anscombe Quartet (R)

# demonstration data from

# Anscombe, F. J. 1973, February. Graphs in statistical analysis.

# The American Statistician 27: 1721.

# define the anscombe data frame

anscombe <- data.frame(

x1 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),

x2 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),

x3 = c(10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5),

x4 = c(8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8),

y1 = c(8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26,10.84, 4.82, 5.68),

y2 = c(9.14, 8.14, 8.74, 8.77, 9.26, 8.1, 6.13, 3.1, 9.13, 7.26, 4.74),

y3 = c(7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73),

y4 = c(6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.5, 5.56, 7.91, 6.89))

# show results from four regression analyses

with(anscombe, print(summary(lm(y1 ~ x1, data = anscombe))))

with(anscombe, print(summary(lm(y2 ~ x2, data = anscombe))))

with(anscombe, print(summary(lm(y3 ~ x3, data = anscombe))))

with(anscombe, print(summary(lm(y4 ~ x4, data = anscombe))))

# place four plots on one page using standard R graphics

# ensuring that all have the same scales

# for horizontal and vertical axes

pdf(file = "fig_anscombe_R.pdf", width = 8.5, height = 8.5)

par(mfrow=c(2,2), mar=c(5.1, 4.1, 4.1, 2.1))

with(anscombe, plot(x1, y1, xlim=c(2,20), ylim=c(2,14), pch = 19,

col = "darkblue", cex = 1.5, las = 1, xlab = "x1", ylab = "y1"))

title("Set I")

with(anscombe,plot(x2, y2, xlim=c(2,20), ylim=c(2,14), pch = 19,

col = "darkblue", cex = 1.5, las = 1, xlab = "x2", ylab = "y2"))

title("Set II")

with(anscombe,plot(x3, y3, xlim=c(2,20), ylim=c(2,14), pch = 19,

col = "darkblue", cex = 1.5, las = 1, xlab = "x3", ylab = "y3"))

title("Set III")

with(anscombe,plot(x4, y4, xlim=c(2,20), ylim=c(2,14), pch = 19,

col = "darkblue", cex = 1.5, las = 1, xlab = "x4", ylab = "y4"))

title("Set IV")

dev.off()

# par(mfrow=c(1,1),mar=c(5.1, 4.1, 4.1, 2.1)) # return to plotting defaults

# Suggestions for the student:

# See if you can develop a quartet of your own,

# or perhaps just a duet, two very different data sets

# with the same fitted model.

Appendix A. Data Science Methods 245

Exhibit A.3. Making Differential Runs Plots for Baseball (R)

# Making Differential Runs Plots for Baseball (R)

# data visualization with R standard graphics

excess.runs.data.frame.ARI <- read.csv("MLB_2007_ARI_data_frame.csv")

pdf(file=paste("fig_differential_runs_ARI.pdf",sep=""),

width = 11, height = 8.5)

par(mfrow=c(1,1), xpd=NA, cex=1)

plot(excess.runs.data.frame.ARI$excess.runs, type="h",

las=1, xlab="Game Number and Opponent", ylab="Differential Runs",

ylim=c(-(max(abs(excess.runs.data.frame.ARI$excess.runs),14) + 1),

(max(abs(excess.runs.data.frame.ARI$excess.runs),14) + 1)))

abline(h=0,lty="solid",xpd=FALSE,lwd=.5)

legend("topright", title=NULL,

legend=c("Home Game ","Away Game "), pch=c(19,21))

# plot all as open circles first

points(excess.runs.data.frame.ARI$excess.runs, pch=21)

# then fill in the circles for the home games

for(i in seq(along=excess.runs.data.frame.ARI$game.number))

if(excess.runs.data.frame.ARI$home.away[i]=="home")

points(excess.runs.data.frame.ARI$game.number[i],

excess.runs.data.frame.ARI$excess.runs[i], pch=19)

for(i in seq(along=excess.runs.data.frame.ARI$game.number))

text(excess.runs.data.frame.ARI$game.number[i],-

(max(abs(excess.runs.data.frame.ARI$excess.runs),15) + 1),

excess.runs.data.frame.ARI$other.team.label[i], cex=.85, pos=4, srt=90)

text(excess.runs.data.frame.ARI$game.number[1],

(max(abs(excess.runs.data.frame.ARI$excess.runs),14) + 1),

map.team.to.name(excess.runs.data.frame.ARI$this.team[1]),cex=2,pos=4)

dev.off()

246 Sports Analytics and Data Science

Exhibit A.4. Moving Fraction Plot: A Basketball Example (R)

# Moving Fraction Plot: A Basketball Example (R)

library(grid) # graphics utilities needed for split-plotting

library(ggplot2) # graphics package with ribbon plot

# read game summary data for the Oklahoma City Thunder

OKC_data <- read.csv("okc_data_2014_2015.csv", stringsAsFactors = FALSE)

# check the structure of the data

print(str(OKC_data))

# create winning fraction plot to explore streakiness during the season

# a window of twelve games is used following Albert and Bennett (2001)

# add game number to data frame

OKC_data$game_number <- seq(1:nrow(OKC_data))

# set binary indicator if this team has won

OKC_data$win_bin <- rep(0, length = nrow(OKC_data))

for (i in seq(along = OKC_data$win_bin))

if (OKC_data$win_team_code[i] == "OKC")

OKC_data$win_bin[i] <- 1

# window across the season twelve games at a time

OKC_data$win_window <- rep(NA, length = nrow(OKC_data))

for (i in seq(along = OKC_data$win_window)) {

if (i > 6)

OKC_data$win_window[i] <-

mean(OKC_data$win_bin[(i - 6):(i + 5)]) * 100

}

moving_fraction_plotting_frame <-

OKC_data[, c("game_number", "win_window")]

moving_fraction_plotting_frame$ymax_topwhite <-

rep(NA, length = nrow(moving_fraction_plotting_frame))

moving_fraction_plotting_frame$ymax_bottomwhite <-

rep(NA, length = nrow(moving_fraction_plotting_frame))

moving_fraction_plotting_frame$ymin_topwhite <-

rep(NA, length = nrow(moving_fraction_plotting_frame))

moving_fraction_plotting_frame$ymin_bottomwhite <-

rep(NA, length = nrow(moving_fraction_plotting_frame))

for (i in seq(along = moving_fraction_plotting_frame$win_window)) {

if (is.na(moving_fraction_plotting_frame$win_window[i])) {

moving_fraction_plotting_frame$ymax_topwhite[i] <- 100

moving_fraction_plotting_frame$ymin_topwhite[i] <- 50.1

moving_fraction_plotting_frame$ymax_bottomwhite[i] <- 49.99

moving_fraction_plotting_frame$ymin_bottomwhite[i] <- 0

}

Appendix A. Data Science Methods 247

if (!is.na(moving_fraction_plotting_frame$win_window[i])) {

if (moving_fraction_plotting_frame$win_window[i] > 50) {

moving_fraction_plotting_frame$ymax_topwhite[i] <- 100

moving_fraction_plotting_frame$ymin_topwhite[i] <-

moving_fraction_plotting_frame$win_window[i]

moving_fraction_plotting_frame$ymax_bottomwhite[i] <- 49.99

moving_fraction_plotting_frame$ymin_bottomwhite[i] <- 0

}

if (moving_fraction_plotting_frame$win_window[i] <= 50) {

moving_fraction_plotting_frame$ymax_topwhite[i] <- 100

moving_fraction_plotting_frame$ymin_topwhite[i] <- 50.1

moving_fraction_plotting_frame$ymax_bottomwhite[i] <-

moving_fraction_plotting_frame$win_window[i]

moving_fraction_plotting_frame$ymin_bottomwhite[i] <- 0

}

}

}

greenmin <- 50.01

greenmax <- 100

redmin <- 0

redmax <- 49.99

pdf(file = "fig_moving_fraction_plot.pdf", width = 8.8, height = 8.5)

ggobject <- ggplot() +

geom_ribbon(data=moving_fraction_plotting_frame,

mapping=aes(x=game_number, ymin=greenmin, ymax=greenmax),

stat="identity",colour="white",fill="darkgreen") +

geom_ribbon(data=moving_fraction_plotting_frame,

mapping=aes(x=game_number, ymin=redmin, ymax=redmax),

stat="identity",colour="white",fill="darkred") +

geom_ribbon(data=moving_fraction_plotting_frame,

mapping=aes(x=game_number, ymin=ymin_topwhite, ymax=ymax_topwhite),

stat="identity",colour="white",fill="white") +

geom_ribbon(data=moving_fraction_plotting_frame,

mapping=aes(x=game_number, ymin=ymin_bottomwhite, ymax=ymax_bottomwhite),

stat="identity",colour="white",fill="white") +

annotate("segment", x = 0, xend = 82, y = 49.99, yend = 50.01) +

ylab("Moving Fraction (Winning Percentage)") +

xlab("Sequence of Games")

print(ggobject)

dev.off()

248 Sports Analytics and Data Science

Exhibit A.5. Visualizing Basketball Games (R)

# Visualizing Basketball Games (R)

library(lubridate) # data/time functions and lakers data frame

# lubridate imports plyr package

library(ggplot2) # statistical graphics, grid graphics assumed

# functions used with grid graphics to split the plotting region

# to set margins and to plot more than one ggplot object on one page/screen

vplayout <- function(x, y)

viewport(layout.pos.row=x, layout.pos.col=y)

# user-defined function to plot a ggplot object with margins

ggplot.print.with.margins <- function(ggplot.object.name,

left.margin.pct=10,

right.margin.pct=10,top.margin.pct=10,bottom.margin.pct=10)

{ # begin function for printing ggplot objects with margins

# margins expressed as percentages of total... use integers

grid.newpage()

pushViewport(viewport(layout=grid.layout(100,100)))

print(ggplot.object.name,

vp=vplayout((0 + top.margin.pct):(100 - bottom.margin.pct),

(0 + left.margin.pct):(100 - right.margin.pct)))

} # end function for printing ggplot objects with margins

# lakers data frame from lubridate includes

# play-by-play data for the Los Angeles Lakers 2008-2009 season

# original data from Parker (2010) http://www.basketballgeek.com/data/

# date: year/month/day text to be converted to date object

# opponent: three-character abbreviation for other team

# game_type: home or away for Los Angeles Lakers

# time: clock time remaining minutes:seconds converted to duration

# period: period of play 1, 2, 3, or 4

# etype: one of ten event types: foul, free throw, jump ball,

# rebound, shot, sub, timeout, turnover, violation

# team: three-character abbreviation for team

# or OFF for neither team as with a jump ball

# player: one of 371 players involved in Los Angeles Lakers games

# result: missed or made

# points: points scored

# type: one of 74 event descriptions: hook, off, layup,

# shooting, personal, jump, pullup jump,

# def, driving layup, driving finger roll layup, regular,

# offensive, 3pt, turnaround jump, putback layup,

# slam dunk, tip, dunk, defensive goaltending,

# hook bank, running layup, official, driving slam dunk,

# short, driving reverse layup, kicked ball, putback dunk,

# technical, alley oop dunk, turnaround fade away, running jump,

# delay of game, defense 3 second, fade away bank, floating jump,

# driving dunk, loose ball, running bank, running dunk,

# fade away jumper, finger roll layup, turnaround hook, reverse layup,

Appendix A. Data Science Methods 249

# reverse dunk, jump hook, jump bank, double technical,

# running hook, driving jump, turnaround bank, step back jump,

# turnaround bank hook, pullup bank, alley oop layup, putback slam dunk,

# flagrant type 1, running reverse layup, running finger roll layup,

# reverse slam dunk, hanging technical, running slam dunk,

# driving bank hook, jump ball, away from play, double personal,

# driving bank, running bank hook, driving hook, lane, clear path,

# jump bank hook, flagrant type 2, inbound

# x, y: shot location, standing behind the offensive teams hoop then

# the X axis runs from left to right and the Y axis runs from

# bottom to top. The center of the hoop is located at (25, 5.25).

# 2008-2009 team abbreviations/code names

team_code_2008 = c("ATL", "BOS", "CHA", "CHI", "CLE",

"DAL", "DEN", "DET", "GSW", "HOU",

"IND", "LAC", "LAL", "MEM", "MIA",

"MIL", "MIN", "NJN", "NOH", "NYK",

"OKC", "ORL", "PHI", "PHX", "POR",

"SAC", "SAS", "TOR", "UTA", "WAS")

# Note. Charlotte Bobcats later became the Charlotte Hornets

# New Orleans Hornets later became the New Orleans Pelicans

team_name_2008 = c("Atlanta Hawks", "Boston Celtics",

"Charlotte Hornets", "Chicago Bulls",

"Cleveland Cavaliers", "Dallas Mavericks",

"Denver Nuggets", "Detroit Pistons",

"Golden State Warriors", "Houston Rockets",

"Indiana Pacers", "Los Angeles Clippers",

"Los Angeles Lakers", "Memphis Grizzlies",

"Miami Heat", "Milwaukee Bucks",

"Minnesota Timberwolves", "New Jersey Nets",

"New Orleans Hornets", "New York Knicks",

"Oklahoma City Thunder", "Orlando Magic",

"Philadelphia 76ers", "Phoenix Suns",

"Portland Trail Blazers", "Sacramento Kings",

"San Antonio Spurs", "Toronto Raptors",

"Utah Jazz", "Washington Wizards")

# Note. Charlotte Bobcats became the Charlotte Hornets

# New Orleans Hornets became the New Orleans Pelicans

# New Jersey Nets became the Brooklyn Nets

# lakers$date <- ymd(lakers$date) # code as date variable

lakers$time <- ms(lakers$time) # code as period object

lakers$time <- as.duration(lakers$time) # code as durations

# convert time to gametime with periods of 12 minutes, overtime 5 minutes

# here we convert to minutes and fractions of minutes

lakers$gametime <- dminutes(c(12, 24, 36, 48, 53)[lakers$period]) -

as.duration(lakers$time)

lakers$minutes <- as.numeric(seconds(lakers$gametime))/60

print(str(lakers)) # examine stucture of the data frame

250 Sports Analytics and Data Science

# get rid of observations with team OFF (jump ball)

lakers_games <- lakers[(lakers$team != "OFF"),]

# route plots to external plotting device... pdf file

pdf(file = "plot_lakers_basketball_2008_2009.pdf",

width = 8.5, height = 8.5)

# ---------------------------------------------

# cycle through all Lakers games for the season

gamedate <- unique(lakers_games$date)

for (igame in seq(along = gamedate)) { # begin for-loop for all games

this_game <- lakers_games[lakers_games$date == gamedate[igame],]

# work with the current game, compute score as cumulative sum for each team

# using ddply function from the plyr package, required for lubridate package

this_game_scores <- ddply(this_game, "team", transform,

score = cumsum(points))

# identify team names and scores for this game

first_team_name <- team_name_2008[which(team_code_2008 == "LAL")]

second_team_name <- team_name_2008[which(team_code_2008 ==

this_game_scores$opponent[1])]

first_team_score <-

max(this_game_scores[(this_game_scores$team == "LAL"), "score"])

second_team_score <-

max(this_game_scores[(this_game_scores$team ==

this_game_scores$opponent[1]), "score"])

