Case 2: 2015 PGA Golf Performance Instructor: G. William ...schwert.simon.rochester.edu/a425/a425_case215a.pdf · Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data

Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis

(c) Prof. G. William Schwert, 2002-2015 1

APS 425

Case 2:

2015 PGA Golf Performance

Instructor: G. William Schwert585-275-2470

[email protected]

Golf Performance Data (A425_CASE215.WF1)

MONEY AVG SGP SGT DRIVACC DRVDIST EVENTS ROUNDS FRP GIR PMD SCRAM SS VIC

Mean 1380740 70.94 0.02 0.11 61.85 290.19 23.75 76.21 52.94 70.77 49.37 58.85 50.28 1.24

Median 1038291 70.93 0.06 0.13 61.54 289.50 25.00 79.00 53.33 70.81 49.00 58.88 50.63 1.00

Maximum 10399715 72.52 0.84 2.34 76.88 319.10 33.00 108.00 91.67 77.51 56.00 66.18 64.66 4.00

Minimum 74660 68.82 -1.35 -1.77 50.29 270.00 12.00 46.00 14.29 61.83 41.00 48.77 36.73 1.00

Std. Dev. 1317136 0.68 0.37 0.73 5.05 9.30 4.52 14.46 15.32 2.63 2.89 3.36 6.33 0.75

Skewness 2.92 -0.09 -0.61 0.24 0.16 0.37 -0.43 -0.35 -0.16 -0.20 -0.15 -0.28 0.02 3.17

Kurtosis 16.35 3.07 3.44 3.47 2.61 3.12 2.41 2.26 2.76 3.14 2.75 3.14 2.58 11.78

Observations 193 193 193 193 193 193 193 193 193 193 193 193 193 33




MONEY AVG SGP SGT DRIVACC DRVDIST EVENTS ROUNDS FRP GIR PMD SCRAM SS

AVG -9.09

SGP 4.07 -4.00

SGT 9.34 -19.09 4.18

DRIVACC 0.08 -1.03 -0.77 0.76

DRVDIST 2.88 -3.09 1.53 3.32 -3.58

EVENTS -2.68 2.80 -0.53 -3.18 -0.25 -2.74

ROUNDS -1.04 0.62 0.98 -0.83 0.00 -1.95 11.75

FRP 4.39 -3.91 3.74 3.85 1.55 0.97 -1.78 -0.74

GIR 2.18 -4.13 0.35 4.09 2.98 1.54 -1.57 -0.37 1.51

PMD 2.15 -1.97 7.65 1.83 -0.99 0.54 0.39 1.36 1.99 -0.56

SCRAM 3.51 -3.26 2.72 3.31 0.46 0.42 -0.24 0.69 2.39 0.63 1.27

SS 1.78 -1.18 2.05 1.61 0.03 -0.43 0.01 0.75 2.72 -0.48 2.15 2.12

VIC 8.09 -3.63 3.21 3.66 -0.74 1.90 -1.75 -0.98 3.22 1.30 2.13 2.77 1.24


• So the obvious variables that are most correlated with winning money are Avg, SGT (total strokes gained), and VIC (victories)

• Let’s start by seeing which parts of the golf game are related to these variables



Derive a Measure of Skill for Iron Shots

• The are two things that determine the likelihood of getting on the green in regulation (GIR)– Driving skill and skill with fairway iron shots– We don’t have a direct measure of skill with irons, so we

derive one indirectly:• Regress GIR on DRVDIST and DRIVACC• Then, the residual from this regression is the part of GIR

that is uncorrelated with driving skill (as measured by DRVDIST and DRIVACC)

• We will call this variable IRON, since it is a proxy for iron accuracy

Derive a Measure of Skill for Iron Shots

If a PGA golfer can improve driving distance by 10 yards, then the percent of greens in regulation improves by 1.5%

If a PGA golfer can improve driving accuracy by 10 percent, then the percent of greens in regulation improves by 3.4%

