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
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 2
Golf Performance Data (A425_CASE215.WF1)
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
Golf Performance Data (A425_CASE215.WF1)
• 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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 3
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 4
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 5
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.)
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 6
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 7
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%)
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 8
•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%
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 9
•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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 10
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 11
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%
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 12
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
Case 2 -- 2015 PGA Performance APS 425 - Advanced Managerial Data Analysis
(c) Prof. G. William Schwert, 2002-2015 13
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