# summary for this game to be used in plot title

this_game_summary_text <-

paste(gsub(" UTC","", ymd(this_game_scores$date)[1]),

" ", first_team_name, " ", this_game_scores$game_type[1],

" (", first_team_score, ") versus ",

second_team_name, " ", "(", second_team_score, ")", sep = "")

# create visualization for this game with annotation shading

# for the second and fourth 12-minute periods in the game

# and with customized legend for the step function score lines

ggplot_object <-

ggplot(data = subset(this_game_scores, team == "LAL"),

aes(x = minutes, y = score)) +

layer(geom = "step", size = 0.75, colour = "purple") +

layer(data = subset(this_game_scores,

team == this_game_scores$opponent[1]),

geom = "step", size = 1.5, colour = "blue") +

annotate("rect", xmin = 12.01, xmax = 24.00,

ymin = min(this_game_scores$score),

ymax = max(this_game_scores$score),

alpha = 0.1, fill = "black") +

annotate("rect", xmin = 36.01, xmax = 48.00,

ymin = min(this_game_scores$score),

ymax = max(this_game_scores$score),

alpha = 0.1, fill = "black") +

Appendix A. Data Science Methods 251

annotate("rect", xmin = 0, xmax = 24.00,

ymin = max(this_game_scores$score) - 15,

ymax = max(this_game_scores$score),

alpha = 1, colour = "darkgrey", fill = "white") +

geom_segment(x = 1.0, xend = 3.0,

y = max(this_game_scores$score) - 5,

yend = max(this_game_scores$score) - 5,

colour = "purple", size = 0.75) +

geom_segment(x = 1.0, xend = 3.0,

y = max(this_game_scores$score) - 10,

yend = max(this_game_scores$score) - 10,

colour = "blue", size = 1.5) +

annotate("text", x = 4, y = max(this_game_scores$score) - 5,

colour = "black", alpha = 0.9, size = 4.5,

label = first_team_name, hjust = 0) +

annotate("text", x = 4, y = max(this_game_scores$score) - 10,

colour = "black", alpha = 0.9, size = 4.5,

label = second_team_name, hjust = 0) +

xlab("Game Minutes") + ylab("Score") +

ggtitle(this_game_summary_text) +

theme(axis.title.x = element_text(size = rel(1.25))) +

theme(axis.title.y = element_text(size = rel(1.25)))

ggplot.print.with.margins(ggplot_object,

left.margin.pct = 5, right.margin.pct = 5,

top.margin.pct = 5, bottom.margin.pct = 5)

} # end for-loop for all games

dev.off() # closer the pdf plotting device

252 Sports Analytics and Data Science

Exhibit A.6. Seeing Data Science as an Eclectic Discipline (R)

# Seeing Data Science as an Eclectic Discipline (R)

# Program for multidimensional scaling of ten academic disciplines

library(MASS) # includes functions for multidimensional scaling

library(wordcloud) # textplot utility to avoid overlapping text

USE_METRIC_MDS <- FALSE # metric versus non-metric toggle

# define a utility function for converting a distance structure

# to a distance matrix as required for some routines and

# for printing of the complete matrix for visual inspection.

make.distance.matrix <- function(distance_structure)

{ n <- attr(distance_structure, "Size")

full <- matrix(0,n,n)

full[lower.tri(full)] <- distance_structure

full+t(full)

}

# enter data into a distance structure as required for various

# distance-based routines. That is, we enter the upper triangle

# of the distance matrix as a single vector of distances

distance_structure <-

as.single(c(35, 45, 40, 43, 18, 32, 3, 20, 19,

8, 12, 9, 33, 30, 25, 7, 21,

1, 15, 16, 13, 41, 17, 10,

28, 36, 31, 42, 5, 26,

39, 38, 37, 4, 44,

2, 11, 34, 24,

14, 29, 6,

23, 22,

27))

# provide a character vector of discipline names

disciplines <- c("Marketing", "Operations Research", "Mathematics",

"Statistics", "Computer Science", "Accounting", "Finance",

"Management", "Data Science", "Economics")

attr(distance_structure, "Size") <- length(disciplines) # set size attribute

# check to see that the distance structure has been entered correctly

# by converting the distance structure to a distance matrix

# using the utility function make.distance.matrix, which we had defined

distance_matrix <- unlist(make.distance.matrix(distance_structure))

cat("\n","Distance Matrix of Academic Disciplines","\n")

print(distance_matrix)

if (USE_METRIC_MDS)

{

# apply the metric multidimensional scaling algorithm and plot the map

mds_solution <- cmdscale(distance_structure, k=2, eig=T)

Appendix A. Data Science Methods 253

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2]

}

# apply the non-metric multidimensional scaling algorithm

# this is more appropriate for rank-order data

# and provides a more satisfactory solution here

if (!USE_METRIC_MDS)

{

mds_solution <- isoMDS(distance_matrix, k = 2, trace = FALSE)

}

pdf(file = "plot_nonmetric_mds_data_science.pdf",

width=11, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

# original solution

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2]

# set up the plot but do not plot points... use names for points

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-25, 25), ylim = c(-25, 25)) # first page of pdf plots

# We plot the city names in the locations where points normally go.

text(First_Dimension, Second_Dimension, labels = disciplines,

offset = 0.0, cex = 1.5)

title("Academic Disciplines (initial solution)")

# reflect the horizontal dimension

# multiply the first dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2]

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-25, 25), ylim = c(-25, 25)) # second page of pdf plots

text(First_Dimension, Second_Dimension, labels = disciplines,

offset = 0.0, cex = 1.5)

title("Academic Disciplines (horizontal reflection)")

# reflect the vertical dimension

# multiply the section dimension by -1 to get reflected image

First_Dimension <- mds_solution$points[,1]

Second_Dimension <- mds_solution$points[,2] * -1

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-25, 25), ylim = c(-25, 25)) # third page of pdf plots

text(First_Dimension, Second_Dimension, labels = disciplines,

offset = 0.0, cex = 1.5)

title("Academic Disciplines (vertical reflection)")

# multiply the first and second dimensions by -1

# for reflection in both horizontal and vertical directions

First_Dimension <- mds_solution$points[,1] * -1

Second_Dimension <- mds_solution$points[,2] * -1

254 Sports Analytics and Data Science

plot(First_Dimension, Second_Dimension, type = "n", cex = 1.5,

xlim = c(-25, 25), ylim = c(-25, 25)) # fourth page of pdf plots

text(First_Dimension, Second_Dimension, labels = disciplines,

offset = 0.0, cex = 1.5)

title("Academic Disciplines (horizontal and vertical reflection)")

dev.off() # closes the pdf plotting device

pdf(file = "plot_pretty_original_mds_data_science.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

First_Dimension <- mds_solution$points[,1] # no reflection

Second_Dimension <- mds_solution$points[,2] # no reflection

# wordcloud utility for plotting with no overlapping text

textplot(x = First_Dimension,

y = Second_Dimension,

words = disciplines,

show.lines = FALSE,

xlim = c(-28, 28), # extent of horizontal axis range

ylim = c(-20, 20), # extent of vertical axis range

xaxt = "n", # suppress tick marks

yaxt = "n", # suppress tick marks

cex = 1.25, # size of text points

mgp = c(0.85, 1, 0.85), # position of axis labels

cex.lab = 1.5, # magnification of axis label text

xlab = "Methods . . . . . . . . . . . . . . . Applications",

ylab = "Mostly Numbers . . . . Numbers and Words")

dev.off() # closes the pdf plotting device

pdf(file = "plot_reflected_mds_data_science.pdf",

width=8.5, height=8.5) # opens pdf plotting device

# use par(mar = c(bottom, left, top, right)) to set up margins on the plot

par(mar=c(7.5, 7.5, 7.5, 5))

First_Dimension <- mds_solution$points[,1] * -1 # reflect horizontal

Second_Dimension <- mds_solution$points[,2] * -1 # reflect vertical

# wordcloud utility for plotting with no overlapping text

textplot(x = First_Dimension,

y = Second_Dimension,

words = disciplines,

show.lines = FALSE,

xlim = c(-28, 28), # extent of horizontal axis range

ylim = c(-20, 20), # extent of vertical axis range

xaxt = "n", # suppress tick marks

yaxt = "n", # suppress tick marks

cex = 1.25, # size of text points

mgp = c(0.85, 1, 0.85), # position of axis labels

cex.lab = 1.5, # magnification of axis label text

xlab = "Applications . . . . . . . . . . . . . . . Methods",

ylab = "Words and Numbers . . . Mostly Numbers")

dev.off() # closes the pdf plotting device

B Professional Leagues and Teams

Table B.1. Women’s National Basketball Association (WNBA)

Conference Team Name Abbreviation

Eastern Atlanta Dream ATL Chicago Sky CHI Connecticut Sun CON Indiana Fever IND New York Liberty NYL Washington Mystics WAS

Western Los Angeles Sparks LAS Minnesota Lynx MIN Phoenix Mercury PHO San Antonio Stars SAS Seattle Storm SEA Tulsa Shock TUL

255

256 Sports Analytics and Data Science

Table B.2. Major League Baseball (MLB)

League Division Team Name Abbreviation

American East Baltimore Orioles BAL Boston Red Sox BOS New York Yankees NYY Tampa Bay Rays TBR Toronto Blue Jays TOR

Central Chicago White Sox CHW Cleveland Indians CLE Detroit Tigers DET Kansas City Royals KCR Minnesota Twins MIN

West Houston Astros HOU Los Angeles Angels LAA Oakland A's OAK Seattle Mariners SEA Texas Rangers TEX

National East Atlanta Braves ATL Miami Marlins MAI New York Mets NYM Philadelphia Phillies PHI Washington Nationals WSN

Central Chicago Cubs CHC Cincinnati Reds CIN Milwaukee Brewers MIL Pittsburgh Pirates PIT St. Louis Cardinals STL

West Arizona Diamondbacks ARI Colorado Rockies COL Los Angeles Dodgers LAD San Diego Padres SDP San Francisco Giants SFG

Appendix B. Professional Leagues and Teams 257

Table B.3. Major League Soccer (MLS)

Conference Team Name Abbreviation

Eastern Chicago Fire CHI Columbus Crew SC CCR D.C. United DCU Montreal Impact MON New England Revolution NER New York City FC NYC New York Red Bulls NYR Orlando City SC ORL Philadelphia Union PHI Toronto FC WAS

Western Colorado Rapids COL FC Dallas FTD Houston Dynamo HOU LA Galaxy LAG Portland Timbers POR Real Salt Lake RSL San Jose Earthquakes SAN Seattle Sounders FC SEA Sporting Kansas City SKC Vancouver Whitecaps FC VAN

258 Sports Analytics and Data Science

Table B.4. National Basketball Association (NBA)

Conference Division Team Name Abbreviation

Eastern Atlantic Boston Celtics BOS Brooklyn Nets BKN New York Knicks NYK Philadelphia 76ers PHI Toronto Raptors TOR

Central Chicago Bulls CHI Cleveland Cavaliers CLE Detroit Pistons DET Indiana Pacers IND Milwaukee Bucks MIL

Southeast Atlanta Hawks ATL Charlotte Hornets CHA Miami Heat MIA Orlando Magic ORL Washington Wizards WAS

Western Southwest Dallas Mavericks DAL Houston Rockets HOU Memphis Grizzlies MEM New Orleans Pelicans NOP San Antonio Spurs SAS

Northwest Denver Nuggets DEN Minnesota Timberwolves MIN Oklahoma City Thunder OKC Portland Trail Blazers POR Utah Jazz UTA

Pacific Golden State Warriors GSW Los Angeles Clippers LAC Los Angeles Lakers LAL Phoenix Suns PHX Sacramento Kings SAC

Appendix B. Professional Leagues and Teams 259

Table B.5. National Football League (NFL)

Conference Division Team Name Abbreviation

American East Buffalo Bills BUF Miami Dolphins MAI New England Patriots NE New York Jets NYJ

North Baltimore Ravens BAL Cincinnati Bengals CIN Cleveland Browns CLE Pittsburgh Steelers PIT

South Houston Texans HOU Indianapolis Colts IND Jacksonville Jaguars JAC Tennessee Titans TEN

West Denver Broncos DEN Kansas City Chiefs KC Oakland Raiders OAK San Diego Chargers SD

National East Dallas Cowboys DAL New York Giants NYG Philadelphia Eagles PHI Washington Redskins WAS

North Chicago Bears CHI Detroit Lions DET Green Bay Packers GB Minnesota Vikings MIN

South Atlanta Falcons ATL Carolina Panthers CAR New Orleans Saints NO Tampa Bay Buccaneers TB

West Arizona Cardinals ARI San Francisco 49ers SF Seattle Seahawks SEA St. Louis Rams STL

260 Sports Analytics and Data Science

Table B.6. National Hockey League (NHL)

Conference Division Team Name Abbreviation

Eastern Atlantic Boston Bruins BOS Buffalo Sabres BUF Detroit Red Wings DET Florida Panthers FLA Montreal Canadiens MON Ottawa Senators OTW Tampa Bay Lightning TBL Toronto Maple Leafs TOR

Metropolitan Carolina Hurricanes CAR Columbus Blue Jackets CBJ New Jersey Devils NJD New York Islanders NYI New York Rangers NYR Philadelphia Flyers PHI Pittsburgh Penguins PIT Washington Capitals WAS

Western Central Chicago Blackhawks CHI Colorado Avalanche COL Dallas Stars DAL Minnesota Wild MIN Nashville Predators NAS St. Louis Blues STL Winnipeg Jets WIN

Pacific Anaheim Ducks ANA Arizona Coyotes ARI Calgary Flames CAL Edmonton Oilers EDM Los Angeles Kings LAK San Jose Sharks SJS Vancouver Canucks VAN

Data Science Glossary

adjacency matrix Consider a network with nodes and links between nodes. We let xij = 1 if node i is linked to node j and let xij = 0 otherwise. Undirected networks yield symmetric matrices. Directed networks yield asymmetric matrices.

agent Also called an “artificial agent.” A program that automatically performs duties for a computer user or a program that behaves like a person within a limited domain of operation.

agent-based modeling Simulation method that can build on discrete event simulation. In agent-based modeling of networks, we acknowledge the fact that individual nodes may differ from one another in roles, motives, behavior, or interactions. Agent-based techniques provide a facility for modeling networks that change with time (dynamic networks).

algebraic modeling system Computer implementation of mathematical programming that separates the structure (algebra) of constrained optimization problems from input data defining the parameters of those problems. Especially useful in sensitivity testing and stochastic programming.

Apache Software Foundation Established in 1999, an open-source community for soft- ware development and maintenance. Provides essential tools for operating on the World Wide Web.

application programming interface (API) Method for processing data requests between systems. Client-side programs interact with server-side applications to obtain data

This glossary defines technical terms and abbreviations used in data science. Readers desiring more complete dictionaries of computer and Internet terms can refer to Hale and Scanlon (1999) and Downing, Covington, Covington, Barrett, and Covington (2012). Moran and Hunt (2009) review terms relevant to website performance in search. Hyslop (2010), Casciano (2011), and Gasston (2011; 2013) review current HTML and CSS concepts. Robbins (2003) provides an intro- ductory treatment for web designers. Amor (2002) and Tannenbaum and Wetherall (2010) review data communications, the Internet, and World Wide Web. See Miller (2015d) for additional dis- cussion of terminology from web and network data science.

