Econometrics Research Paper

Golf Performance: Key Attributes for a New Age

Introduction:

According to the National Golf Foundation, golf is one of the most popular sports in the United

States. With a participation rate of 8.2%, it ranks just behind tennis as the 7th most popular sport

by TV viewership (Das). Unlike many sports, where athleticism was assumed to be a key

component of success, this realization has been a recent phenomenon in Golf. Seeing

photographs of Ben Hogan or Arnold Palmer smoking while considering a shot reinforces this

opinion or John Daly’s admission: "I went in the locker room and downed like five beers, and I

think I shot 4 under on the front nine.” (Torres)

That attitude has now changed. Golfers today are noticeably fitter, leaner and more athletic in

appearance to even the most casual observer. In 1997, John Daly became the first golfer on the

PGA Tour to average more than 300 yards per drive. That year, he drove the ball 30 yards longer

than the average Tour player. Now, 22 years later, the entire PGA Tour averages 295.3 yards off

the tee — the longest average ever. In 1980 (the first year that the PGA Tour’s driving distance

stats are available), Dan Pohl led the field while averaging 274.3 yards per drive. The Tour

average was a meek 256.89 yards (Wilco).

What this paper seeks to answer is: with the geometry of golf changing with longer driving

distance, what determines the success of a professional golfer? The common golf phrase “drive

for show and putt for dough” is thought of as gospel. This paper will take it further and answer

the questions: does making one-putts on the last day of tournament demonstrate a “killer factor”

of being able to perform when the money is on the line?” Or, does the golfer who averages

longer distance on one-putts indicate higher skill level on the green?

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Secondly, we want to answer questions such as “if a pro golfer could improve driving distance

by 10 yards, what effect would that have on his average score? How will it affect prize money?

The interest in golf models should be reignited as the PGA tour commissioner recently

announced that the PGA will allow legalized gambling on-site as soon as the 2020 season

(Leonard).

Literature review:

The change in golf driving distance has been controversial. This increase has led to calls for

changes in ball and club regulation. The PGA of America has resisted such requests.

“Based on the information we have seen, we are highly skeptical that rolling back the golf ball in whole or part will be in the best interest of the sport and our collective efforts to grow the game.”

PGA of America CEO, Pete Bevacqua responding to concerns on technology’s role in changing the distance increases in golf shots. (Gray)

The changes to golf due to increased driving distance were studied by Alexander and Kern who

first challenged the adage of “drive for show, putt for dough”. They argued that the game of the

21st century is all about power, citing the fact that in 2001, the players listed in the top ten in

driving distance on the PGA tour earned 30% more in total prize money than the 10 best putters

on the tour. Their study added limited support to this idea (2, 59).

Numerous papers have explored the components that determine golf score, commonly using

standard golf shot types in a model to determine season-ending average score or season ending

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earnings. Callan and Scott determined that a player’s season-ending score can be illustrated as:

The variable names are described on page five and six except for the following:

1. RANK is the average ranking for a golfer in the season. 2. SCORE is the average score throughout all tournament rounds. 3. EVENTS is the number of tour events entered in the given season, EARN is the SEASON

ending tournament earnings. 4. TOURNC is the number of tournaments completed (7).

This model is representative of much of the research on the subject with Finley and Halsey

showing that GIR, scrambling, distance, driving accuracy, sand saves, “bounce back” (how

effectively a golfer follows a bogie hole with a birdie hole) and putts-per-round provided an 𝑅"

value of over 94% (1104). This is intuitive. The more effectively that a golfer can move from the

tee-box to the green in the fewest strokes, the more likely that golfer would be able to score well.

The most radical, and arguably effective measure was introduced in the book “Every Shot

Counts” where the author had professional and amateur golfers mark their score cards with their

exact location on the course (now performed with lasers), and developed a “strokes gained”

statistic that measures the number of strokes that are gained from a statistical baseline. His “SG

approach” measurement is now included in PGA official statistics and will be used for this study.

Interestingly, the first chapter in his book is titled “putting is overrated” (Brodie, 17,18).

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Heiny argued that if a player hits the ball far enough, driving accuracy is not an important

statistic, citing the rise in p-value of driving accuracy from .1193 in 1992 to .3959 in 2003. He

quoted tour pro Hal Sutton’s 2003 comments: “If you were to ask everyone out there if you

wanted distance or accuracy, they would say distance.”(18).