These variable explain about 36% of the variation in GIR



Derive a Measure of Accuracy for Iron Shots

So we will create a new variable, IRON, which transforms the regression residual to have the same mean and standard deviation as GIR, but which is uncorrelated with the driving variables

GIR RESID

Mean 70.76767 0.00000

Median 70.81000 -0.09015

Maximum 77.51000 6.44972

Minimum 61.83000 -6.68168

Std. Dev. 2.62597 2.09722

Skewness -0.20388 -0.09785

Kurtosis 3.13884 3.39556

Observations 193 193

Derive a Measure of Accuracy for Iron Shots

So we will create a new variable, IRON, which transforms the regression residual to have the same mean and standard deviation as GIR, but which is uncorrelated with the driving variables

GIR DRVDIST DRIVACC IRON

GIR 1.000 0.195 0.381 0.799

DRVDIST 0.195 1.000 -0.526 0.000

DRIVACC 0.381 -0.526 1.000 0.000

IRON 0.799 0.000 0.000 1.000



Simple Model for Strokes Gained from Tee to Green

All of the performance variables have the right sign and are significant

• 10 yards more in driving distance is associated with 0.5 strokes gained

• 10 percent more drives in the fairway is associated with 0.7 strokes gained

• 10 percent more GIR (adjusted for driving) is associated with 0.8 strokes gained

• 10 percent more sand saves is associated with 0.2 strokes gained

Residual Plots

The errors are fairly normally distributed, but the highest performing players are positive outliers (Jordan Spieth, Jim Furyk, Kevin Na, Sergio Garcia, etc.)



Residual Plots

Note that the data are ordered by the first and last name of the player, soJim Furyk is in the middle (# 93) as is Jordan Spieth (#106)

Simple Model for Money Winnings

Improving putting by one stroke per round would increase winnings by $1.28 million

Improving driving distance by 10 yards increases winnings by $858 thousand

Improving driving and iron accuracy by 10 percent increases winnings by $752 thousand and $411 thousand, respectively

Improving sand saves by 10 percent increases winnings by $405 thousand

This model explains 40% of the variation in money won



Residual Plots

The errors are positively skewed and the highest earning players are positive outliers (Jordan Spieth, Jason Day, Bubba Watson, Zack Johnson, Jim Furyk)

Model for Log of Money Winnings

To address skewness in money winnings (and residuals), try using Logs for dependent variable

Adjusted R2 is 51%, which is better than the model for raw data (40%)



•These residuals look much more normal•Jarque-Bera test has big p-value

Residual Plots for Log Model

Model for Log of Money Winnings

Add the number of events and the “final round performance,” both of which have a positive effect on money winning

Adjusted R2 is 54%



•These residuals look incredibly normal•Jarque-Bera test has big p-value

Residual Plots for Log Model

Forecasts of Money Earnings

Forecast Money and log(Money), the latter with std errors



Large Forecast Errors

These are the lists of the biggest under and over-performers in terms of money winnings, compared with the performance statistics. The over-performers are the people who won large-prize tournaments. The group on the left should win more money than they do (even though Jason Day and Brooks Koepka did in fact win a lot of money).