261

262 Sports Analytics and Data Science

within a defined structure, such as JavaScript Object Notation (JSON) or extensible markup language (XML). Often utilizes a representational state transfer (REST) for data interchange.

ARPANET Military-sponsored wide-area network, precursor to the Internet.

ASP Abbreviation for an Application Services Provider, a firm that provides outsourced application services. Also, in Microsoft systems, Active Server Pages.

association rules Machine learning models for identifying most frequently occurring item-sets or combinations of binary variables. Useful in market basket analysis and recommender systems.

bandwidth An expression that relates to the speed at which information travels over a network. The words “low bandwidth” mean slower speed and “high bandwidth” mean faster speed.

Bayesian statistics Inferential statistics built on probability theory, in particular, Bayes Theorem. Data are used to update a prior probability distribution, which represents researcher beliefs or assumptions about the world. The result of the updating process is a posterior probability distribution.

best-case/worst-case approach In decision analysis, the process of exploring extreme out- comes described as best case and worst case. A third situation commonly included in a best-case/worst-case approach is the expected outcome between the two extremes.

betweenness centrality Usually computed for nodes, this is an index that reflects the degree to which a node lies on the shortest path between other pairs of nodes. An index of node importance. For a network link, betweenness is similarly computed and represents the degree to which a link lies on the shortest path between pairs of nodes.

big data Term initiated by information technology firms to refer to the glut of data being collected and stored. Data are arriving at a faster pace and in larger quantities than ever before. Distributed, scalable database systems may be needed to accommodate the volume, velocity, and variety of data. NoSQL systems are often used in this context.

binary variable A variable that takes only two values, often coded as 0 and 1.

blog Shortened form of “weblog.” An asynchronous method of communication on the web. Often a personal column or diary, composed of short entries, perhaps relating to a specific topic. A blog can also involve multiple users interacting with a host or moderator, in which case it is a message board or asynchronous focus group with the discussion organized around themes or threads.

bootstrap sampling Resampling technique that involves repeated sampling with replace- ment from a sample. Provides method for estimating sampling distributions and the properties of statistics under random sampling. Working with a sample of N obser- vations, each bootstrap sample is a random sample of size N with replacement. Like cross-validation, bootstrap sampling can be used to evaluate predictive modeling tech- niques.

Data Science Glossary 263

boundary (of a network) The extent of the network with its included nodes and links. Defines where the network begins and ends—the population of interest.

bps Bits per second. Measure of speed across a communications link. Sometimes referred to as the “baud rate.”

brute force approach Process of exploring many alternatives (thousands or millions of options), taking advantage of computing power.

C, C++, C# Variations on the popular computer language C. Programs written in these languages require compilation prior to execution. C is a procedural language. C++ and C# (pronounced “C sharp”) are object-oriented extensions of C.

CART Abbreviation for “classification and regression trees.” Recursive partitioning method for tree-structured models used for both classification and regression problems. A ma- chine learning method.

cascading style sheet (CSS) Set of HTML rules for a website. Current version is CSS3.

chat room A virtual meeting room on the Internet where participants gather and speak to each other in real-time. May be public (open to anybody, space permitting) or private (requiring passwords to get in). Also called a “real-time focus group” or “synchronous focus group.” An online focus group with the moderator and participants present at the same time.

classical statistics Most commonly associated with classical hypothesis testing in which a null (no-relationship or no-differences) hypothesis is set up in order to be rejected in favor of an alternative hypothesis. When we reject the null hypothesis, we say we have a statistically significant result. Bayesian statistics presents an alternative to classical statistics.

classification Group of supervised learning methods designed to predict the value of a categorical variable or class. Distinct from regression.

client A computer through which users interact with the network or Internet. Web clients communicate with web servers. “Client” is also used to refer to the person or organi- zation for which research is conducted, the user of research and information services.

client-server application A computer application implemented with client and server computers communicating over the Internet.

closeness centrality A measure of node importance that characterizes how close a node is to all other nodes in the network, where closeness is the number of hops or links between nodes.

cluster analysis Multivariate statistical method for identifying groups in data. One pri- mary use in business is in market segmentation.

comma-delimited text (csv) File format and extension commonly used as input to spread- sheet programs and systems for statistical analysis.

264 Sports Analytics and Data Science

compile cycle Phrase used to describe the program development process with languages like C/C++/C and Java. We program, then compile, then execute the compiled code. This is in contrast with programming languages that are interpreted and have no formal compilation step.

conjoint analysis Better described as conjoint measurement. Statistical methods applied to the analysis of conjoint surveys, in an effort to measure consumer attitudes about a number of product attributes simultaneously.

content analysis The analysis of the meaning of text from qualitative research. Sometimes called thematic, semantic, and network text analysis, content analysis often starts with simple word counts. Also see text measures.

cookie Data stored on a research user’s workstation that may be used to identify the participant and to keep information about past transactions.

corpus A document collection (often a collection of transcripts) used in text analysis and text mining. The plural is “corpora.”

crawler (web crawler) A computer program for automated data acquisition from the web. Also called a spider, bot, or robot.

cross-sectional data Units of study are organized in ways that assume independence from one unit to the next. Data items are not adjacent in time or geography, so they are not dependent or related to one another.

cross-validation Resampling technique designed to test predictive modeling techniques. A sample is split repeatedly into training and test subsamples. Each predictive model is fit to the training subsample and evaluated on the test subsample. Multi-fold cross validation splits the sample into K subsamples, and on each iteration, one of the K sub- samples is used for testing and the other subsamples are used for fitting the model. Results for the K subsamples are averaged to provide an estimate of out-of-sample pre- dictive accuracy. Leave-one-out cross-validation sets K equal to the size of the sample, so that only one sample observation is used as the test subsample on each iteration. Cross-validation is sometimes referred to as internal cross-validation because it is inter- nal to the sample.

data mining Machine learning with large data sets. See machine learning.

data visualization General term for statistical graphics and information design graphics. Used for discovery (exploratory data analysis), diagnostics (model development and checking), and display (presentation, visual communication).

declarative language A computer program in which the statements provide as assertion about a desired result, rather than a sequence of steps for achieving a result. Examples are Prolog and SQL.

degree (of a network) Each node in an undirected network has a degree or number of links to other nodes. An index of node importance.

Data Science Glossary 265

degree centrality For a node, another term for degree. The average degree across all nodes in a network. A summary statistic for networks.

degree distribution The distribution or set of degree values for all nodes in a network.

density (of a network) The the proportion of actual links out of the set of all possible links. A completely unconnected or disconnected set of nodes has zero links, while a completely connected network of n nodes or clique has n(n−1)2 links. If l is the number of links in a network, then network density is given by the formula ln(n−1)/2 .

descriptive statistics Traditional statistical methods that are not intended to draw infer- ences from samples to populations. Statistical summaries of data that are neither ex- planatory nor predictive. Distinct from methods described as inferential statistics. Also called descriptives.

Document Object Model (DOM) Rules that define the proper arrangement or hierarchy of nodes (tree structure) for HTML on web pages.

eigenvector centrality For a node, we consider a node as important if it is close to other nodes of importance, which are in turn close to other nodes of importance, and so on. Much as the first principle component characterizes common variability in a set of variables, eigenvector centrality characterizes the degree to which a node is central to the set of nodes comprising the network.

Elasticsearch Open-source solution for document indexing, storage, search, and selection. Like Solr, it builds on Apache Lucene and Java-based algorithms for text analytics. Developed for distributed document stores.

e-mail Store-and-forward method for sending messages over the Internet. Sometimes used for interviewing and for surveys.

emoticon Use of characters on a keyboard to indicate emotions in online communication. Capital letters can be used for emphasis or to indicate a raised voice. Some of the more popular examples with special characters include :-) for a smile or happy response, ;-) for a wink or “just kidding,” and :-( for an unhappy or disapproving response. Also called “emoji.”

ethnography Observational or field study of social and consumer behavior in real life settings.

expected value A weighted average of values, with probabilities defining the weights. For observations, the expected value is the arithmetic mean.

experimental research Research setting in which the environment or aspects of the en- vironment can be manipulated by the researcher. Distinct versions of the environment represent experimental treatments. There is randomization through random assign- ment of subjects to treatments. As much as possible, there is control of factors that can have an effect on subject response. This type of research setting is contrasted with an

266 Sports Analytics and Data Science

observational research setting, in which no aspect of the environment can be manipulated by the researcher.

explanatory model A model relating one or more explanatory variables to one or more re- sponse variables. Understanding the underlying mechanism relating explanatory and response variables is an important aspect of the explanatory model, in contrast with a model that is purely predictive.

explanatory variable Variable used to predict or explain another variable (the response variable).

factor analysis Multivariate statistical procedure based on linear algebra. Useful in in- dentifying underlying dimensions in data. Builds on the foundation of principal com- ponents analysis. Distinct from principal components in that it focuses on common variance, not total variance. May be used to reduce the number of explanatory vari- ables needed for a predictive model.

frame An element of web design. Some web pages are constructed using frames, blocks of a page that a user can navigate within while all other frames remain static. For example, some online facilities utilize frames, with one frame for the chat stream, one for the text entry area, and another for stimuli to be displayed.

ftp File transfer protocol, one of a number of networking standards used over the Internet.

functional language Computer language that treats programming as an evaluation of mathematical functions, mapping sets of input values into sets of output values. A declarative programming paradigm. Examples are Scheme, Lisp, and Erlang. Pro- gramming in a functional style can be done within languages that are described as procedural or object-oriented.

game theory Specialization within mathematics and economics dealing with players, their knowledge, objectives, and strategies for achieving objectives. There are both competi- tive and cooperative games. As it is typically used, the term has no special reference to sports.

genetic algorithm Heuristic method guided by gene and mutation ideas from biology and population genetics. Used to solve problems that are not easily solved by traditional optimization or constrained optimization methods.

generalized linear model Class of predictive models (supervised learning models) from traditional statistics. These include linear regression, logistic regression, and Poisson regression, among other methods. The right-hand side of the prediction formula is a linear combination of explanatory variables.

generative grammar Linguistic term referring to the rules that we use to form meaningful utterances. A general term for morphology, syntax, and semantics.

Go (Golang) Open-source computer language originally developed at Google. Like C, C++, and C#, Go requires a compile cycle. Employs a concurrency model designed for fast execution in a distributed processing environment.

Data Science Glossary 267

graph theory Branch of mathematics introduced by Euler in the eighteenth century. Deals with mathematical structures that represent objects (nodes, vertices) and their relations (links, edges). Mathematical foundation of network science or social network analysis.

grounded theory A methodology for analyzing and interpreting qualitative data. The- ory is derived from the data. The analysis involves identifying categories and coding data by categories. Common themes and concepts emerge from observed relationships among categories.

Hadoop An open-source distributed file system on which database systems can be built. Not itself a database system. Often associated with discussions of big data.

heuristic Rule in complex modeling situations. Useful in optimization problems that cannot be easily addressed by mathematical programming.

hierarchical modeling Also called multi-level modeling. Traditional statistical modeling employing levels of parameters that must be estimated. Most commonly associated with Bayesian statistics.

HTML Hypertext markup language. Standard codes or tags in text files used to format web pages. The implemention of the DOM. Current version is HTML5. See cascading style sheet (CSS).

HTTP Hypertext transfer protocol. The dominant method for client-server communica- tion over the web.

indexing Process of coding text documents or database records so they may be easily located in the future.

inferential statistics Traditional statistical methods that draw inferences from samples to populations. The fitted models may be explanatory or predictive. Distinct from methods described as descriptive statistics.

information retrieval (search) A fundamental unsupervised application of text analytics. Text documents are indexed, making them searchable. A user searching for information enters a text query, which is matched up with the index for the text documents.

integer programming Methods of constrained optimization in which decision variables take integer values only. A special case is integer programming with binary decision variables.

integrated development environment (IDE) An integrated development environment fosters efficient code development by providing a graphical user interface, a programming- language-aware editor, debugging utilities, and a convenient mechanism for compiling and executing code.

Internet A public data communications network consisting of many interconnected net- works worldwide.

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Internet of Things (IoT) A network of physical objects with embedded electronics for communicating over a network.

intranet A data communications network internal to an organization.

IRC Internet Relay Chat, a form of chat room software.

ISP Internet Services Provider. An organization that provides connection services to the Internet. These organizations usually provide software applications that run over the Internet, such as browsers and search engines.

IT Abbreviation for “information technology.”

Java A general-purpose programming language introduced into the public domain by Sun Microsystems, with updates and support from Oracle. Especially useful in the de- velopment of online applications. Java programs require compilation prior to execution (a compile cycle).

JavaScript An object-oriented scripting language for the web. Preeminent language for client-side event handling. Embedded in web browsers. Implemented as a stand-alone language in Node.js, which can be used on the server side. JavaScript and Java are distinct languages.

JavaScript Object Notation (JSON) JavaScript data structure with unordered name/value pairs. Provides storage for arrays, strings, numbers, logical (boolean true/false), and the special value null. May be utilized directly in JavaScript code used in web pages.

JPEG Graphical bit-mapped file format for images.

knapsack problem A special case of integer programming. Gets its name from a knapsack or backpack that can hold only a certain total weight or volume of items. Each item to be placed in the knapsack has a certain weight or volume as well as a value to the person who is stuffing the knapsack. The objective is to maximize the value while satisfying the weight or volume constraint. The standard knapsack problem has binary decision variables (one item of each type which may or may not be placed in the knapsack) and one constraint, such as weight or volume capacity for the knapsack, but not both. The knapsack problem may be generalized to the case for which multiple items of each type may be placed inside, yielding an integer knapsack problem. It may also be generalized to the case of multiple constraints, such as restricting both the weight and a volume of the knapsack. With multiple constraints, we have the multidimensional knapsack problem (MKP).

kbps Kilobits per second. Measure of speed across a communications link.

keyword One word or a group of words used in search queries and indexed by search engine providers.

LAMP A public-domain suite for the development of online applications, this refers to the Linux operating system, Apache web server, MySQL database, and Perl, PHP, or Python programming languages.

Data Science Glossary 269

levels of measurement Dating back to the work of S. S. Stevens (1946), the distinction among nominal (categorical), ordinal (ranks), interval, and ratio measures.

linear regression Also called ordinary least-squared regression or just regression. A form of generalized linear model using a linear combination of explanatory variables to pre- dict a continuous response variable or variable having meaningful magnitude.

linear programming Methods of constrained optimization in which decision variables take continuous values only.

listserv An automated or moderated e-mail group (MEG). E-mail addresses of all partici- pants (respondents and moderator) are programmed into a listserv. Moderator initiates the thread of discussion. Any response to that message automatically goes to anybody on the listserv.

logistic regression A form of generalized linear model using a linear combination of explanatory variables to predict a discrete binary response variable.

longitudinal data Multiple observations for person or units of study across time periods, but also organized by cross-sections. Methods of analysis are called multiple time se- ries, panel, or longitudinal data analysis. Adjacent units in time can be expected to be more highly related to one another than units more distant in time.

