PERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS
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1 PERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS C. Barry Pftzner and Chrs Spence, Department of Economcs/Busness, Randolph-Macon College, Ashland, VA, bpftzne@rmc.edu, cspence@rmc.edu ABSTRACT Ths paper nvestgates the determnants of player performance as measured by scorng average and earnngs on the European Professonal Golf Assocaton (EPGA) tour for the 2006 season. Among other fndngs, ths research shows that the percentage of greens reached n regulaton (GIR) and putts per round (PPR) are by far the most mportant determnants of both scorng average and earnngs on the EPGA. We further fnd that drvng dstance and drvng accuracy are approxmately equally mportant n determnng scorng average. INTRODUCTION Professonal golf tours keep a varety of performance statstcs presumed to measure mportant sklls related to success. One domnant statstc s greens n regulaton the percentage of golf holes for whch the player reaches the surface of the green n at least two fewer strokes than the par score for that hole. Other major statstcs nclude drvng dstance (DD), drvng accuracy (DA) whch measures the percentage of drves n the farway of the hole beng played, sand saves (SS) whch measures the percentage wth whch a player takes two or fewer strokes to hole the ball from greensde bunkers, putts per round (PPR), and putts per green reached n regulaton (PPG). Each of those measures, GIR, DD, DA, SS, PPR (or PPG), are related n theory to scorng and scorng s clearly related to monetary success. The purpose of ths paper s to provde emprcal estmates to ad n determnng f and how those statstcs are related to scorng average and money wnnngs as measures of success on the European PGA golf tour. Ths paper wll employ regresson technques to capture the nfluence of the measures of the sklls enumerated n the prevous paragraph on success on the EPGA tour. LITERATURE REVIEW There are several strans of research on professonal golf performance based on the statstcs compled by the PGA and LPGA and EPGA tours. One of the frst studes of the statstcal determnants of success n professonal golf was by Davdson and Templn [2]. Utlzng data from the 1983 PGA (119 of the top 125 money wnners) n a multple regresson framework, Davdson and Templn found that greens n regulaton (GIR), puttng (PPR), and a combned drvng effcency measure were capable of explanng 86% of the varaton n scorng average for the PGA tour, wth GIR the most mportant sngle varable. When the dependent varable was earnngs, puttng was slghtly more mportant statstcally than the other explanatory varables, based on standardzed beta coeffcents. Shmanske [11], also usng a multple regresson framework for data from the 1986 PGA tour (the top 60 money wnners), fnds that puttng and drvng dstance are the two most mportant sklls n determnng success on the PGA tour. When player money wnnngs per event are the dependent varable, he fnds no sgnfcant role for GIR as an explanatory varable. Shmanske also attempts to estmate the greatest payoff for practce, and fnds the greatest payoff s for puttng practce. Belkn et al. [1] utlze PGA statstcs for three years ( ) n correlaton and step-wse regresson frameworks. Ther research confrms the mportance of GIR and putts per round (PPR) as domnant varables n determnng scorng average, wth lesser, but statstcally
2 mportant roles for drvng dstance, drvng accuracy and sand saves. They conclude that ther research confrms the mportance of tour statstcs n predctng scorng average. A 1995 paper by Englehardt [4] concludes that the rankngs of the top 10 money wnners are not sgnfcantly correlated wth GIR for 1993 and 1994 PGA seasons, and ctes an ncreasngly mportant role for total drvng, whch s the sum of the ranks n drvng dstance and drvng accuracy. Ths study utlzes, however, a sample sze of only 10. Moy and Law [8] fnd evdence that conflcts wth that from Englehardt for the same PGA year. They fnd statstcally mportant roles for drvng dstance, drvng accuracy, GIR, and puttng n determnng earnngs on the PGA tour for the 1993 season. The latter study utlzes a multple regresson framework and a much larger sample sze than Englehardt. Moy and Law s work also ncludes analyss of the LPGA and the Senor PGA tours and they offer the general concluson that a well rounded game s necessary for success n professonal golf. Nero [9] usng data from the 1996 PGA tour fnds statstcally mportant roles for drvng dstance, drvng accuracy, puttng, and sand saves n determnng money won. Interestngly, Nero does not nclude GIR n hs analyss. Nero also estmates a fronter earnngs functon n an attempt to dentfy the most effcent golfers that s those golfers who earn more than that predcted by the regresson equaton. Dorsal and Rotunda [3] usng data from the top 42 players on 1990 PGA tour found that GIR was the most mportant varable determnng scorng average, and that drvng accuracy was more mportant than drvng dstance. Ther analyss ncluded smple correlaton analyss and multple regresson technques. They also used scorng average, top 10 fnshes, and money wnnngs as dependent varables. METHODOLOGY The prmary research method for ths paper s multple regresson analyss wth scorng average and money won per event as the dependent varables (the money wnnngs equaton s estmated n log form due to heteroskedastc resduals n the untransformed verson), and the general set of performance statstcs as the explanatory varables. The general models may be represented as: SA = β o + β1 GIR + β2dd + β3da + β4ppr + β5ss + ε, (1) and ln( M / E ) β SS + ε (2) = o + β1gir + β2 ln DD + β3da + β4 ln PPR + β5 Where, SA = Scorng average (strokes per round) M/E = money wnnngs per event GIR = greens n regulaton (percentage of greens reached n regulaton or fewer strokes) DD = drvng dstance n yards DA = drvng accuracy (the percentage of drves n the farway) PPR = putts per round SS = percentage of sand saves, and the subscrpt refers to the th observaton (here the ndvdual player), and ln s symbol for the natural log.