Methodology: Data was obtained from the PGA tour statistics website for the 150 top money winners in the

2019 season. Variables were selected based on domain knowledge and to prevent perfect

collinearity (such as putts over 10’ and putts under 10’). Below are summary statistics of the

data:

Variable Description

1. Score was used as the dependent variable as a proxy for earnings (78% correlation)

because tournaments paid different levels of prize money and several golfers only

competed in one or two tournaments as they primarily play on the European tour.

2. Money is the official amount of tour winnings for the 2019 season.

3. Avg. Approach is the “strokes gained” statistic that measures the number of strokes that

are gained from a statistical baseline on approach shots.

4. Distance is driving distance in yards.

5. GIR is the measure of greens-in-regulation. The percentage of time that a golfer gets on

the green with two putts to make par.

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6. OneputtR4 is the “killer factor.” Percentage of time that a player sinks his first putt on

the green on the fourth day of the tournament.

7. Percmade is the percentage of holes that the player sinks his first putt.

8. Rounds is the number of rounds played in the 2019 season.

9. Scbperc is the percentage of time that a player misses the green in regulation, but still

makes par or better.

10. Daccuracy is the percentage of time a player hits his first shot (drive) into the fairway.

11. Puttdist is the distance to the average made putt in inches.

12. Sandsv is the percentage of time that a player lands in a sand trap and still saves par.

13. Puttavg is the average number of putts that a player has taken on each hole in the 2019

season.

We used score as a proxy for prize money. Money was not used as an independent variable in

our model of average score because score has the strongest effect on prize winnings. However,

the high level of correlation (-.77) suggests this was an acceptable substitute.

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After the data was gathered the scoring data followed a normal distribution and had of standard

deviation of .5681 strokes.

To further explore the data, Pearson correlation coefficients were developed and are listed in the

table below. High levels of multicollinearity were seen. However, this was expected as measures

such as driving accuracy and driving distance would show a strong negative correlation. The

interesting thing is the relationship to score is much higher for driving distance (-.252) than

driving accuracy (-.118) from a simple correlation viewpoint.

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Correlation Matrix

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An initial linear regression model was run on the full set of variables:

After running the data through the model, only the variables Scbperc, puttavg, Daccuracy,

Sandsv, distance and Avgapprch appeared significant at the 1% level. The model exhibited an 𝑅"

of .8071, an adjusted 𝑅" of .7909 and a p-value of 2.2e-16. The model was highly significant,

showing that a substantial portion of the variation in scores could be explained by the

independent variables.

A new model was run excluding the insignificant variables. This model exhibited an 𝑅" of .803,

an adjusted 𝑅" of .7943 and a p-value of 2.2e-16. This adjusted 𝑅" value was a slight

improvement

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An F-test was then run on the variables that appeared to be insignificant in the unrestricted model

to see if they were jointly significant. Using ANOVA, they were found to be jointly insignificant

with a p-value of 0.7285.

Insignificant variables were then tested one at a time for impact on score to test for individual

significance. GIR (greens in regulation) proved significant individually with a p-value of 1.11e-

06, as did permade (percentage of one-putts made). These two variables were added back into

the model and run with the results of:

Hence, this improved the model slightly.

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A test was then conducted for heteroskedasticity using the White Test. With a p-value of .5191

there was no reason to reject the null hypothesis of homoskedasticity or to report robust standard

errors.

Finally, an examination of the effect of regressing the natural log of score was performed and

showed virtually no change.

The variables Percmade and GIR added back into the model. This provided the optimal model,

which can be expressed as:

Score = 71.757 - .00166GIR - .07052Scbper - .03371Daccuracy + 9.066puttavg (SE) (5.640) (.01859) (.01122) (.00720) (2.1153)

- .01669Sandsv - .03561Distance - .657047Avgapprch + .02822percmade (.00457) (.00416) (.07429) (.03386)

Two surprises appeared in the final model. First, the positive relationship between percentage of

one-putts made and score. Intuitively, one would assume that if you sink more of your first putts

you would have a lower score. The explanation for this could be that a player who is making a

higher percentage of one-putts is taking more strokes to reach the hole and is thus, much closer

on his first putt since he was closer on most recent approach shot. The other surprise is the

relative strength of the variable Avgapprch. As discussed in the literature review, this measure is

a new statistic measuring approach shots from a statistical locational baseline versus the field.

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With the model developed, the prediction accuracy was then tested. The actual values fell within

the 5% confidence intervals which equates to approximately one stroke.

As a final check, the residuals were reviewed to ensure the normality requirement was

maintained.

Conclusions: The results of this analysis lead to several important conclusions. Most importantly, we have

answered the question proposed at the beginning of this document: What key skills determine

the success of a professional golfer? Those are the skills in the final model.