Lucene Open-source algorithms for information retrieval (search). Foundation for Solr and Elasticsearch search applications.

machine learning Algorithms for analyzing data that use the data themselves to specify the form of the model. Machine learning methods are data-adaptive methods rather than traditional (classical or Bayesian) statistical methods, in which model specification and distributional assumptions are made in advance of analyzing the data. Common machine learning methods include tree-structured modeling, support vector machines, neural networks, and nave Bayes models. Sometimes called statistical learning and data mining.

Markov chain A stochastic process, finite/discrete or continuous, having the Markov property that the future is independent of the past. This is easiest to illustrate with a finite Markov chain. There are distinct states, and for any two states i and j, the probability of going from i to j is Pij regardless of the previous states of the process. The Pij values are called transition probabilities.

mathematical programming Methods of constrained optimization. General term for lin- ear programming, quadratic programming, and integer programming.

measurement The assignment of numbers to attributes according to rules.

mixed integer programming Methods of constrained optimization in which decision vari- ables take integer or continuous values.

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model Representation of the world in a way that can be captured by computer code. Ex- amples are stochastic (probability) and statistical models, mathematical programming, and simulation models.

modem Modulator demodulator. Communications equipment that encodes and decodes data for transmission over a communications network.

MongoDB Open-source document-oriented database system, often used for storing text data from the World Wide Web, social media, and information system processing logs. MongoDB is an example of a NoSQL database system.

morphology A branch of linguistics. Rules for forming complex words. Also see genera- tive grammar.

multi-level categorical variable Categorical variable that takes more than two values, as opposed to a binary variable. Also called a multinomial variable.

multiple imputation The preferred method of handing missing data is multiple imputa- tion. That is, we create a number of alternative data sets using existing data to predict what the missing data values may be, and then we analyze each of the resulting data sets.

MySQL A popular open-source, relational database system. Now distributed by Oracle Corporation.

näive Bayes model Machine learning model for classification that builds on the repeated application of Bayes theorem. It is called näive because it assumes that individual ex- planatory variables act independently in determining the response.

natural language processing (NLP) Using grammatical rules to mimic human communi- cation and convert natural language into structured text for further analysis. Natural language refers to the words and the rules that we use to form meaningful utterances.

netiquette Social behavior appropriate for working on the Internet. For example, typing USING ALL CAPITAL LETTERS is considered poor netiquette, as it is considered to be the online equivalent of shouting.

network Interconnected objects—nodes and the links connecting them. A data communi- cations network contains computer system nodes and data communication links. The links are electronic circuits, wired or wireless. Following the mathematics of graph theory, nodes are also called vertices and links are called edges.

network science Interdisciplinary study of networks, drawing on the mathematics of graph theory, physics, and the social sciences.

neural network Biologically inspired machine learning method that implicitly represents interactions among explanatory variables and non-linear relationships among explana- tory variables and the response. Connections among explanatory variables are set up in a network structure leading to ultimate connections to the response. May be used for classification or regression.

Data Science Glossary 271

NoSQL A database system that is distinct from a relational (SQL) system. Common NoSQL databases include key-value pairs, document, column-based, and graph-based systems.

object-oriented language Computer language that builds on classes of objects, which pro- vide a structure for embedding both data and methods for processing data. Examples are Java, Ruby, Python, and R.

observational research Distinct from experimental research. The researcher is unable to con- trol the environment or manipulate environmental conditions. Rather, the researcher observes events as they occur in the environment, making measures as things happen. Most business research is observational research.

offline Any methodology that does not make use of the Internet or World Wide Web, such as in-person focus groups or telephone focus groups.

online Any methodology that makes use of the Internet or World Wide Web, such as real-time chats, bulletin boards (message boards), and listservs (MEGs).

online community An aggregation of individuals that emerges through communication over the Internet. That is, a group of individuals that interacts online over an extended period of time. Also called virtual community. When used for primary research, an online community may consist of a group of fifty to two hundred people who have been recruited to participate in research about related topics over a period of three to twelve months. The research may incorporate a variety of methods, including online surveys, real-time focus groups, and bulletin boards.

operations research General term for technologies such as mathematical programming, queuing theory, and simulation methods.

organic search Natural search in which the search engine finds the most relevant matches to the user’s query. By far the most important component of relevance is the links a web page receives from other web pages. Organic search is distinct from paid search, in which search results are advertisements and links paid for by advertisers.

outlier Observed value of a variable that is outside the range of most other observed values.

PageRank Algorithm for computing the importance, credibility, or relevance of links in a web search. Analogous to eigenvector centrality.

paid search Search results that are advertisements and links paid for by advertisers. Dis- tinct from organic or natural search results.

panel A group of respondents that has been recruited to participate in many studies over a period of time.

panel data Another term for longitudinal data. Not necessarily related to a panel as a group of respondents.

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parameter Quantitative characteristic of a population distribution.

parser (text parser) A computer program that prepares text for subsequent analysis, re- placing one character string sequence with another. Often implemented with regular expressions.

Perl “Practical Extraction and Report Language.” Text processing and scripting language used extensively in web applications.

PHP Personal home page. A scripting language alternative to Perl, used extensively in web applications.

Poisson distribution Probability distribution for a discrete variable taking non-negative integer values. Useful in modeling counts, including runs scored and points scored in sports. Gets its name from the French mathematician Siméon Denis Poisson.

Poisson regression A form of generalized linear model using a linear combination of explanatory variables to predict a discrete response taking non-negative integer values (counts). Like the Poisson distribution, it gets its name from the French mathematician Siméon Denis Poisson.

population Complete set of observations of interest to the researcher. Samples are selected from a sampling frame identifying members of the population.

population distribution The distribution of interest to the researcher. Characterized by population parameters.

post (noun) Posting made by a participant (moderator, respondent, or observer) in a blog. A statement or question made by a participant in a real-time online group. (verb) To send a message.

posterior distribution Probability distribution of a parameter. In Bayesian statistics, the posterior distribution is obtained by using Bayes theorem along with a prior distribu- tion and the likelihood function for the sample data. It is “posterior” in the sense that it is the end product of a Bayesian data analysis, whereas the prior distribution begins the process. The Bayesian statistician uses Bayes theorem to revise his beliefs about population parameters, beginning with a prior distribution and ending with a poste- rior distribution. A “belief” in this context refers to a mathematical representation of the population or the unknown.

PostgreSQL A popular open-source, relational database system, written as “PostgreSQL” and often referred to simply as “Postgres.”

predictive model A model designed to predict as yet unobserved values of a response variable using observed values of explanatory variables. The objective is for the model to predict the response accurately, whether or not the underlying mechanism relating explanatory and response variables is understood.

principal component analysis Multivariate statistical procedure based on linear algebra. Useful in identifying underlying dimensions in data. Foundation for factor analysis.

Data Science Glossary 273

May be used to reduce the number of explanatory variables needed for a predictive model.

prior distribution Probability distribution of a parameter at the beginning of a Bayesian data analysis. The prior distribution (also referred to as the “prior”) is in place before any data are collected or analyzed. It represents the researcher’s prior belief about the population parameter.

procedural language Computer language that describes an algorithm or sequence of steps to achieve a certain result. Examples include Basic, Fortran and C. Python and R are often used as though they were procedural languages, ignoring their object-oriented foundations.

psychographics Demographics relating to psychological factors.

Python Open-source, object-oriented, general-purpose computer language. Widely used for text and data processing and web programming, as well as for traditional statistics and machine learning. Python programs do not require a compile cycle, so they are more quickly developed than programs in C/C++/C or Java.

queuing theory Q Mathematical models for understanding queuing or wait-time pro- cesses. Especially useful in the analysis of scheduling and traffic problems.

R Open-source, object-oriented language for programming with data. Widely used for traditional statistics, machine learning, and data visualization. R programs do not re- quire a compile cycle, so they are more quickly developed than programs in C/C++/C or Java.

random forests Machine learning method that uses a community or ensemble of tree- structured models. The method of random forests is an exemplary ensemble method. When building a random forest, we combine the predictions of thousands of tree- structured models. Prior to building each tree, we sample across explanatory variables without replacement, and we sample across observations with replacement (bootstrap sampling). After thousands of trees have been constructed, we average their predic- tions. See bootstrap sampling.

random network (random graph) A set of nodes connected by links in a purely random fashion.

random variable Real-valued quantities of interest. Continuous random variables can take any value along a segment of the real number line. Discrete random variables take integer values along the real number line.,

regression Group of supervised learning methods designed to predict the value of a vari- able with meaningful magnitude. Distinct from classification.

regular expressions Specialized syntax for identifying character strings, as needed for efficient search and text processing. Implemented in operating system shell search tools and various host languages, including Perl, Java, JavaScript, Python, and R.

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relational database Database composed of tables with row-and-column structure. Rows are often referred to as records, columns as fields.

reliability (of a measure) The degree to which repeated measures of the same trait agree with one another, as in test-retest reliability or split-half reliability. For multi-item scales, reliability is reflected in indices of internal consistency. These measures must be taken at about the same time. Reliability is not to be confused with stability, which refers to the degree to which measures relate to one another over time.

resampling Statistical procedure that involves repeated sampling from a sample. See bootstrap sampling and cross-validation.

sampling Process by which a subset of the population (rather than the entire population) is used for analysis and modeling.

sampling distribution Statistical term for the distribution of a sample statistic across re- peated samples from the population. Foundation for drawing inferences about the population using statistics from the sample.

sampling frame List of members of the population from which a sample is drawn.

Scala Open-source, object-oriented, general-purpose computer language that can utilize Java JVM libraries. Foundation language for Apache Spark.

scatter plot Statistical graphic for displaying the values of two continuous variables. Use- ful to examining relationships between variables.

scraper (web scraper) A computer program for identifying specific portions of data from the web. Utilized in the context of automated data acquisition from the web (web crawling) and often implemented with XPath syntax.

semantics A branch of linguistics. The study of meaning expressed through language. Also see generative grammar.

semantic web An idea for having web-based data defined and linked in a way that can be used by computers as well as by people. This requires wide acceptance of information coding standards such as XML.

semi-supervised learning Combination of supervised and unsupervised learning. Some observations have known response values, others do not. Common situation in text analytics.

sensitivity analysis Within mathematical programming, sensitivity analysis explores the degree to which the optimal solution is stable to variation in input data defining the pa- rameters of the model. A method, model, or process is “sensitive” when small changes in input result in large changes in output.

simulated annealing Heuristic modeling method inspired by the annealing process in metallurgy. Useful in optimization problems that cannot be easily addressed by math- ematical programming.

Data Science Glossary 275

simulation Capturing the essence of things in a computer program, so the computer program mimics or simulates behavior. Variations include discrete event simulation, process simulation, and agent-based modeling.

social network analysis Term used by social scientists when referring to applications of network science to the study of interactions between individuals, groups, or organiza- tions.

Solr Open-source solution for document indexing, storage, search, and selection. Like Elasticsearch, it builds on Apache Lucene and Java-based algorithms for text analytics.

Spark Real-time analytics environment that builds on Scala. Part of the Apache Software Foundation.

spatial data Observations have geocodes or location data affixed. Common geocodes are longitude and latitude. Methods of analysis are called spatial data analysis. Adjacent units in space are expected to be more highly related to one another than units more distant in space.

SQL Structured query language. A declarative syntax for describing a desired result and getting it back from a database. Associated with relational database systems.

stemming (word stemming) In text analytics, stripping affixes or reducing a word to its base or stem.

stochastic process A collection of random variables, either discrete or continuous.

stochastic programming Mathematical programming with uncertain input data. Rather than specify parameters as fixed input data, we use probability distributions. More easily implemented with algebraic modeling systems.

supervised learning In traditional statistics or machine learning, a model that recognizes the distinction between explanatory and response variables, with the explanatory vari- ables being used to predict the response variables. Major types of supervised learning include classification and regression.

support vector machine Machine learning method for classification that utilizes decision boundaries defined across sets of explanatory variables dividing the sample observa- tions into groups. These decision boundaries are known as support vectors.

syntax A branch of linguistics. Rules for forming phrases and sentences. Also see gener- ative grammar.

system logging Computer systems keep records of what is happening. These records themselves can serve the purposes of consumer and business research. NoSQL databases are frequently employed for this purpose.

TCP/IP Transmission Control Protocol/Internet Protocol. Basic protocol for computer-to- computer communications over the Internet.

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telnet Terminal-to-computer communication protocol used over the Internet.

text analysis General term for methods of analysis and interpretation of text, including content analysis, grounded theory construction, and text mining.

text measure Scores on attributes that describe text as in sentiment analysis. Text mea- sures can be used to assess personality, consumer preferences, and political opinions, just as survey instruments can. Text measures begin with unstructured text (docu- ments, transcripts) as their input data, rather than forced-choice questionnaire responses.

text mining The automated or partially automated processing of text. It involves impos- ing structure upon text and extracting relevant information from text. Like data min- ing, it is often associated with the analysis of large databases or document collections (corpora).

TF-IDF The term frequency-inverse document frequency measurement model. We note the frequency of distinct terms in each document, relative to the frequency of those terms across the entire document collection. A vector of TF-IDF values represents each document. Utilized in information retrieval (search) and various text analytics meth- ods.

thread A thread of discussion or conversation. The sequence of online messages relat- ing to a particular topic. Questions and statements that lead to other questions and statements. A term more prevalent in asynchronous focus groups (bulletin boards or message boards) than in real-time focus groups.

time series Multiple observations for a person or unit of study across time periods. Meth- ods of analysis are called time series analysis. Adjacent units in time can be expected to be more highly related to one another than units more distant in time.

traditional statistics General term for both classical and Bayesian methods, as opposed to machine learning methods. With traditional statistics, we specify the model in advance of analysis and make assumptions about underlying population distributions prior to fitting the model to sample data.

transitivity A measure of connectedness of a network. Also known as the average clus- tering coefficient of a network. Usually computed from the adjacency matrix as the proportion of fully connected triples (triads). A triad or triple is a set of three nodes, and a closed triad is a set of three nodes with links between each pair of nodes.

tree-structured model A model for classification or regression that builds a tree structure in relating explanatory variables to the response. The most important or useful ex- planatory variable is at the top of the tree. Variables become less important going from the top to the bottom of the tree. Implicitly represents interactions among explanatory variables in predicting the response. See CART.

unsupervised learning In traditional statistics or machine learning, a model that does not make a distinction between explanatory and response variables. Examples are associa- tion rules, cluster analysis, and principal components analysis. See machine learning.

Data Science Glossary 277

URL Uniform resource locator, address for Internet information resources.

Usenet Wide-area network precursor of the Internet.

validity (of a measure) The degree to which a measure measures what it is supposed to measure.

virtual community Another term for online community. Aggregation of individuals that emerges through communication over the Internet

virtual facility Adjective used to describe online the analogue of a real, physical research facility. For example, an online focus group software provides a virtual facility, analo- gous to a real in-person focus group.

virtual private network (VPN) Secure network connection for point-to-point communi- cation over the Internet.

web presence The degree to which an organization, brand, website, or web landing page is getting recognized on the web. What is often called “search engine optimization” (SEO) is one part of web presence. One way to assess web presence is to see where a site falls on the list of organic search results.