3 SUMMARY STATISTICS ON THE EPGA TOUR Table I represents the summary statstcs for the 2006 EPGA tour. For 2006, the EPGA tour reported full statstcs on 178 players. Unlke the PGA tour n the Unted States, the EPGA tour n 2006 was not domnated by a sngle player. Paul Casey was the leadng money wnner (2.5 mllon euro), Sergo Garca had the lowest stroke average (70.04), but the gaps between those leaders and the other top players were relatvely small. Table I: Summary Statstcs for the 2006 EPGA Tour Varable Mean Standard Devaton Mnmum Maxmum Scorng Average (SA) Greens n Regulaton (GIR) 66.08% 3.63% 57.8% 75.6% Drvng Dstance (DD) Drvng Accuracy (DA) 59.51% 5.89% 42.0% 75.6% Putts per Round (PPR) Sand Save Percentage (SS) 51.92% 8.63% 24.6% 75.9% Putts per GIR (PPG) Money Wnnngs (M) 390, , , ,454, (n = 178) SOME REGRESSION RESULTS In ths secton we present and dscuss the regresson results for scorng average and money wnnngs. Scorng Average Table II presents the results of the regressons wth scorng average (SA) as the dependent varable. The column ttled Regresson 1 contans the emprcal estmates for equaton 1 from above. The coeffcents for each varable have the antcpated sgns, however only GIR and PPR are strongly sgnfcant n the statstcal sense (DD s weakly sgnfcant). The equaton explans over 85% of the varaton n scorng average and the standard error s slghtly over one-quarter of a stroke. It s clear from regresson 1 n Table II that GIR and PPR are domnant varables n the equaton, and PPR s farly near ts theoretcal value of 1. In order to assess the effects of varables such as drvng dstance and accuracy, we offer Regresson 2. Snce DD and DA are domnated by GIR as explanatory varables n equaton 1, at least n part because the percentage of greens that a golfer hts n regulaton s n fact determned by the dstance and accuracy of hs drves, we elmnate GIR from Regresson 2. In ths way we beleve a clearer assessment of those sklls, and some evdence of the value of each can be estmated. Notce that all of the varables remanng n Regresson 2 are sgned n accord to theory and statstcally sgnfcant. However, wthout GIR n the regresson, the explanatory power of the regresson s sgnfcantly reduced the adjusted R-squared value s only.33. It s often consdered a controversy as to whether drvng dstance (DD) or drvng accuracy (DA) s more mportant for professonal golfers. Much of the recent commentary (and some research) tends to emphasze dstance over accuracy. We offer Regresson 2 as contradctory evdence. Frst, each of those two varables s statstcally sgnfcant at approxmately the same levels. Second, assumng regresson 2 s properly specfed, some ndcaton of the relatve mportance of the two varables may be offered. Suppose other thngs equal, a player mproved one standard devaton n each
4 of DD and DA. Drvng dstance would ncrease by 9.97 yards and drvng accuracy would rse by 5.89%. The product of the coeffcent estmate and the respectve one standard devaton change would represent the change n scorng average. For DD ths procedure would lower scorng average by.361 strokes per round ( ) and for DA, the correspondng effect would lower scorng by.352 strokes per round ( ). Whle t s clear that each of these varables s mportant n scorng average, t s not at all clear whch s the more mportant nfluence on scorng average for the EPGA tour. Based on ths analyss, ther respectve contrbutons appear to be approxmately the same. Table II: Regresson Results: Scorng Average = Dependent Varable Varable/ Summary Regresson 1 Regresson 2 Regresson 3 Regresson 4 Statstcs Constant GIR * * * (-25.13) (-8.14) (-29.86) PPR * * * (26.03) (7.33) (28.82) DD *** * (-1.62) (-6.40) DA * (-0.78) (-6.28) SS ** (-.415) (-2.28) 2 R SEE F k, n-k * 22.94* 66.30* * (notes: n = 178; k = number of regressors; t-statstcs n parentheses; *, **, *** ndcate sgnfcance at α <.01,.05, and.10, respectvely) Regressons 3 and 4 are examples