PLAYER_NAME MONEY MONEYF ERROR

Will Wilcox $1,168,302 $5,965,025 -$4,796,723

Lee Westwood $946,628 $3,170,507 -$2,223,879

Jason Day $7,551,205 $9,520,675 -$1,969,470

Brooks Koepka $3,391,267 $5,043,084 -$1,651,817

Russell Henley $2,090,190 $3,531,349 -$1,441,159

Hudson Swafford $915,804 $2,109,315 -$1,193,511

Aaron Baddeley $439,925 $1,542,264 -$1,102,339

Keegan Bradley $1,441,948 $2,392,838 -$950,890

Carlos Ortiz $947,059 $1,897,597 -$950,538

Martin Laird $1,124,988 $2,055,393 -$930,405

PLAYER_NAME MONEY MONEYF ERROR

Jordan Spieth $10,399,715 $3,332,436 $7,067,279

Zach Johnson $4,314,187 $1,258,412 $3,055,775

Jim Furyk $3,421,639 $779,670 $2,641,969

Dustin Johnson $4,927,498 $2,740,960 $2,186,538

Bubba Watson $6,313,185 $4,319,222 $1,993,963

Patrick Reed $3,085,254 $1,119,292 $1,965,962

J.B. Holmes $3,418,336 $1,616,546 $1,801,790

Jimmy Walker $4,316,632 $2,527,276 $1,789,356

Charley Hoffman $3,312,669 $1,555,485 $1,757,184

Paul Casey $3,112,386 $1,421,738 $1,690,648

Jordan Spieth Dummy Variable

– observation 106 is Jordan Spieth, so create a dummy variable• Spieth = 0, except for obs 106, where it equals 1



Model for Log of Money Winnings, including Rory Dummy

-Jordan Spieth earned about 118% more than his performance statistics would have predicted [t-stat is 9.3]

Summary Statistics

•You can use the range of the variables (and the standard deviations) to get a sense about the “economic significance” of the different measures of golf performance

•How much does the dependent variable (Log(Money)) change for a one standard deviation change in each independent variable?

Coef Std Dev Econ SignifDRVDIST 0.062 9.301 57.2%DRIVACC 0.061 5.049 30.6%IRON 0.030 2.626 7.9%SS 0.028 6.331 17.5%SGP 0.918 0.372 34.1%FRP 0.010 15.319 15.2%EVENTS 0.026 4.521 11.6%



Interpretation: Increase Each Variable by One Standard Deviation

•If you increase driving length by 9.3 yards, earnings increase by 57.2% (after multiplying the economic significance of DRVDIST by its coefficient in the equation for Log(Money))

•Increasing driving accuracy by 5.0% will increase earnings by 30.6%

•Increasing Strokes Gained Putting (SGP) by 0.37 per round will increase earnings by 34.1%

Coef Std DevEcon Signif

DRVDIST 0.062 9.301 57.2%

DRIVACC 0.061 5.049 30.6%

IRON 0.030 2.626 7.9%

SS 0.028 6.331 17.5%

SGP 0.918 0.372 34.1%

FRP 0.010 15.319 15.2%

EVENTS 0.026 4.521 11.6%

Executive Summary

•Thus, it pays to work on all aspects of your golf game

•Driving distance & accuracy

•Iron accuracy

•Putting

•Psychology (in the sense that performance under pressure, such as the lst round) is also important



Why Are Jordan Spieth, Jason Day and Zach Johnson Good?

•Jordan’s main strength is putting and final round performance, compared with the average PGA player (z-scores = 1.62 and 1.98)

•Jason’s strength is everything, except for driving and iron accuracy

•Zach’s strength is driving accuracy (z-score = 1.85)

Avg Std DevJordanSpieth z-score Jason Day z-score

Zach Johnson z-score

DRVDIST 290.2 9.3 292.4 0.24 314.3 2.59 282.7 -0.80

DRIVACC 61.8 5.0 63.0 0.23 55.9 -1.17 71.2 1.85

IRON 70.8 2.6 70.4 -0.13 72.7 0.72 70.8 0.01

SS 50.3 6.3 57.9 1.20 59.8 1.50 56.2 0.93

SGP 0.0 0.4 0.6 1.62 0.7 1.94 0.0 -0.15

FRP 52.9 15.3 83.3 1.98 85.7 2.14 62.5 0.62

EVENTS 23.8 4.5 22.0 -0.39 17.0 -1.49 22.0 -0.39

Links

Eviews workfilehttp://schwert.ssb.rochester.edu/a425/a425_case215a.wf1

Excel worksheethttp://schwert.ssb.rochester.edu/a425/a425_case215a.zip

APS 425 Home Pagehttp://schwert.ssb.rochester.edu/a425/a425main.htm

Documents

Case 2: 2015 PGA Golf Performance Instructor: G. William ...schwert.simon.rochester.edu/a425/a425_case215a.pdf · Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data