Help with Optimization and Decision Support Modeling for Business project

Maximizing UA Men’s Basketball Performance

(Authors' names are anonymized)

Agenda ● Introduction

○ Problem Definition ○ Motivation

● Model Formulation ○ Data ○ Model

● Results/Findings/Implications ○ Solution Findings ○ Solution Implications ○ Model Validation

● Conclusion ○ Summary ○ Future Work

Introduction ● Problem: The University of Arizona Men’s Basketball team wants to improve

their average overall team performance. ○ Maximize combined team +/- per game played given player statistics and position and play time

constraints.

● Motivation: ○ To remain a leader in the PAC-12 ○ To make it to at least the Final Four in March Madness

■ Conferences receive NCAA funding based on tournament performance, which is then distributed to schools. Each team in conference earns one unit per game played in the tournament and this is paid for the next 6 years with some annual adjustments.[1]

● 2022 Unit Size= $338,887. Paid out to teams over 6 years ≃$2,033,322

● EX: Pac-12’s earned 11 units in 2016, resulting in a total six-year payout of $18,762,162

by 2022

Model Formulation ● The data that are gathered in this investigation come from two separate

sources: ○ Season Average Team Stats: Sportsradar.com ○ Individual Player Total Stats: sports-reference.com

● Stat Categories of Interest: ○ Field Goals Made (FGM) ○ 3 Point Field Goals Made (3PM) ○ 2 Point Field Goals Made (2PM) ○ Free Throws Made (FTM) ○ Offensive Rebounds (OR) ○ Defensive Rebounds (DR) ○ Personal Fouls (PF)

○ Rebounds ( R) ○ Assists (A) ○ Steals (Stl) ○ Blocks ○ Points (Pts) ○ Turnovers (T)

Model Formulation ● Once the data were gathered, each player’s season total amount for a

particular stat category was divided by the total amount of minutes they played this season.

○ Example: Adama Bal ■ Total Minutes: 104 ■ Total Field Goals Made: 13 ■ Field Goals Per Minute Played: 13/104 = 0.125

● After performing this calculation for each player and stat category, this information was input as the project data

Model Formulation ● Objective Function: Maximize the combined team +/- statistic

○ Big Idea: Using each player’s +/- statistic per minute, we can maximize combined +/-

● Decision Variable: Xi, how many minutes player i should play.

Model Formulation ● Constraints:

○ Stat Constraints ■ At least achieve season averages for each stat category to give the team the best chance

to win a game. ● Two “Negative” Stat Categories: Personal Fouls and Turnovers

○ Fatigue & Injury Constraints ■ Limit amount of time players can play to limit fatigue and injuries

● Generally Accepted Value: 36 minutes ○ Assuming overtime does not happen

○ Minute Constraints: ■ There is a limited amount of minutes available to give to the entire team

● 200 Minutes (40 minutes regulation * 5 players) ● Front Court: No More Than 80 Minutes (Conditioning Concerns) ● Back Court: No Less Than 120 Minutes (More Durable)

○ Minutes Played Integer Constraint

Results- Findings ● Linear Programming Solution:

● Total +/- of Game= 58.35

● Integer Programming Solution:

● Total +/- of Game= 57.44 ● LP slightly more optimal but less realistic

Results- Implications ● Solution is sensitive ● Team performance will

worsen if Pelle Larsson plays ○ He’s a key 6th man but

less efficient than starters

Results- Implications ● If minimum 3 point field goals per

game decreases to 7.70, overall team performance increases to 59.5

● If minimum defensive rebounds per game decreases to 28.26, overall team performance increases to 59.67

● If minimum assists per game decreases to 19.66, overall team performance increases to 61.01 ○ Players with less assists on average

but overall better +/- get more playing time

Results- Implications

Results- Implications ● Increased Minutes: Bennedict, Kerr,

Jordan, Justin, Azuolas, & Christian ○ Largest Increases: Christian, Azuolas, & Justin

● Decreased Minutes: Adama, Dalen, Grant, Tautvilas, Shane, Oumar, & Pelle ○ Largest Decreases: Pelle, Oumar, & Shane

● Big Idea: Maximize minutes of most productive players and decrease minutes of least productive players.

● Most Competitive Minutes: Backcourt

Conclusion ● Investigative Question

○ How should we assign UA player minutes to exceed the average statistical performance? ○ Big Idea: Maximize team +/- by assigning minutes based on player per minute stat contributions

● Solution & Findings ○ Player Minute Increases: Bennedict, Kerr, Jordan, Justin, Azuolas, & Christian ○ Player Minute Decreases: Adama, Dalen, Grant, Tautvilas, Shane, Oumar, & Pelle ○ Big Idea: Maximize minutes played by most productive players

■ Garbage Time Minutes ■ Most Competitive Allocation of Minutes: Backcourt

● Future work ○ Develop regression and classification models to predict overall team performance ○ Add more constraints after conferring with coaching staff ○ Add more statistical categories that may be of interest to the coaching staff ○ Develop a model for the UA Women’s Basketball Team

References 1. https://www.latimes.com/sports/story/2021-04-03/march-madness-pac-12-succ

ess-additional-money 2. https://developer.sportradar.com/member/register 3. https://www.sports-reference.com/cbb/schools/arizona/2022.html