of more parsmonous estmatons. In Regresson 3, greens n regulaton (GIR) alone explan 26% of the varance n scorng average. It s nterestng to note that the correspondng statstc s smlar for the US PGA tour, but approxmately 75% for the LPGA tour (see [10]). Fnally, Regresson 4 ndcates that an equaton ncludng only GIR and PPR explans as much of the varance n scorng average as does Regresson 1. Put dfferently, only 15% of the varance of scorng average s explaned by factors other than GIR and PPR. We also expermented wth putts per green n regulaton (PPG) rather than PPR. It turns out that when GIR s n the equaton, PPR s a stronger explanatory varable, and when GIR s not n the equaton, PPG s the better explanatory varable. The reason for ths, we beleve, s that players who mss a larger proporton of greens (lower GIR) have fewer total putts (because they are able to get the ball closer to the hole when they eventually get the ball on the green). Indeed the smple correlaton between GIR and PPR s 0.535, clear evdence of the effect we descrbe. Tournament Wnnngs Snce dfferent tournaments have dfferent purses, tournament wnnngs per event s a more dffcult varable to explan. Table III depcts the results of the regressons amed at predctng tournament wnnngs. In the specfcatons presented here, the form of the dependent varable s the natural log of
5 tournament money wnnng per event (ln(m/e)). Snce t s necessary to control for the number of events that a partcular player enters, wnnng per event s a natural transformaton. 1 The log form s chosen for two reasons: frst, the resduals are heteroskedastc unless the log transformaton s used and, second, the predcted wnnng per event s bounded by zero n log form, but predcted money per event can be negatve wthout the log transformaton. Table III: Regresson Results: Log of Money per Event = Dependent Varable Varable/ Summary Regresson 1 Regresson 2 Regresson 3 Regresson 4 Statstcs Constant GIR * * * (12.89) (7.12) (15.09) Ln(PPR) * * * (-12.13) (-4.81) (-12.71) Ln(DD) * (0.495) (4.82) DA * (-0.452) (4.31) SS (0.957).0210* (2.37) 2 R SEE F k, n-k * 11.89* 50.67* * (notes: n = 178; k = number of regressors; t-statstcs n parentheses; * ndcates sgnfcance at α <.01,.05, and.10, respectvely) The explanatory varables PPR and DD are n log form so that ther coeffcents are nterpreted as estmates of elastctes. Snce the other varables are already n percentages, they are not n log form. Ther coeffcents (GIR DA, SS) when multpled by 100) are sometmes called sem-elastctes,.e., the percentage change n the (untransformed) dependent varable due to a one unt change n the ndependent varable. Regresson 1 of Table III explans approxmately 59% of the varaton n the log of money per event across players on the EPGA tour. Agan, the coeffcents on sand save percentage (SS), drvng dstance (DD) and drvng accuracy (DA), suggest lttle ndependent predctve power for any of those varables n regresson 1. The coeffcent for GIR suggests that a one-unt change n GIR mples a 26.13% ncrease n money wnnngs per tournament. The coeffcent for PPR suggests that a 1% decrease n putts per round leads to a 30.92% rse n money wnnngs per event. Snce DD and DA operate through GIR, ther nterpretaton s left for regresson 2. In regresson 2, the GIR varable s dropped. Notce that the coeffcents for PPR, DD, DA, and SS are all correctly sgned and statstcally sgnfcant. Regresson 2 s offered to assess (as n Table II) the effects of DD and DA on the dependent varable wthout GIR absorbng most of ther effects. In that regresson, the elastcty of money wnnngs per event wth respect to PPR s estmated to be 15.0%, that s, a one percent decrease n PPR mples a 15% ncrease n money per event. In regresson 2, the mpled elastcty of DD s 12.6%, meanng that f DD ncreases by 1%, 1 It s also (of course) possble to control for events entered by enterng the number of events as an explanatory varable.