Wiki An exercise in collective expression on the web. Software that facilitates the process of generating a website that is editable by a group of contributors. Wiki web pages may be edited by anyone at any time, from any device with web browser access. Term comes from Hawaiian word “wiki,” meaning “quick.”

World Wide Web (web) Hypertext-linked data available over the Internet. These data are, for the most part, unstructured or semi-structured text that must be scraped and parsed prior to input to predictive models. WWW is an abbreviation for the World Wide Web.

XML Extensible markup language. Similar in structure and appearance to HTML, XML has a distinct purpose. It is a way of marking up data that describes the nature of the data.

XPath A specialized syntax for navigating across the nodes and attributes of the Docu- ment Object Model (DOM) and extracting relevant data.

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Baseball Glossary

ahead in the count From the batter’s point of view, a situation in which he has more balls than strikes. Opposite of behind in the count.

All Star Game In Major League Baseball, a game played toward the middle of the baseball season with players selected from various teams for their exceptional skills.

American League In Major League Baseball, one of two leagues composed of fifteen teams, five in each of three divisions. The American League allows the designated hitter. See National League.

around the horn Baseball slang for throwing the ball around the infield after completing a play with no one on base.

at bats (AB) Batting appearance in which the batter does not receive a base-on-balls (walk), is not hit by a pitch, and does not sacrifice (by bunt of sacrifice fly). The total at bats is used as the denominator in computing a player’s batting average. A subset of plate appearances.

away team The team that is playing a game away from its home stadium. Also called visiting team.

bailing out Baseball slang for a batter who’s foot closest to the pitcher moves away from home plate when swinging at the ball. May happen to a batter regardless of his batting stance (closed or open). Also, known as stepping in the bucket.

balk While pitching from the stretch with a runner on base, the pitcher must come to a complete stop before throwing to a position player covering the on-base runner. A balk

Developed in conjunction with Martin (2016), this is a guide to terms used by baseball players, managers, analysts, and fans. It provides an introduction to the language of the game as it has evolved over more than two hundred years of play in the United States. Official definitions of terms are provided by Major League Baseball (2015a). Hample (2007) reviews baseball slang. Rip- ken and Ripken (2004, 2007) explain baseball fundamentals for players and coaches. Additional useful resources are the MLB.com website and the Wikipedia (2015) Glossary of Baseball.

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is failing to come to a complete stop, and the runner is awarded the next base as a penalty to the team on the field.

ball A pitch outside the strike zone and is not hit by the batter. Any ball that touches the ground prior to reaching home plate.

ban on women Between 1952 and 1992, there was a ban on women in Major League Base- ball.

base One of four points that a runner must touch to score a run: first base, second base, third base, and home base (home plate).

base on balls (BB) The batter is awarded first base without hitting the ball because he receives four balls before getting three strikes. Also called a walk because the batter typically walks rather than runs to first base.

base runner Offensive player on base (first, second, or third base).

bases loaded Baseball slang for having runners on first, second, and third base.

base coach Team member in uniform designated by the manager to help with advising runners on the base paths. The first base coach advises runners on first about running to second base. The third base coach advises runners about running to home base.

base hit A hit in which the batter reaches as far as first base. See single (1B).

baserunner Offensive player who has reached one of the bases safely and remains on-base until the inning is over.

baserunning error An offensive player runs outside the base path or fails to touch a base. Counts as an out for the batting team, but is not recorded as an error in the box score for the team. Recorded errors are for the fielding team only.

batter Initial role of offensive player. Uses bat to hit the ball thrown by the pitcher. Stands in the batter’s box. Also called hitter.

batter in the hole Offensive player in the dugout set to be the batter after the batter on deck.

batter on deck Offensive player due next in the batter’s box. That is, the player set to follow the batter currently at bat. There is a special area called the next batter’s box where the batter on deck is supposed to stand or kneel.

batter’s box Area in which batter must stand while at bat.

battery The pitcher and catcher as a unit.

batting average (BA, AVG) Hits divided by at bats (with walks and sacrifices not counted in at bats):

BA = Hits

At Bats

Baseball Glossary 281

A batting average above 0.300 is highly valued. Batting below 0.200 (sometimes called the Mendoza Line) is tolerated only for pitchers and exceptionally good catchers and infielders. The average regular-season BA across the thirty MLB teams in the 2014 season was 0.251 (Sports Reference LLC 2015a). A rule of thumb in selecting batters is to look for BA values above 0.250—that is, we look for batters who get a hit about one in every four at bats. Hitters batting above 0.300 are rare.

batting stance A batter’s position in the batter’s box relative to home plate prior to the pitcher’s throwing the ball. Also see closed batting stance and open batting stance.

batting (team) The team on offense, as opposed to the team on defense (on the field).

behind in the count From the batter’s point of view, a situation in which he has more strikes than balls. Also called down in the count or in the hole. Opposite of ahead in the count.

bench Seating area for a team. Also called the dugout. Players not in the line-up are referred to as sitting on the bench. A team with talented players not in the line-up is said to have bench strength or a deep bench. Idiomatic expression: when an organization has many talented employees, it is said to have bench strength.

big leagues Major League Baseball. Affectionately called “the bigs.”

BIP (BPIP) Ball in play or ball put into play. When counting balls and strikes for a pitcher, balls put into play by hitters are strikes.

bloop single Term used for a ball that falls for a hit between the infielders and the out- fielders. Also called a “Texas Leaguer.”

bunt Batting strategy that involves holding the bat in a fixed position, rather than swing- ing the bat. With two strikes, a bunted foul ball results in a third strike.

call As a verb, the umpire calls plays (calls a pitch a ball or strike, calls a hit ball fair or foul, and calls a runner safe or out). As a noun, the umpire makes calls.

called game A game canceled or postponed by the umpire. Prior to lighted stadiums, a game might have been called due to darkness. Currently, games are commonly called due to rain.

catcher Defensive player who crouches behind home plate and catches balls thrown by the pitcher. The only player on the fielding team positioned in foul territory. Position number 2.

caught looking The batter is called out on strikes without swinging the bat.

caught off base A base runner is permitted to step off base but may be tagged out by a defensive player when off base.

caught stealing (CS) On an attempted steal, a base runner is tagged out prior to reaching the next base.

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center fielder Defensive player who plays in the middle of the outfield, between the left fielder and right fielder. Position number 8.

Championship Series At the end of the regular season, following the Wild Card Game, there are two Division Series playoffs in each league. The winners of these Division Series play each other in a best-of-seven series known as a Championship Series, one in the American League and one in the National League.

changeup An off-speed pitch (MLB speeds 70–85 mph). Speed, rather than movement, is what distinguishes this pitch from a fastball. Comes in various forms, including the circle changeup, three-finger changeup, and four-finger changeup (also known as a palm ball).

check swing A batter begins to swing at a pitched ball, but not far enough to be called a strike. Whether a batter’s swing is a check swing or a strike swinging is a matter of judgment. The call can be made by the home plate umpire, with possible appeal to the first base umpire for a right-handed batter or to the third base umpire for a left-handed batter.

choking up Holding the bat with hands away from the bottom (bat handle end) of the bat. A technique used by singles hitters who take shorter swings and have more control of the bat.

chop single Base hit in which the batter intentionally hits the ball down toward the ground so that it bounces high and is hard to catch in time to throw the batter out at first base.

clean-up hitter The fourth hitter in the line-up, selected because he has a good chance to get a hit with other runners on base.

closed batting stance A batter’s position in the batter’s box in which the foot closest to the pitcher is closer to home plate than the foot farthest from the pitcher.

closer Relief pitcher who ends a game.

clutch hitter A hitter who does well with runners on base and/or when the game is coming to an end and his team needs runs to avoid a loss.

coach Team member in uniform designated by the manager to help with coaching duties such as acting as a base coach.

command A pitcher with command can throws strikes when he needs to throw stikes. Also see control.

control A pitcher with control can throws strikes much more often than balls. Also see command.

cover the bases A player on the fielding team covers a base by standing close to the base. By being close to the base the fielder is ready to execute a tag out or a force out. Having a defensive player on every base is covering the bases. Idiomatic expression: when

Baseball Glossary 283

we prepare for every possibility, we cover the bases. When referring to a single base in baseball, it is common to use the phrase cover the bag, as a fielder would do for a pick-off play.

crowd the plate Batter stands in the batter’s box very close to home plate.

curveball (curve) A breaking ball much slower than a fastball (MLB speed 65–80 mph). With a right-handed pitcher throwing to a right-handed hitter or with a left-handed pitcher throwing to a left-handed hitter, a curve ball breaks away from the hitter. The standard curveball is the overhand curveball, affectionately known as Uncle Charlie or the hook. Some pitchers throw what is known as a knuckle curveball.

cut fastball (cutter) Also called a cut fastball. A fastball with movement.

cut-off position A position on the field of play between an outfielder and home plate. With a runner rounding the bases and heading for home, the outfielder can throw a ball toward home plate using a low trajectory, so an infielder in the cut-off position can intercept the ball and throw to another base, usually second base, to prevent another runner from advancing around the bases. Alternatively, the infielder cutting off the ball from the outfield can decide to throw the ball home enabling the catcher to tag the runner out. Because the infielder is closer to home base than the outfielder, the infielder’s throw is likely to be more accurate than the outfielder’s. Many outfielders do not have strong throws to home base, so throwing to the player in the cut-off position is essential.

dead ball Ball out of play, resulting in temporary suspension of play.

dead ball era Pre-1920 baseball. Period during which very few balls were used during games. There was no requirement to use a new white ball. Contrasted with live ball era.

dead red hitter A batter who can hit only when he gets the type of pitch he is looking for, such as a fastball. But when thrown another pitch, such as a curve, he has trouble hitting.

defense Team on the field, as opposed to the team that is up to bat (offense).

defensive indifference A runner on base attempts to take the next base, and the team on the field allows it. The situation occurs late in a game when the team on the field has a lead of more than one run, so an additional run by the hitting team will not win the game. When the official scorer rules defensive indifference, the runner’s act of taking the next base is not recorded as a stolen base.

designated hitter (DH) A player who has a place in the batting order but does not play a position in the field. This player hits in place of the weakest hitting player who takes the field (usually the pitcher). In Major League Baseball, the designated hitter role may be used in the American League, but not the National League.

diamond Another word for the baseball field of play. Gets its name from the square/diamond shape of the infield defined by the four bases.

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dig in Batter uses spikes on shoes to make a hole in the batter’s box.

Division Series After the end of the regular season, a best-of-five series of playoff games within a league between winners of the three divisions and/or the Wild Card Game. There are two division series within each league.

double (2B) A hit in which the batter reaches as far as second base. Also called a two- bagger.

double-header Two games played the same day. A standard double-header has two games with a short break between them. A day-night double-header has a number of hours between the games.

double play Getting two outs on one play. Various double plays are designated by player position numbers. For example, a 4-6-3 double play involves a throw from the second baseman to the shortstop, followed by a throw from the shortstop to the first baseman. An unassisted double play is a double play executed by one player alone.

double-switch Player substitution involving two players. Often used to substitute a posi- tion player along with a relief pitcher, with the position player (usually a better hitter) placed in the line-up so that he hits before the pitcher (usually a poorer hitter).

dugout Seating area for a team. Also called the bench.

earned run average (ERA) Index of pitching performance. The number of runs allowed (not due to errors) per nine innings of play. Also see WHIP.

expected runs Computed for any half-inning state or game situation, the number of runs the hitting team can expect to earn through the end of the half-inning. The computation is based on historical play-by-play data for the state or game situation. Expected runs are especially useful in the evaluation of alternative playing strategies, such as whether to use the sacrifice bunt or whether to attempt a stolen base.

extra-base hit Hit greater than a single. That is, a double, triple, or home run.

fair ball Ball hit inside the foul lines.

fair territory Region inside the foul lines.

fan Short for “fanatic” or “fancier.” Another earlier term was “crank.” A consumer of the sport, someone who loves the game and/or a particular team.

fantasy baseball Fans of baseball pretend to manage a Major League Baseball team by assembling a team of players. Enables fans to make decisions as if they were owners of teams. An early term for this activity was rotisserie baseball.

fastball Faster than any other type of pitch, has MLB speeds 80–100 mph. Comes in various forms defined by the pitcher’s grip on the ball, including the four-seam fastball, two-seem fastball, cut fastball (also called a cutter), and a split-finger fastball (also called a splitter). The four-seam fastball is faster but has less movement than other fastballs.

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fielder Player on defense.

fielder’s choice Batter arrives at first base because a fielder elects to get a runner out in place of the batter. Batter is not awarded a hit.

fielding error A defensive play that should have resulted in an out, but does not. Due to catching, not throwing. Also see throwing error.

first base The base a batter/hitter must touch first in order to get a hit.

first baseman Defensive player and infielder who plays closest to first base. His position number is 3.

five-tool player A player with strong baseball skills for running, fielding, throwing, hit- ting, and hitting with power.

fly ball Ball hit in the air, as opposed to a ground ball, but not hit low in the air, as opposed to a line drive.

fly out Ball hit in the air and caught in the air, resulting in an out. May be in fair or foul territory. Also called a fly ball out. Different from a ground out.

forfeited game Game ended by the umpire-in-chief in favor of a team that is leading by a score of nine to nothing or for violation of the rules of the game.

force out As opposed to a tag out, an out recorded when a defensive player with ball in hand or glove touches the base that a runner must advance toward because previous bases are occupied or about to be occupied. Also called a force play. Also see neighbor- hood play.

foul ball Ball hit out of play, outside the foul lines.

foul territory Region outside the foul lines.

foul tip A foul ball that comes directly off the batter’s bat and into the catcher’s glove or hand. It counts as a strike, including a third strike.

frame (a pitch) Catcher’s attempt to catch a ball thrown by a pitcher in a way that appears to be within the strike zone even if it does not fall within the strike zone.

free agent Player not under contract to any specific team and eligible to sign with any team.

full count Three balls and two strikes on the batter.

game (G) A baseball game or appearance in a game.

grand slam A home run with the bases loaded.

ground ball Ball hit on the ground, as opposed to a line drive or fly ball.

