The Importance of Skill and Luck on the PGA Tour by Carl Ackermann Robert A. Connolly Richard J. Rendleman, Jr. Department of Finance Kenan-Flagler Business School Kenan-Flagler Business School 329 Mendoza College of Business CB3490, McColl Building CB3490, McColl Building University of Notre Dame UNC - Chapel Hill UNC - Chapel Hill Notre Dame, Indiana 46556-5646 Chapel Hill, NC 27599-3490 Chapel Hill, NC 27599-3490 (574) 631-8407 (phone) (919) 962-0053 (phone) (919) 962-3188 (phone) (574) 631-5255 (fax) (919) 962-5539 (fax) (919) 962-2068 (fax) [email protected] [email protected] [email protected] We thank Tom Gresik and seminar participants at the University of Notre Dame for helpful comments. Please direct all correspondence to Richard Rendleman. The Importance of Skill and Luck on the PGA Tour Abstract Using a variety of methods, we study the relative contributions of skill and luck in determining the scores of professional golfers who play on the PGA Tour in the U.S. Fixed effects modeling establishes the presence of important changes in skill over the multi-year sample used in our empirical analysis. We apply a set of tests in the literature for hot hands, and employ a markov- switching model on scores of individual golfers. The results from standard tests reveal modest evidence of hot hands, while the markov-switching approach delivers clear evidence of hot hands among some of the best players on the Tour. 1 The Importance of Skill and Luck on the PGA Tour 1. Introduction Like all sports, outcomes in golf involve elements of both skill and luck. Perhaps the highest level of skill in golf is displayed on the PGA Tour. Even among these highly skilled players, however, a small portion of each 18-hole score can be attributed to luck, or what players and commentators often refer to as “good and bad breaks” (sometimes called the “rub of the green”). The purpose of our work is to determine the extent to which skill and luck combine to determine 18-hole scores in PGA Tour events. We are also interested in the question of whether PGA players experience “hot or cold hands,” or runs of exceptionally good or bad scores, due to temporary changes in their levels of skill. From a psychological standpoint, understanding the extent to which luck plays a role in determining 18-hole golf scores is important. Clearly, a player would not want to make swing changes to correct abnormally high scores that were due, primarily, to bad luck. Similarly, a player who shoots a low round should not get discouraged if he cannot sustain that level of play, especially if good luck was the primary reason for his low score. In some cases, the luck factor in a round of golf can be easily identified. In the final round of the 2002 Bay Hill Invitational, David Duval’s approach shot to the 16th hole hit the pin and bounced back into a water hazard fronting the green. Duval took a nine on the hole. Few would argue that Duval’s score of nine was due to bad judgment or a sudden change in his skill level, and it is highly unlikely that Duval made swing changes to correct the type of shot he made on 16. In contrast, the good fortune experienced by Craig Perks in the final round of the 2002 Players Championship when he chipped in on holes 16 and 18 and sunk a 28-foot putt for birdie on the 17th hole en route to victory is not something that Perks can expect to repeat on a regular basis. Only time will tell whether Perks’ victory, his first on the PGA Tour, reflected exceptional ability or four consecutive days of exceptionally good luck. In other cases, specific occurrences of good and bad luck may not be nearly as easy to identify. Luck simply occurs in small quantities as part of the game. Even a player as highly skilled as Tiger Woods cannot produce a perfect swing on every shot. As a result, a certain element of luck is introduced to a shot even before contact with the ball is made. 2 In the next two sections of the paper, we show that after adjusting a player’s score for his general skill level and the difficulty of the course on the day a round is played, the standard deviation of residual golf scores on the PGA Tour is approximately 2.7 strokes per round.1 Although we have no direct evidence, we suspect that the standard deviation of residual scores would be much higher for amateur golfers. In Sections 3 and 4, we also investigate the nature and extent of hot and cold hands (streaky play) using a variety of tests, including a markov-switching model (originally suggested by Albert (1993)). We apply tests from the sports statistics literature (i.e., runs tests, markov-chain tests, and logistic models of performance persistence), but they produce quite limited evidence of hot and cold hands. By contrast, our markov-switching model tests show that streaky play exists, has intuitively reasonable characteristics (e.g., streaks have a relatively short life and are mean-reverting), but streaky play is apparent in only a minority of the top PGA golfers whose individual play we study. A final section summarizes the paper. 2. Data and Statistical Methodology We have collected individual scores for every player in every stroke-play PGA Tour event for years 1998-2001.2 Our data cover scores of players who made and missed cuts.3 It also includes scores for players who withdrew from tournaments and who were disqualified; as long as we have a score, we use it.4 Our data also include indications of where each round was played. This is especially important for tournaments such as the Bob Hope Chrysler Classic played on more than one course. 1. In a related paper that focuses primarily on the performance of Tiger Woods, Berry (2001) estimates the mean standard deviation of golf scores from a predicted score to be 3.12 strokes. His predicted score is based on a random effects model that takes into account the skill level of each player and the intrinsic difficulty of each round. 2. Our data include all stroke play events for which participants receive credit for earning official PGA Tour money, even though some of the events, including all four “majors,” are not actually run by the PGA Tour. The data were collected, primarily, from internet sources that include the following: www.pgatour.com, www.golfweek.com, www.golfonline.com, www.golfnews.augustachronicle.com, www.insidetheropes.com, and www.golftoday.com. When we were unable to obtain all necessary data from these sources, we checked national and local newspapers, and in some instances, contacted tournament headquarters directly. 3. Although there are a few exceptions, after the second round of a typical PGA Tour event, the field is reduced to the 70 players, including ties, with the lowest scores after the first two rounds. 3 In an effort to separate the effects of skill and luck, we employ two statistical models to predict a player’s score in each of his 18-hole rounds. In model 1, the simplest of the two models, a player’s predicted score for a given round reflects two things: i) the level of skill he displays throughout the entire 1998-2001 period and ii) the difficulty of the course on the day the round is played. In model 2, an individual player’s skill level is allowed to change through time. The basic form of model 1 is described below. 2.1. Performance Model 1 = Let scoreij, denote the 18-hole score of player i (with in1,2,... ) in PGA Tour round j (with jm=1,2,... ). For statistical purposes, a round is defined as an 18-hole round of play on a specific course.5 The predicted score for player i in round j is determined by the following fixed-effect 6 multiple regression model: nm =+α βγ + +ε scoreij, ∑∑kk player c round c ij, (1) kc==22 = In (1), playerk is a player dummy that takes on a value of 1 if ik and zero otherwise, = ε roundc is a round dummy that takes on a value of 1 if jc and zero otherwise, and ij, is an error ε = = term with E ()ij, 0 . In the model, Tiger Woods is player k 1, and the first round of the 1998 Mercedes Championships, the first event of our sample, is round c =1. Therefore, the regression intercept, α , represents the score that Tiger would be expected to shoot in the first round of the β 1998 Mercedes Championships, k represents the additional amount that player k would be γ expected to score in the first round of the 1998 Mercedes, and c denotes the additional amount that 4. Typically, the daily scores of a player who withdraws or is disqualified from a PGA Tour event are not shown in the final summary of scores. However, in these cases we went back to the scoring summaries at the end of each round prior to withdrawal or disqualification to pick up the earlier scores. 5. Most PGA Tour events are played on a single course over a four-day period, with a single 18-hole round scheduled for each day. As such, for statistical purposes, these tournaments consist of four rounds. However, over the 1998-2001 period, seven tournaments per year were played on more than one course. In the Bob Hope Chrysler Classic, the first four rounds are played on four different courses using a rotation that assigns each tournament participant to each of the four courses over the first four days.