6 wnnngs per event are estmated to ncrease by 12.6%. The sem-elastcty for DA s estmated to be 6.64%. 2 Regresson 3 s offered to assess the effect of GIR alone on money wnnngs per tournament. GIR n ths estmaton has an mpled sem-elastcty of 14.5%, and explans almost 22% of the varance n tournament wnnngs. Fnally Regresson 4 suggests that GIR and PPR explan approxmately 60% of the varaton n money wnnngs per event across players the same proporton as the less parsmonous model n Regresson 1. Further the GIR and PPR coeffcent estmates for Regresson 4 are nearly dentcal to those of Regresson 1. CONCLUSIONS We present evdence of the determnants of success on the European Professonal Golf Assocaton (EPGA) tour. Whether the measure of success n scorng average or money wnnngs, the percentage of greens reached n regulaton (GIR) and a measure of puttng success (here, putts per round) are domnant explanatory varables n regresson formats. To asses the effects of drvng accuracy and drvng dstance, t s necessary to remove GIR from the estmatng equatons. Those formulatons suggest that drvng accuracy and drvng dstance are approxmately equally mportant n determnng scorng average. A comparson of the Unted States PGA tour, the European PGA tour, and the Lades PGA tour s a potental future project. REFERENCES [1] Belkn, D.S., Gansneder, B., Pckens, M., Rotella, R.J., & Stregel, D. (1994) Predctablty and Stablty of Professonal Golf Assocaton Tour Statstcs. Perceptual and Motor Sklls, 78, [2] Davdson, J. D. & Templn, T. J. (1986) Determnants of Success Among Professonal Golfers. Research Quarterly for Exercse and Sport, 57, [3] Dorsel, T. N. & Rotunda, R. J. (2001) Low Scores, Top 10 Fnshes, and Bg Money: An Analyss of Professonal Golf Assocaton Tour Statstcs and How These Relate to Overall Performance. Perceptual and Motor Sklls, 92, [4] Engelhardt, G. M. (1995) It s Not How You Drve, It s How You Arrve : The Myth. Perceptual and Motor Sklls, 80, [5] Englehardt, G. M. (1997) Dfferences n Shot-Makng Sklls among Hgh and Low Money Wnners on the PGA Tour. Perceptual and Motor Sklls, 84, [6] Englehardt, G. M. (2002) Drvng Dstance and Drvng Accuracy Equals Total Drvng: Reply to Dorsel and Rotunda. Perceptual and Motor Sklls, 95, One must be careful wth ths nterpretaton. Snce the explanatory varable s n percentage form, a one unt change s one percentage pont, but that s a larger percentage of the mean of the varable, snce all mean percentages for these varables are consderably less than 100%.
7 [7] Jones, R.E. (1990) A Correlaton Analyss of the Professonal Golf Assocaton (PGA) Statstcal Rankng for In A.J. Cochran (Ed.), Scence and Golf: Proceedngs of the Frst World Scentfc Conference of Golf. London: E & FN Spon [8] Moy, R. L. and Law, T. (1998) Determnants of Professonal Golf Tournament Earnngs. The Amercan Economst, 42, [9] Nero, P. (2001) Relatve Salary Effcency of PGA Tour Golfers. The Amercan Economst, 45, [10] Pftzner, C.B. and Rshel, T. (2005) Performance and Compensaton on the LPGA Tour: A Statstcal Analyss, Internatonal Journal of Performance Analyss n Sport, Unversty of Wales Insttute, Cardff, Volume 5, Number 3. [11] Shmanske, S. (1992) Human Captal Formaton n Professonal Sports: Evdence from the PGA Tour. Atlantc Economc Journal, 20, [12] Wseman, F., Chatterjee, S. Wseman, D. and Chatterjee, N. (1994) An Analyss of 1992 Performance Statstcs for Players of the U.S. PGA, Senor PGA, and LPGA Tours. In A.J. Cochran and M. R. Farrally (Eds.), Scence and Golf: II. [13] Proceedngs of the World Scentfc Congress of Golf. London: E & FN Spon [14] Woolrdge, Jeffrey M., Introductory Econometrcs: A Modern Approach, South-Western College Publshng, 2000.
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