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ground out Batter is thrown out at first base after hitting a ground ball to one of the fielders. As opposed to a fly out.

ground-rule double When a hit bounces over a fence, leaving the field of play, the batter is awarded second base (a double).

hit (H) Batter hits the ball and reaches a base safely without the aid of an error, fielder’s choice, walk, or hit-by-pitch. Includes singles, doubles, triples, and home runs. Id- iomatic expression: a popular item is called a hit.

hit-and-run Offensive strategy intended to give the runner a head-start in moving to the next base. The batter tries to hit the ball regardless of where it is thrown in order to protect the runner.

hit batsman (hit by pitch, HBP) When a pitched ball hits the batter’s body, the batter is awarded first base.

hit for the cycle A hitter gets at least one single, double, triple, and home run in a game. An unusual accomplishment.

hitter Another term for batter.

hitting slump A batter is having trouble hitting for a number of games in a row, either having no hits or having very few hits.

hitting streak A batter is doing exceptionally well at the plate. Usually assessed by the number of games in a row with at least one hit. Joe DiMaggio holds the record, hitting safely in 56 consecutive games.

hitter’s park Parks such as Coors Field in Denver and Fenway Park in Boston are known to be favorable to hitters, yielding higher expected runs across all in-game states. As opposed to a pitcher’s park.

hitting for power Hitting home runs.

holding runner on base Activity of the first baseman, standing close to first base when a runner is at first base, so that the runner will take stay closer to the base (take less of a lead) to avoid being tagged out if the pitcher were to throw the ball to the first baseman. This is done so that the runner is less likely to steal second base.

home plate Flat rubber marker with a square shape facing toward the pitcher and a trian- gular side facing away from the pitcher. Catchers work in a crouched position behind home plate. When batting, players stand beside home plate in the batter’s box. And after running around the bases, they must touch home plate to score a run. Also called home base.

home run (HR) A hit in which the batter reaches as far as home plate. Also called a homer or the long ball. Usually obtained by hitting the ball over the fences. For an inside-the- part home run, the ball stays in the field of play while the batter runs around the bases,

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touching home plate safely. Idiomatic expression: when we do a good job on a project, we say we have hit a home run.

home team The team that is playing a game away in its home stadium. Also see away team or visiting team.

illegal pitch A pitch delivered by the pitcher without his pivot foot on the pitcher’s plate, a quick pitch, or a balk.

infielder Defensive player who plays close to the bases.

inning Unit of play in a baseball game. An inning consists of three outs. A full inning consists of the visiting team batting, followed by the home team batting. The top of the inning is the portion of the inning in which the visiting team is batting. The bottom of the inning is the portion of the inning with the home team batting.

intentional base on balls The pitcher gives a batter a base on balls without trying to throw strikes. Used as baseball strategy to avoid pitching to the hitter (who may be a good hitter) or to put a runner on first base so that force-outs are possible.

interference Offensive interference occurs when the batting team interferes with, ob- structs, impedes, or confuses any fielder attempting to make a play. For example, a runner hit by the ball while running interferes with the fielder trying to catch the ball. This is referred to as being soaked, and the runner is called out. Defensive interference occurs when the catcher’s glove touches the bat, affecting the batter’s swing or prevent- ing him from hitting the ball. There can also be umpire interference and spectator/fan interference.

in the hole From the batter’s point of view, a situation in which he has more strikes than balls. Also called down in the count.

keystone sack Another term for second base.

knuckleball A very slow pitch (MLB speeds 55–70 mph) with little spin that moves in an unpredictable manner. Also called a knuckler.

lead-off hitter The first hitter in the line-up, selected to begin the team’s hitting because he has a good chance of getting on base.

leave the yard (go yard) Baseball slang for hitting a home run.

left fielder (LF) Defensive player who plays on the left side of the outfield where “left side” is defined by looking at the field from home plate. Position number 7. Idiomatic expression: crazy ideas come out of left field.

left on base (LOB) Player on base while the team reaches three outs, ending that batting team’s half-inning.

lefty Player who bats or throws left-handed.

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line drive Ball hit in the air, as opposed to a ground ball, but not hit high in the air, as opposed to a fly ball.

lineup The order of players/hitters for a team submitted to the home plate umpire at the beginning of the game, with changes reported to the umpire during the game.

live ball A ball that is in play, as opposed to a dead ball.

live ball era After 1920 there was a requirement to use a new white ball in Major League Baseball. Contrasted with dead ball era.

making the turn A runner running to first base is permitted to run beyond the base and toward foul territory. If instead of running toward foul territory, the runner begins on the path to second base, he is referred to as making the turn and may be tagged out by a fielder.

manager Person responsible for a team’s actions on the field. May be one of the players.

manufactured run Run generated by a “small ball” strategy of getting runners on base and advancing them one base at a time by singles, walks, and stolen bases, as opposed to extra-base hits.

Mendoza Line Named after Mario Mendoza, a big league shortstop who’s lifetime batting average was .215. The Mendoza Line is a .200 batting average, thought to be a mini- mally acceptable batting average for a position player. A better term for this line might be the “Uecker Line,” after Bob Uecker, a strong defensive catcher whose career batting average with the Braves in Milwaukee and Atlanta, 1962–1967, was exactly .200.

men on base Batting team’s runners on first, second, and/or third base.

middle reliever Pitcher who enters a game after the start of the game and before the end of the game. Distinct from the starting pitcher and the closer.

middle infielder Second baseman or shortstop. See up the middle.

MLB Major League Baseball. Professional baseball organization in the United States. Currently composed of thirty teams in two leagues, fifteen in the American League and fifteen in the National League.

National League In Major League Baseball, one of two leagues composed of fifteen teams, five in each of three divisions. The National League does not allow the designated hitter. See American League.

neighborhood play When there is a close play at second base with the runner sliding into the base, a force out may be recorded even if the second baseman does not keep his foot on the base. As long as the second baseman’s foot is in the neighborhood of second base, the force out is recorded. This is to avoid injuries to the players who are wearing spikes on their shoes. See force out.

Baseball Glossary 289

no hitter Pitcher pitches nine innings without allowing a hit, although batters may reach base through walks or errors. Also see perfect game.

no-no Baseball slang for a no hitter. Think in terms of no hits and no runs scored by the other team. Also see perfect game.

obstruction A fielder impeding the progress of a runner while not in possession of the ball.

offense Team up to bat, as opposed to the team that in the field (defense).

official scorer Person designated to keep records of the game and make decisions about hits versus fielding errors.

on the field (team) The team on the field is the team playing defense, as opposed to the batting team.

on-base percentage (OBP) Proportion of plate appearances in which a batter reaches base through a hit, walk, or hit by pitch. Does not include reaching base by a fielding er- ror, fielder’s choice, dropped/uncaught third strike, fielder’s obstruction, or catcher’s interference. Also called on-base average (OBA). Usually presented as a proportion, not a percentage. Popularized by the Lewis (2003) book Moneyball and the subsequent movie by the same name, OBP is seen as a better index of offensive performance than batting average. Computed as

OBP = (Hits + Walks + Hit by Pitch)

(At Bats + Walks + Hit by Pitch + Sacri f ices)

Getting a walk or being hit by a pitch has the same effect as a base hit for the batter himself—they move the batter to first base without an out being recorded. The average regular-season OBP across the thirty MLB teams in the 2014 season was 0.314 (Sports Reference LLC 2015a). A rule of thumb in selecting good batters is to look for OBP values above 0.333—that is, we look for batters who get on base about one in every three plate appearances.

on-base percentage plus slugging (OPS) Measure of overall hitting prowess.

OPS = OBP + SLG

The average regular-season OPS across the thirty MLB teams in the 2014 season was 0.700 (Sports Reference LLC 2015a).

open batting stance A batter’s position in the batter’s box in which the foot closest to the pitcher is further away from home plate than the foot farthest from the pitcher.

out One of three units of play for the batting team. That is, there are three outs in a half- inning.

“out” Umpire call indicating that an out is to be recorded.

outfielder Defensive player who plays far away from the bases.

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overslide At second or third base, a runner can, after touching the base, go beyond the base and lose contact with the base. When the player loses contact with the base, he may be tagged out by a fielder. An overslide can occur at second and third base. An overslide is not relevant at first base where running beyond the base and toward foul territory is permitted. An overslide is not relevant at home base, where running beyond home base after scoring a run completes the runner’s path around the bases.

pace of play Also called pace of game. Major League Baseball has been experimenting with ways to speed up the game, focusing on unnecessary delays by pitchers or batters. This is controversial because the leisurely pace and lack of a time clock are attractions of baseball. The introduction of video replay affects pace of play, making games longer.

passed ball Pitch that gets past the catcher that is the fault of the catcher, as opposed to a wild pitch, which is the fault of the pitcher.

PECOTA A measurement and prediction system that uses player-comparable age curves as its base data. The name refers to Bill Pecota, a Kansas City Royals infielder from the 1980s.

perfect game Pitcher pitches nine innings without allowing a runner to reach base—no hits, no walks, no errors. Twenty-seven batters come to the plate, and they all make outs.

pick off assignment Designation of the fielder responsible for covering the bag for a pick off play. Relevant to pick offs at second base, where either the second baseman or the shortstop could cover the bag.

pick off play A pitcher throws to first, second, or third base in an attempt to catch a runner off base. The fielder receiving the ball must tag the runner out before the runner touches a base. Most commonly executed with a runner at first base.

pinch hitter Player batting for another player, replacing the original player in the lineup. The original player may not return to the game.

pinch runner Player running for another player who happens to be on base, replacing the original player in the lineup. The original player may not return to the game.

pitch Ball delivered by the pitcher to the batter.

pitch count The number of pitches (balls plus strikes) thrown by a pitcher after his entry into a game. This number is watched carefully by managers. A starting pitcher’s pitch count of one hundred is seen as a warning signal by many managers. With higher pitch counts, pitchers are more susceptible to injuries. At higher pitch counts, a pitcher’s fastball velocity is reduced. The pitcher is less effective in getting outs. Pitch count also refers to the number of pitches that a batter has faced in a given at-bat. The offensive team may employ a high-pitch-count strategy, attempting to take more pitches (balls and strikes) to drive up the starting pitcher’s pitch count, thus forcing that pitcher out of the game. This was one of the strategies popularized by the Lewis (2003) book Moneyball and the subsequent movie by the same name.

Baseball Glossary 291

pitcher (P) Defensive player responsible for throwing the ball to the batter. Position num- ber 1.

pitcher’s duel A game in which two dominant pitches are pitching, with very few runs being scored.

pitcher’s park Parks such as U.S. Cellular Field in Chicago and AT&T Park in San Fran- cisco are known to be favorable to pitchers, yielding lower expected runs across all in-game states. As opposed to a hitter’s park.

pitcher’s plate A rectangular hard rubber platform near the middle of the pitcher’s mound. The pitcher’s pivot foot must be on the pitcher’s plate prior to delivering the ball to the batter. Also called the rubber.

pitching from the stretch Instead of using a full windup, the pitcher uses a partial windup, coming to a full stop before throwing. Typically used when there is a runner on base.

pitching depth Number of pitchers a team has available for a game.

pitching mound Raised circular area from which the pitcher pitches.

pitching rotation The ordered set of four or five players that a team uses as its starting pitchers. Across games in the regular season, starting pitchers usually have a fixed sequence of appearance so that each pitcher has three or four days rest between starts.

pivot foot Pitcher’s foot that must be in contact with the pitcher’s plate when delivering the ball to the batter.

place hitter Hitter who controls the bat so well as to place the ball where no fielders can get to it, while keeping the ball in the park.

plate Baseball slang verb for scoring a run. Comes from the term “home plate.” So “they plate two” means “they score two runs.”

plate appearance Sum of at bats, walks, hit by pitches and sacrifices.

Plate A p perances = At Bats + Walks + Hit by Pitch + Sacri f ices

platooning A managerial strategy in which different lineups are used when facing right- handed versus left-handed pitchers. For example, the lineup may include more right- handed hitters when the starting pitcher of the opposing team is left-handed and more left-handed hitters when the starting pitcher of the opposing team is right-handed. This is done because right-handed hitters are expected to be less effective against right- handed pitchers and left-handed hitters are expected to be less effective against left- handed pitchers. These differences in effectiveness are due to the fact that a curve ball breaks away from a like-handed hitter, making it harder to hit.

“play ball” Umpire-in-chief’s order to begin the game.

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pop-up Ball hit in the air that does not travel far. Usually caught by an infielder, catcher, or pitcher.

position number Number associated with field position and used for official scoring: (1) pitcher, (2) catcher, (3) first baseman, (4) second baseman, (5) third baseman, (6) short- stop, (7) left fielder, (8) center fielder, and (9) right fielder.

position player Player other than the pitcher. That is, an infielder, outfielder, or catcher.

power hitter Baseball player who hits home runs.

productive at bat An at bat that advances a runner in some way, including a hit, sacri- fice bunt, sacrifice fly, or hitting behind a runner to advance the runner. Also called a productive out, with the opposite being an unproductive out.

pull hitter A right-handed batter who usually hits the ball between second and third base or to left field. Alternatively, a left-handed batter who usually hits the ball between first and second base or to right field. In response to pull hitters, some fielding teams put on a shift, moving players away from their normal positions.

pull the string Baseball slang for fooling a batter with a pitch, usually a curveball.

quick pitch A pitch delivered by the pitcher without giving the batter sufficient time to get situated in the batter’s box. Also called a quick return.

reaching for the fences Baseball player who tries to hit home runs.

regulation game Game that counts as an official completed game. Some games are can- celed. Others are postponed without being complete and must be completed at a later time or date.

relief pitcher Pitcher who enters the game after the starting pitcher has been removed from the game.

replay review A subset of umpire calls is subject to video replay review by umpires lo- cated in a remote location. These reviewable calls include potential home run calls, non- home-run boundary calls, specified fair/foul ball calls, force out/tag out calls, catches in the outfield, hit-by-pitch calls, collisions at home plate, tag-up calls, and various force-out/tag-out calls. Balls and strikes called by the home plate umpire are not re- viewable.

retouch Runner returning to base after passing a base. Runner must be touching the base to avoid being tagged out by a fielder.

reverse curve A breaking ball that moves in the opposite direction from a curveball. Also called a screwball or fall-away.

right fielder (RF) Defensive player who plays on the right side of the outfield where “right side” is defined by looking at the field from home plate. Position number 9.

Baseball Glossary 293

RISP Symbol for a runner in scoring position, which is a runner on second or third base because a single is usually enough to get that runner home.

rounding the bases Baseball slang for running around the bases, from first to second, to third, to home.

run Unit of scoring in baseball. Also called a score. Analogous to a point in football or basketball.

run batted in (RBI) When a runner scores as a result of a batter’s hit, sacrifice, or fielder’s choice out, the batter gets an RBI.

run down A runner caught between bases may be tagged out by a fielder. Often two or more fielders are involved in this activity, throwing the ball back and forth in an attempt to tag the runner out.

runner Offensive player no longer at bat, but on the base paths.

sacrifice bunt A bunt that successfully advances a baserunner.

sacrifice fly A line drive or fly ball that successfully advances a baserunner. The baserun- ner must tag the current base and advance to the next base without being tagged out.

“safe” Umpire call, awarding a base to a runner.

scoring position A runner on second or third base is referred to as a runner in scoring position because a single is usually enough to get that runner home.

screwball A breaking ball that moves in the opposite direction from a curveball. Also called a reverse curve or fall-away.

season In Major League Baseball, a baseball season consists of 162 games, 81 away games and 81 home games.

second base Base in the middle of the infield, between first and third bases. Also called the keystone sack.

second baseman Defensive player, infielder who plays closest to second base. Position number 4.

secondary lead A baserunner takes his initial lead off the base while the pitcher is in his windup. But after the pitcher throws the ball, the baserunner moves further away from the base. This additional distance from the base is known as a secondary lead.

semi-intentional walk A walk in which the pitcher pitches to the batter with the intention of walking him but without the catcher signaling an intentional walk. The event is recorded as a walk, rather than an intentional walk.

set position Legal pitching position usually used when offensive players are on base. In the set position, the pitcher comes to a complete stop prior to throwing the ball. The other legal position is the windup position. Also see balk.