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1. Driving distance and driving accuracy have a similar effect on average score with

coefficients of -.034 and -.036 respectively.

2. Scrambling percentage (the percentage of time that a player misses the green in

regulation, but still makes par or better) has more than twice the impact on score than

either driving distance or driving accuracy. This metric has not shown this level of

strength in previous studies, and could be a reflection of how longer driving distance

leads to lower driving accuracy requiring higher skill in scrambling to make up for the

additional out-of-fairway shots

3. The expected “killer factor” that is often discussed on television of the golfer with laser-

focused putting skills on the last day of a tournament (one putt in round four) is not

significant on either average score or money earned.

4. The “strokes gained” measurement statistic from Brodie, is a strong tool for determining

golf success, and is a strong addition for future modelling. Like the scrambling measure,

the level of approach efficiency is very impactful on performance.

5. At the highest level of golf, marginal changes are difficult to achieve. The narrow standard

deviation levels reflect that. While it might be tempting to recommend to a golfer to

practice enough to take a half stroke off of his putting average, that can be akin to asking

an Olympic sprinter to “just” take a second from his 100-meter dash time.

6. The model is very accurate in capturing the amount of variation expressed in a golfer’s

average score by the independent variables (approximately 80%)

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7. The model is also very accurate in predicting scores with the information contained in the

independent variables-within approximately one stroke at the 5% confidence level.

With the information in this paper and earlier studies, the obvious question is “why don’t players

concentrate on approach shots and putting instead of trying to always hit the ball so hard?” It is

fair speculation to say that good putters don’t have fan appeal, groupies and large followings on

the course. People love to see power.

We discussed in the literature review section the Alexander and Kern (2005) paper which

proposed that the 21st century golfer was all about power, and that in 2001 the top ten drivers

earned 30% more than the top ten putters. The 2019 numbers show the opposite. In 2019, the

top ten putters earned 31% more ($2,298,662) than the top ten drivers ($1,600,195).

Based on this study, what do we tell the young golfer who thinks that a new driver will add ten

yards to his drive and be a game changer? Tell him to expect a drop in his average score of a

third of a stroke. What do we tell the pro golfer who finds a new putter that can take a half a

stroke from his putting average? Tell him to find a new tax attorney. He is about to become a

wealthy man.

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Further Study: This analysis is simply a starting point. Additional research could be done to determine the odds

of a player winning based on a logistical regression (bet/no bet) model. I would like to take this

model to a point of accuracy that would achieve a higher probability of predicting winners than

the casinos’ service charge, which requires a win rate of 52.4%. A logical next step would be to

take the PGA courses and determine the key course attributes (such as narrow fairways or long

holes) and match those to the strengths of a particular golfer. A classification tree could be used

to determine the sub groups who’s strengths match a particular course.

.

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Bibliography

1. Alexander, Donal and Kern, Willima. “Drive for Show and Putt for Dough?” Journal of

Sports Economics, Volume 6 (1) 15-Feb 1, 2005.

2. Brodie, Mark. N. “Every Shot Counts” Gotham Books 2014. Print

3. Callan, Scott J, and Janet M. Thomas. “Modelling the Determinants of a Professional

Golfer’s Tournament Earnings: A Multiequation approach” Journal of Sports Economics,

Volume 8 (4) August 1st, 2007 https://doi.org/10.1177/1527002506287697

4. Das, Sourav. “Top 10 Most Popular Sports in America 2019” sportsshow.net, November

25, 2019 https://sportsshow.net/most-popular-sports-in-america/

5. Finley, Peter S., and Jason J Halsey. “Determinants of PGA Tour Success: An Examination

of Relationships among Performance, Scoring and Earnings.” Perceptual and Motor Skills,

Volume 98, 1100-1106

6. Gray, Wil. “PGA of America “sceptical” on rolling back the ball”; TheGolfChannel.com,

March 5, 2018 https://www.golfchannel.com/news/pga-tour-pga-america-issue-statements-study

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7. Heiny, Erik. “PGA Tour Pro: Long, but Not so Straight.” Chance; Volume 21(1)-Feb 15,

2009

8. Leonard, Todd. “PGA Tour goes all in on Legalized Gambling.” San Diego Union

Tribune.com, November 30, 2019.

9. Torres, Aaron. “John Daly admits he once drank five beers in the middle of a PGA

round.” FoxSports.com November 15, 2016

10. Wilco, Daniel. “How driving distance has changed over the past 40 years on the PGA

Tour.” PGATOUR.COM, July 3, 2018