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shadow ball Baseball pantomime or playing with an imaginary ball to entertain fans. Popularized in the black baseball teams during the depression.

shift On-the-field players playing out of position to adjust to the particular strengths of the hitter. For a right-handed pull hitter, for example, a shift may involve the second baseman playing between second base and third base, instead of in his normal position between second base and first base. The use of the shift is controversial. Fielders play- ing away from their normal positions may be less proficient in making double plays, executing pick offs, and taking cut-off positions. The shift also affects the integrity of baseball data. Suppose a third baseman is in a shift, playing between first base and sec- ond base with a left-handed pull hitter at bat. When that third baseman fields a ground ball between first and second base, throwing the batter out at first, the play is recorded as a 5-3 put out, implying that the ball was hit toward third base.

shine ball The pitcher rubs the ball clean on one side using his uniform, while applying dirt or powder on the other side. Employed to affect the ball’s trajectory.

shutout A complete nine-inning game thrown by one pitcher with no runs scored by the opposing team..

shortstop Defensive player, infielder who, like the third baseman, plays between second base and third base. But the shortstop is further from third base than the third baseman. Position number 6.

side-arm delivery Pitching delivery in between a common overhand delivery and an underhand delivery (as in softball).

single (1B) A hit in which the batter reaches as far as first base. Also called a base hit.

slider A ball gripped like a two-seam fastball, but slightly off-center. With MLB speeds 70–85 mph, it is not as fast as a fastball but breaks in the same direction as a curveball.

slugging percentage (SLG) Measure of hitting power. Babe Ruth’s slugging percentage was 0.690, the MLB all-time record. The maximum value possible is 4.0, implying that a player hits a home run in every at bat. Computed as

SLG = (Singles + (2 × Doubles) + (3 × Tri ples) + (4 × Home Runs)

At Bats

The average regular-season SLG across the thirty MLB teams in the 2014 season was 0.386 (Sports Reference LLC 2015a).

small ball Baseball strategy based on base hits, walks, and stolen bases. That is, runs are scored by advancing by one base at a time—manufactured runs. Also called an inside game, suggesting that the action is inside the base paths.

spin rate The rate of a pitched ball’s spin on its way from the pitcher’s hand to home plate. Fastballs with the same speed in miles per hour may have very different spin rates. Fastballs with low spin rates (fewer than 2,000 revolutions per minute) are sometimes

Baseball Glossary 295

called “heavy.” They appear to sink. Fastballs with high spin rates (more than 2,500 revolutions per minute) have more movement.

spitball Also called a spitter. The pitcher applies saliva or some foreign substance to the ball, which may affect the ball’s trajectory. Spitballs are not allowed in Major League Baseball, although some pitchers have been suspected of throwing spitballs.

squeeze play A batter bunts with a runner on third and fewer than two outs, trying to bring the runner home. With a suicide squeeze, the runner on third begins running home as the pitcher begins to throw the ball. With a safety squeeze, the runner on third begins running after the batter bunts the ball.

starting pitcher The pitcher who is in the starting line-up for a game, as opposed to a relief pitcher.

steal (stolen base, SB) Advancing from first to second base, second to third, or third to home without the assistance of a hit, passed ball, or wild pitch. The MLB success rate in stolen bases since 1990 is around 70 percent (Baumer and Zimbalist 2014).

stepping in the bucket Baseball slang for a batter whose foot closest to the pitcher moves away from home plate when swinging at the ball. May happen to a batter regardless of his batting stance (closed or open). Also, known as bailing out.

strike For a called strike, a pitched ball within the strike zone that the batter does not swing at on any strike. Or a ball that the batter hits foul on a first or second strike. For a strike swinging, a ball that the batter swings at but does not hit on any strike. Or, on a third strike, a ball that the batter swings at and hits foul directly into the catcher’s glove or hand, which is also known as a foul tip. Or, on an attempted bunt on the third strike, a bunt that is hit outside the foul lines is a strike swinging. For keeping a complete record of balls and strikes, any ball that is put into play (regardless of its position in the strike zone) is counted as a strike.

strikeout (K) A batter gets three strikes before getting four balls. Can be a strikeout look- ing or called strike three with the batter not swinging at the ball or a strikeout swinging. The symbol K represents a strikeout and may be thought of as coming from the word “knockout” or from the letter “k” in “strikeout.” The K is sometimes written backwards to indicate a strikeout looking. If first base is unoccupied by a runner and the catcher fails to catch the third strike, then the batter can be granted first base if he reaches that base before being forced out. The symbol SO is used to represent a strikeout or the number of strikeouts by a batter.

strike zone Rectangular region with its base width and depth defined by the area of home plate and its height defined by reference to the batter, extending from the batter’s kneecap to approximately three baseballs above the batter’s belt. Formerly, the upper range of the strike zone was the batter’s shoulders. The effective strike zone varies from one umpire to the next. A smaller or narrow strike zone favors the batter. A larger or wide strike zone favors the pitcher. Baseball analysts measure the size of the strike zone by area in square feet.

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suspended game A called game to be completed at a later time/date.

sweep Baseball slang for winning all games in a short series (usually three or four games) with another team. Also known as a “clean sweep.”

switch hitter Batter who can hit either from the left or right side.

switch pitcher Pitcher who can throw with either hand. Extremely rare player.

tagging up When there are fewer than three outs, a runner may keep his foot on a base, wait until a fly ball is caught, and then run to the next base. Upon tagging up in this way, the runner will be granted the next base if he is not tagged out by a fielder prior to touching the next base.

tag out As opposed to a force out, an out recorded for a runner by tagging him with the ball or glove containing the ball before the runner can touch the base. Also called a tag play.

take a lead (off base) A runner moves away from the base he is positioned at and in the direction of the next base in order to get a head start in running to or stealing the next base. See holding runner on base.

take a pitcher deep Baseball slang for hitting a home run.

Texas Leaguer Term used for a ball that falls for a hit between the infielders and the out- fielders. Also called a “bloop single.” The Texas League is a Double-A minor league baseball league, but there is no evidence that this type of hit is any more prevalent in that league than in any other league.

third base The base after first and second base that a runner must touch on his way to home plate to score a run.

third baseman Defensive player, infielder who plays closest to third base. Position num- ber 5.

three-bagger A hit in which the batter reaches as far as third base. Also called a triple.

throw Any act of throwing the ball in play other than pitching to the batter.

throwing error A defensive play that should have resulted in an out, but does not. Due to throwing, not catching. Also see fielding error.

tie game Regulation game called with home and away teams having the same number of runs. Rare event in baseball.

“time” An umpire call, interrupting play. The ball is dead while time is called.

tip a pitch An action by the pitcher that reveals the type of pitch that is being thrown. This could be the pitcher’s position on the pitcher’s plate (rubber), arm angle, or release point. If any of these varies with the type of pitch, an astute batter may be able to make

Baseball Glossary 297

an inference about the type of pitch being thrown. Knowing the type of pitch that is being thrown gives the batter an advantage in hitting.

total bases (TB) The number of bases a player gains as a result of hits. That is, the number of singles, plus two times the number of doubles, three times the number of triples, and four times the number of home runs.

triple (3B) A hit in which the batter reaches as far as third base. Also called a three-bagger.

triple crown Batter across the regular season who leads the league in batting average, home runs, and runs batted in.

triple-play Getting three outs on one play. Various triple plays are designated by player position numbers. For example, a 5-4-3 triple-play involves a throw from the third baseman to the second baseman, followed by a throw from the second baseman to the first baseman. An unassisted triple-play is a triple-play performed by one player alone.

two-bagger A hit in which the batter reaches as far as second base. Also called a double (2B).

umpire Person enforcing the official rules of Major League Baseball, calling safe or out on the base paths, fair or foul balls, and balls or strikes at home base. Four umpires are set for regular season games, associated with each of the bases and with the umpire at home base calling balls and strikes. In playoff games two additional umpires are added, one for the right field line and one for the left field line.

umpire-in-chief Lead umpire of the umpiring crew.

up the middle Sound defense up the middle refers to the play of the middle infielders (sec- ond baseman and shortstop) and the center fielder. Many teams put their best fielders in these positions because so many balls are hit toward the middle of the field (up the middle).

up to bat (team) The batting team or team on offense, as opposed to the fielding team.

visiting team The team that is playing a game away from its home stadium. Also called away team.

VORP A player’s value over a replacement player of average ability at the same position. Expressed in units of runs per game. A summary performance measure similar to WAR.

walk Batter awarded first base because four balls are called before three strikes. Also called a base on balls (BB).

walk-off balk A pitcher’s balk that brings a runner on third home to win a game in the bottom of the ninth inning. A very rare event. Could also be called a balk-off win.

walk-off hit A hit that scores a run for the home team in the bottom of the ninth inning, winning the game.

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walk-off home run A home run for the home team in the bottom of the ninth inning, winning the game.

WAR (WARP) Wins above replacement (player) across an entire season. A player’s value over a replacement player of average ability at the same position. A WAR value of 5, say, means that the team will win five fewer runs across the entire season if it has to replace the player. Expressed in units of wins across the season, with ten runs being equivalent to one win. Various proprietary versions of this measure exist, one varia- tion being wins above replacement player (WARP). WAR is a summary performance measure similar to VORP. The measure openWAR represents an open-source measure of WAR, which permits calculation from public-domain data sources.

WHIP Walks and hits allowed per inning pitched. Like earned run average (ERA), a summary measure of pitching performance.

Wild Card Game After the end of the regular season, a one-game playoff game between two wildcard teams, which are the teams with the best records without having won their divisions.

wild pitch Pitch that gets past the catcher that is the fault of the pitcher, as opposed to a passed ball, which is the fault of the catcher. A wild pitch is viewed as uncatchable.

windup position Legal pitching position usually used when there are no offensive players on base. In the windup position, the pitcher does not come to a complete stop prior to throwing the ball. The other legal position is the set position.

World Series Best-of-seven game playoff at the end of the Major League Baseball season, featuring the winner of the American League Championship Series (pennant) against the winner of the National League Championship Series (pennant). Played every year since 1903, with the exception of 1904 and 1994.

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Index

A adjacency matrix, 261 advertising research, 229 agent, 261 agent-based modeling, 261 Akaike information criterion (AIC), 54 algebraic modeling system, 145, 261 Apache Hadoop, see Hadoop Apache Lucene, see Lucene Apache Software Foundation, 261 Apache Spark, see Spark API, see application programming interface application programming interface, 175, 178,

179, 261 ARPANET, 175, 262 ASP, 262 association rules, 262 asynchronous focus group, see blog

B bandwidth, 262 baseball term

“out”, 289 “play ball”, 291 “safe”, 293 “time”, 296 ahead in the count, 279 All Star Game, 279 American League, 279 around the horn, 279 at bats (AB), 279 away team, 279 bailing out, 279 balk, 279 ball, 280 ban on women, 280 base, 280 base coach, 280

base hit, 280 base on balls (BB), 280 base runner, 280 baserunner, 280 baserunning error, 280 bases loaded, 280 batter, 280 batter in the hole, 280 batter on deck, 280 batter’s box, 280 battery, 280 batting average (BA, AVG), 280 batting stance, 281 batting team, 281 behind in the count, 281 bench, 281 big leagues, 281 BIP (BPIP), 281 bloop single, 281 bunt, 281 call, 281 called game, 281 catcher, 281 caught looking, 281 caught off base, 281 caught stealing (CS), 281 center fielder, 282 Championship Series, 282 changeup, 282 check swing, 282 choking up, 282 chop single, 282 clean-up hitter, 282 closed batting stance, 282 closer, 282 clutch hitter, 282 coach, 282 command, 282 control, 282

329

330 Sports Analytics and Data Science

cover the bases, 282 crowd the plate, 283 curveball (curve), 283 cut fastball (cutter), 283 cut-off position, 283 dead ball, 283 dead ball era, 283 dead red hitter, 283 defense, 283 defensive indifference, 283 designated hitter (DH), 283 diamond, 283 dig in, 284 Division Series, 284 double (2B), 284 double play, 284 double-header, 284 double-switch, 284 dugout, 284 earned run average (ERA), 284 expected runs, 62–65, 284 extra-base hit, 284 fair ball, 284 fair territory, 284 fan, 284 fantasy baseball, 284 fastball, 284 fielder, 285 fielder’s choice, 285 fielding error, 285 first base, 285 first baseman, 285 five-tool player, 285 fly ball, 285 fly out, 285 force out, 285 forfeited game, 285 foul ball, 285 foul territory, 285 foul tip, 285 frame (a pitch), 285 free agent, 285 full count, 285 game (G), 285 grand slam, 285 ground ball, 285 ground out, 286 ground-rule double, 286 hit (H), 286 hit batsman (hit by pitch, HBP), 286 hit for the cycle, 286 hit-and-run, 286 hitter, 286 hitter’s park, 286

hitting for power, 286 hitting slump, 286 hitting streak, 286 holding runner on base, 286 home plate, 286 home run (HR), 286 home team, 287 illegal pitch, 287 in the hole, 287 infielder, 287 inning, 287 intentional base on balls, 287 interference, 287 keystone sack, 287 knuckleball, 287 lead-off hitter, 287 leave the yard (go yard), 287 left fielder (LF), 287 left on base (LOB), 287 lefty, 287 line drive, 288 lineup, 288 live ball, 288 live ball era, 288 making the turn, 288 manager, 288 manufactured run, 193, 288 men on base, 288 Mendoza Line, 288 middle infielder, 288 middle reliever, 288 National League, 288 neighborhood play, 288 no hitter, 289 no-no, 289 obstruction, 289 offense, 289 official scorer, 289 on the field (team), 289 on-base percentage (OBP), 289 open batting stance, 289 out, 289 outfielder, 289 overslide, 290 pace of play, 290 passed ball, 290 PECOTA, 33, 34, 290 perfect game, 290 pick off assignment, 290 pick off play, 290 pinch hitter, 290 pinch runner, 290 pitch, 290 pitch count, 290

Index 331

pitcher (P), 291 pitcher’s duel, 291 pitcher’s park, 291 pitcher’s plate, 291 pitching depth, 291 pitching from the stretch, 291 pitching mound, 291 pitching rotation, 291 pivot foot, 291 place hitter, 291 plate, 291 plate appearance, 291 platooning, 291 pop-up, 292 position number, 292 position player, 292 power hitter, 292 productive at bat, 292 pull hitter, 292 pull the string, 292 quick pitch, 292 reaching for the fences, 292 regulation game, 292 relief pitcher, 292 replay review, 292 retouch, 292 reverse curve, 292 right fielder (RF), 292 RISP, 293 rounding the bases, 293 run, 293 run batted in (RBI), 293 run down, 293 runner, 293 sacrifice bunt, 293 sacrifice fly, 293 scoring position, 293 screwball, 293 season, 293 second base, 293 second baseman, 293 secondary lead, 293 semi-intentional walk, 293 set position, 293 shadow ball, 294 shift, 294 shine ball, 294 shortstop, 294 shutout, 294 side-arm delivery, 294 single (1B), 294 slider, 294 slugging percentage (SLG), 294 small ball, 294

spin rate, 294 spitball, 295 squeeze play, 295 starting pitcher, 295 steal (stolen base, SB), 295 stepping in the bucket, 295 strike, 295 strike zone, 295 strikeout (K), 295 suspended game, 296 sweep, 296 switch hitter, 296 switch pitcher, 296 tag out, 296 tagging up, 296 take a lead (off base), 296 take a pitcher deep, 296 Texas Leaguer, 296 third base, 296 third baseman, 296 three-bagger, 296 throw, 296 throwing error, 296 tie game, 296 tip a pitch, 296 total bases (TB), 297 triple (3B), 297 triple crown, 297 triple-play, 297 two-bagger, 297 umpire, 297 umpire-in-chief, 297 up the middle, 297 up to bat (team), 297 visiting team, 297 VORP, 297 walk, 297 walk-off balk, 297 walk-off hit, 297 walk-off home run, 298 WAR (WARP), 298 WHIP, 298 Wild Card Game, 298 wild pitch, 298 windup position, 298 World Series, 298

Bayesian statistics, 54, 144, 198, 199, 204, 205, 262

Bayes information criterion (BIC), 54 Bayes’ theorem, 204 hierarchical modeling, 79, 267

best-case/worst-case approach, 144, 262 betweenness centrality, 232, 262 big data, 262

332 Sports Analytics and Data Science

binary variable, 262 biologically-inspired methods, 216 black box model, 215 bootstrap method, 55, 57 bootstrap sampling, 262 bot, see crawler (web crawler) boundary (of a network), 263 bps, 263 brand positioning, see marketing, brand posi-

tioning breakeven analysis, see cost-volume-profit

analysis brute force approach, 263 bulletin board, see blog

C C, C++, C#, 172, 173, 263 CART, 263 cascading style sheet (CSS), 263 case study

Return of the Bobbleheads, 112 censoring, 112, 206, 207 chat room, 263 choice uncertainty, see decision analysis classical statistics, 199, 203, 205, 263

null hypothesis, 203 power, 204 statistical significance, 203, 204

classification, 198, 211–213, 215, 263 predictive accuracy, 211–213

client, 263 client-server application, 263 closeness centrality, 232, 263 cloud computing, 183 cluster analysis, 71, 73, 122, 216, 263 coefficient of determination, 211 comma-delimited text (csv), 263 compile cycle, 264 complexity, of model, 213 conjoint analysis, 78, 79, 264 consumer heterogeneity, see market segmenta-

tion, consumer heterogeneity consumer surplus, see pricing research, con-

sumer surplus content analysis, 264 continuous random variable, see random vari-

able, continuous cookie, 264 corpus, 264 cost-volume-profit analysis, 135–138 crawler, 175–178, 183, 264 cross-sectional data, 264 cross-validation, 55, 56, 214, 264 CSS, see cascading style sheet (CSS)

csv, see comma-delimited text (csv) cumulative frequency distribution, see data vi-

sualization, cumulative frequency distri- bution

customer lifetime value, 125 CVP analysis, see cost-volume-profit analysis Cython, 172

D data mining, see machine learning data organization, 227 data partitioning, 55 data preparation, 181

missing data, 182 data science, 197, 198 data visualization, 264

biplot, 81 box plot, 102, 104 cumulative frequency distribution, 239, 248 diagnostics, 109, 213 differential runs plot, 236 heat map, 161, 162 histogram, 10, 154, 157, 159, 160 lattice plot, 10, 105–108, 238 moving fraction plot, 237, 245, 246 Sankey diagram, 80 scatter plot, 11 spine chart, 72, 77, 78, 82, 88 strip plot, 105, 107

data-adaptive research, 52, 53 database system, 180, 181

MongoDB, 183, 270 MySQL, 270 non-relational, 183 NoSQL, 271 PostgreSQL, 183, 272 relational, 181, 183

decision analysis, 142, 143 decision tree, see decision analysis decision uncertainty, see decision analysis declarative language, 264 degree (of a network), 264 degree centrality, 265 degree distribution, 265 density (of a network), 265 descriptive statistics, 265 discounted cash flow analysis, 139–141

discount rate, 139 net present value (NPV), 139 payback period, 140 return on investment (ROI), 140

discrete random variable, see random variable, discrete

Document Object Model (DOM), 176, 265, 267

Index 333

document store, 173, 177, 179, 180 DOM, see Document Object Model (DOM)

E e-mail, 265 eigenvector centrality, 232, 265 Elasticsearch, 173, 182, 183, 225, 265 Elo rating/ranking system, 40 emoji, see emoticon emoticon, 265 ethnography, 265 expected value, 265 experimental research, 265 explanatory model, 198, 266 explanatory variable, 51, 52, 124, 207, 266 exploratory data analysis, 102

F factor analysis, 81, 266 fantasy sports, 35, 129, 130 forecasting, 229 Fortran, 172 frame, 266 ftp, 266 functional language, 266

G game theory, 266 game-day strategy, see strategy, playing General Inquirer, 223 generalized linear model, 214, 266 generative grammar, 266 genetic algorithm, 266 genetic algorithms, 216 Go (Golang), 172, 182, 266 graph theory, 267 grounded theory, 267

H Hadoop, 267 heuristic, 216, 267 hierarchical modeling, see Bayesian statistics,

hierarchical modeling HTML, 175, 267 HTTP, 267

I imputation, see multiple imputation in-game strategy, see strategy, playing indexing, 267 inferential statistics, 267 information retrieval, 182, 183, 220, 225, 267

injuries, 185, 189 integer knapsack problem, see mathematical

programming, knapsack problem integer programming, 267, see mathematical

programming, integer programming integrated development environment (IDE),

267 interaction effect, 213 Internet, 175, 267 Internet of Things, 170, 268 Internet Services Provider, 268 intranet, 268 investment analysis, see discounted cash flow

analysis IoT, see Internet of Things IRC, 268 IT, 268

J Java, 172, 173, 268 Java Virtual Machine, see Java JavaScript, 268 JavaScript Object Notation (JSON), 179, 268 JPEG, 268 JSON, see JavaScript Object Notation (JSON) JVM, see Java

K kbps, 268 keyword, 268

L LAMP, 268 leading indicator, 229 leave-one-out cross-validation, see cross-validation levels of measurement, 269 linear model, 207, 214 linear predictor, 207 linear programming, 269, see mathematical

programming, linear programming linear regression, 269 Linux, 173, 183 listserv, 269 logging, see system logging logistic regression, 42, 52, 211, 269 longitudinal data, 269 Lucene, 173, 225, 269

334 Sports Analytics and Data Science

M machine learning, 215, 216, 269 Major League Baseball, see MLB Major League Soccer, see MLS market basket analysis, 73 market response model, 111, 226–229 market segmentation, 79, 120–122

consumer heterogeneity, 127, 131 marketing

competitive analysis, 128, 129 mass marketing, 123 one-to-one marketing, 123 product positioning, 71, 72, 74 strategy, 128, 129 substitute products, 74 target marketing, 120

marketing mix model, 111, 228 Markov chain, 62, 269

transition probability, 62, 269 mass marketing, see marketing, mass market-

ing mathematical programming, 127, 200, 269

integer programming, 200, 201, 267 knapsack problem, 41, 200, 201, 268 linear programming, 200, 269 mixed integer programming, 200, 269 stochastic programming, 134, 145, 275

measurement, 23–35, 269 accessible measure, 31 comprehensible measure, 31, 32 construct validity, 24, 27 content validity, 24, 224 convergent validity, 27 discriminant validity, 27 explicit measure, 31 face validity, 24, 224 levels of measurement, 28–29 multitrait-multimethod matrix, 24–26 predictive validity, 24 reliability, 24–26, 30, 274 tractable measure, 31 transparent measure, 31, 33 validity, 24, 26, 27, 31, 32, 277

MEG, see listserv mixed integer programming, 269, see math-

ematical programming, mixed integer programming

MKP (multidimensional knapsack problem), see mathematical programming, knap- sack problem

MLB, 4, 5, 9–11, 64, 65, 170, 201, 232, 233, 256, 288

MLS, 257 model, 270

model-dependent research, 52, 53 modem, 270 Moneyball, 9 MongoDB, see database system, MongoDB morphology, 270 multi-fold cross-validation, see cross-validation multi-level categorical variable, 270 multi-level modeling, see Bayesian statistics,

hierarchical modeling multidimensional knapsack problem, see math-

ematical programming, knapsack prob- lem

multidimensional scaling, 71, 72, 81 Jaccard index, 73 perceptual map, 12, 13, 70–72, 241 similarity judgment, 71–73

multinomial variable, see multi-level categori- cal variable

multiple imputation, 270 multivariate methods, 81 MySQL, see database system, MySQL

N näive Bayes model, 270 National Basketball Association, see NBA National Football League, see NFL National Hockey League, see NHL natural language processing, see text analytics,

natural language processing NBA, 4, 6, 9, 10, 12, 38–40, 65–67, 170, 238, 239,

258 nearest-neighbor analysis, 73 net present value, see discounted cash flow

analysis, net present value (NPV) netiquette, 270 network, 270 network science, 270 neural network, 270 NFL, 4, 7, 9, 10, 170, 259 NHL, 260 NLP, see text analytics, natural language

processing NoSQL, see database system, NoSQL NPV, see discounted cash flow analysis, net

present value (NPV)

O object-oriented language, 271 observational research, 271 on-base percentage plus slugging (OPS), 289 one-to-one marketing, see marketing, one-to-

one marketing online community, 271, 277

Index 335

operations research, 271 optimization, 216 organic search, 271 Orme, B. K., 131 outlier, 271 over-fitting, 213

P PageRank, 271 paid search, 271 paired comparisons, 42 panel, 271 panel data, 271, see longitudinal data parameter, 272 parametric models, 213 parser, 176, 177, 272 payback period, see discounted cash flow anal-

ysis PECOTA, see baseball term, PECOTA perceptual map, see multidimensional scaling,

perceptual map Perl, 272 PHP, 272 Poisson distribution, 272 Poisson regression, 206, 207, 210, 214, 272 population, 272 population distribution, 272 Porter five-forces model, 128, 129 post, 272 posterior distribution, 272 PostgreSQL, see database system, PostgreSQL predictive analytics

definition, 51 predictive model, 198, 272 preference scaling, 81 price elasticity, see pricing research, price elas-

ticity price sensitivity, see pricing research, price sen-

sitivity pricing research, 126

consumer surplus, 128 price elasticity, 126 price sensitivity, 127 reference price, 127 three Cs of pricing, 126 willingness to pay, 75, 78, 79, 126, 127

principal component analysis, 81, 216, 272 prior distribution, 273 probability, 64

binomial distribution, 158 negative binomial distribution, 156, 158, 161 Poisson distribution, 156, 158, 161

procedural language, 273

product positioning, 81, see marketing, prod- uct positioning

psychographics, 273 Python, 171–173, 182, 273 Python package

json, 189 matplotlib, 86, 116, 242 numpy, 86, 99, 116, 168, 242 os, 186 pandas, 99, 116, 242 patsy, 99 scipy, 116, 168 scrapy, 186 sklearn, 86 statsmodels, 99, 116, 242 twitter, 189

Q queuing theory, 273

R R, 171–173, 182, 273 R package

car, 113 ggplot2, 18, 245, 246, 248 grid, 18, 245, 246, 248 lattice, 16, 113, 167 lubridate, 248 MASS, 83 plyr, 248 support.CEs, 88

R-squared, 211 random forests, 273 random network (random graph), 231, 273 random variable, 273

continuous, 273 discrete, 273

real-time analytics, 171, 172, 182 real-time focus group, see chat room recency-frequency-monetary value (RFM) model,

126 reference price, see pricing research, reference

price regression, 52, 108–111, 197, 206, 213, 273

nonlinear regression, 214 robust methods, 214 time series regression, 228

regular expressions, 178, 273 regularized regression, 213 relational database, 274 reliability, see measurement, reliability resampling, 274 response, 51 response variable, 124, 206

336 Sports Analytics and Data Science

return on investment, see discounted cash flow analysis

robot, see crawler (web crawler) ROI, see discounted cash flow analysis root-mean-square error (RMSE), 211

S sales forecasting, 226, 228 sampling, 274

sampling variability, 204 sampling distribution, 274 sampling frame, 274 Scala, 172, 274 scatter plot, 274 scheduling, 216 scraper, 176, 177, 274 search, see information retrieval semantic web, 274 semantics, 274 semi-supervised learning, 216, 274 sensitivity analysis, 145, 274 sentiment analysis, 222–225 shrinkage estimators, 213 similarity judgment, see multidimensional

scaling, similarity judgment simulated annealing, 274 simulation, 148, 153, 214, 275

benchmark study, 214, 215 game-day, 59, 151, 152 what-if analysis, 198

small-world network, 231 smoothing methods, 213

splines, 214 social network analysis, 230, 275 Solr, 225, 275 Spark, 172, 182, 275 spatial data, 275 spider, see crawler (web crawler) SQL, 181, 275 statistic

interval estimate, 203 p-value, 203 point estimate, 203 test statistic, 203

statistical learning, see machine learning stemming (word stemming), 275 stochastic process, 275 stochastic programming, see mathematical

programming, stochastic programming strategy

playing, 61–68 strength of schedule, 38 structured query language, see SQL

substitute product, see marketing, substitute product

supervised learning, 206, 216, 222, 275 support vector machine, 275 survival analysis, 206, 207 synchronous focus group, see chat room syntax, 275 system logging, 275

T target marketing, see marketing, target market-

ing TCP/IP, 275 telnet, 276 term frequency-inverse document frequency,

see TF-IDF text analytics, 217–225

content analysis, 223 document annotation, 35 generative grammar, 217, 218 latent Dirichlet allocation, 216 latent semantic analysis, 216 morphology, 218 natural language processing, 217, 224, 270 semantics, 218 stemming, 219 syntax, 218 terms-by-documents matrix, 219, 221 text analysis, 276 text feature, 35 text measure, 35, 223–225 text summarization, 222 thematic analysis, 216, 223

text measure, 276 text mining, 276 text parser, see parser TF-IDF, 220, 276 thread, of discussion, 276 time series, 276 time series analysis, 226–229

ARIMA model, 227 state space model, 228

time-value of money, 142 traditional research, 52 traditional statistics, 276 training-and-test regimen, 54, 55, 105, 108, 198,

199 transition probability, see Markov chain, tran-

sition probability transitivity, 276 tree-structured model, 276

Index 337

U unidimensional scaling, 38, 40, 42, 43 unsupervised learning, 216, 220, 276 URL, 175, 277 Usenet, 277

V validity, see measurement, validity variable transformation, 213 virtual facility, 277 virtual private network (VPN), 277 VPN, see virtual private network

W web, see World Wide Web

web board, see blog web presence testing, 277 web scraper, see scraper weblog, see blog Wiki, 277 willingness to pay, see pricing research, will-

ingness to pay WNBA, 255 Women’s National Basketball Association, see

WNBA World Wide Web, 174, 175, 183, 277 WWW, see World Wide Web

X XML, 277 XPath, 176, 277