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Tournament Selection Efficiency: an Analysis of the PGA TOUR's

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Tournament Selection Efficiency: an Analysis of the PGA TOUR's Tournament Selection Efficiency: An Analysis of the PGA TOUR's FedExCup1 Robert A. Connolly and Richard J. Rendleman, Jr. October 10, 2012 1Robert A. Connolly is Associate Professor, Kenan-Flagler Business School, University of North Carolina, Chapel Hill. Richard J. Rendleman, Jr. is Visiting Professor, Tuck School of Business at Dartmouth and Professor Emeritus, Kenan-Flagler Business School, University of North Carolina, Chapel Hill. The authors thank the PGA TOUR for providing the data used in connection with this study, Pranab Sen, Nicholas Hall and Dmitry Ryvkin for helpful comments on an earlier version of the paper and Ken Lovell for providing com- ments on the present version. Please address comments to Robert Connolly (email: robert [email protected]; phone: (919) 962-0053) or to Richard J. Rendleman, Jr. (e-mail: richard [email protected]; phone: (919) 962-3188). Tournament Selection Efficiency: An Analysis of the PGA TOUR's FedExCup Abstract Analytical descriptions of tournament selection efficiency properties can be elusive for realistic tournament structures. Combining a Monte Carlo simulation with a statistical model of player skill and random variation in scoring, we estimate the selection efficiency of the PGA TOUR's FedExCup, a very complex multi-stage golf competition, which distributes $35 million in prize money, including $10 million to the winner. Our assessments of efficiency are based on traditional selection efficiency measures. We also introduce three new measures of efficiency which focus on the ability of a given tournament structure to identify properly the relative skills of all tournament participants and to distribute efficiently all of the tournament's prize money. We find that reason- able deviations from the present FedExCup structure do not yield large differences in the various measures of efficiency. 1 Introduction In this study, we analyze the selection efficiency of the PGA TOUR’s FedExCup, a large-scale athletic competition involving a regular season followed by a series of playoff rounds and a “finals” event, where an overall champion is crowned. FedEx- Cup competition began in 2007. Each year, at the completion of the competition, a total of $35 million in prize money is distributed to 150 players, with those in the top three finishing positions earning $10 million, $3 million and $2 million, respectively.1 Research into selection efficiency highlights the importance of the criterion for assessing tournament properties.2 Most who study tournament competition em- phasize the probability that the best player will be declared the winner (“predictive power”) as the critical measure of tournament selection efficiency. Largely main- taining the focus of the selection efficiency literature on a single player, Ryvkin and Ortmann (2008) and Ryvkin (2010) introduce two additional selection efficiency measures, the expected skill level of the tournament winner and the expected skill ranking of the winner. They develop the properties of these selection efficiency measures in simulated tournament competition. While we use these efficiency measures in our work, we also develop three new measures of selection efficiency that evaluate the overall efficiency of a tourna- ment structure, not just the the mean skill and mean skill rank of the first-place fin- isher and the expected finishing position of the most highly-skilled player. Much of the existing literature (e.g., Ryvkin (2010), Ryvkin and Ortmann (2008)) assumes a specific set of distributions (e.g., normal, Pareto, and exponential) to describe com- petitor skill and random variation in performance. In this paper, we integrate an empirical model of skill and random variation in performance with a detailed tour- nament simulation to explore the selection efficiency of FedExCup competition. We do not specify the matrix of winning probabilities as in some studies; instead, it is generated naturally from the underlying estimated distributions of competitor skill and random variation and the tournament structure itself. In the next section of the paper we describe the characteristics of FedExCup competition. We develop tournament selection efficiency measures in Section 3. We present an overview of the statistical foundations of our work in Section 4, describe our simulation methods in Section 5, and present results and a discussion of practical implications of our work in Section 6. We summarize our findings in the final section. Appendix A describes the details of our simulation. 1See http://www.pgatour.com/r/stats/info/?02396. 2See Ryvkin and Ortmann (2008) for an excellent recap of existing work along these lines. 2 Characteristics of FedExCup Competition 2.1 Structure of FedExCup Competition Under current FedExCup rules, similar in structure to NASCAR’s Sprint Cup points system, PGA TOUR members accumulate FedExCup points during the 35-week regular PGA TOUR season.3 As shown in the “Regular Season Points” portion of Table 1, points are awarded in each regular season PGA TOUR-sanctioned event to those who make cuts using a non-linear points distribution schedule, with the greatest number of points given to top finishers relative to those finishing near the bottom. At the end of the regular season, PGA TOUR members who rank 1 - 125 in FedExCup points are eligible to participate in the FedExCup Playoffs, a series of four regular 72-hole stroke play events, beginning in late August. In the Playoffs, points continue to be accumulated, but at a rate equal to five times that of regular season events. The field of FedExCup participants is reduced to 100 after the first round of the Playoffs (The Barclays), reduced again to 70 after the second Playoffs round (the Deutsche Bank Championship), and reduced again to 30 after the third round (the BMW Championship). At the conclusion of the third round, FedExCup points for the final 30 players are reset according to a predetermined schedule, with the FedExCup Finals being conducted in connection with THE TOUR Championship. The player who has accumulated the greatest number of FedExCup points after THE TOUR Championship wins the FedExCup.4 2.2 FedExCup Competition Objectives It is clear that the objectives of FedExCup competition are multidimensional and complex. From the November 25, 2008 interview with PGA TOUR Commissioner Tim Finchem (PGA TOUR (2008)), it is possible to identify a number of these dimensions. 1. The points system should identify and reward players who have performed exceptionally well throughout the regular season and Playoffs. As such, among those who qualify for the Playoffs, performance during the regular season should have a bearing on final FedExCup standings. 3The rules associated with FedExCup competition have been changed twice. Detail about the revisions is presented in Hall and Potts (2010). 4A primer on the structure and point accumulation and reset rules may also be found at http://www.pgatour.com/fedexcup/playoffs-primer/index.html. 2. The Playoffs should build toward a climactic finish, creating a “playoff-type feel,” holding fan interest and generating significant TV revenue throughout the Playoffs. 3. The points system should be structured so that the FedExCup winner is not determined prior to the Finals. (In 2008, Vijay Singh only needed to “show up” at the Finals to win the FedExCup. This led to significant changes in the points structure at the end of the 2008 PGA TOUR season.) 4. The points system should give each participant in the Finals a mathematical chance of winning. We note that Bill Haas, the 2011 FedExCup winner and lowest-seeded player to ever win, was seeded 25th among the 30 players who competed in the Finals.5 5. The points system should be easy to understand. Under the current system, any player among the top five going into the Finals who wins the final event (THE TOUR Championship) also wins the FedExCup. Otherwise, under- standing the system, especially during the heat of competition, can be very difficult. We do not attempt to quantify the PGA TOUR’s objectives, as summarized above. Instead, we evaluate the optimal selection efficiency of FedExCup compe- tition based on two decision variables. The first is the Playoffs points multiple. Presently, Playoffs points are five times regular season points. This has a poten- tial impact on Commissioner Finchem’s objective points 1 and 2 above. Talking with PGA TOUR officials, we understand that the TOUR reassesses the FedExCup points structure at the end of every season and that this multiple is an important part of the discussion. Reflecting these discussions, we vary the multiple between 1 and 5 in integer increments. Our second decision variable is whether or not to reset accumulated FedExCup points at the end of the third Playoffs round. The present reset system is structured to satisfy objectives 3 and 4 and guarantee that any player among the top five going into the Finals who wins the final event will win the FedExCup (objective 5, at least in part). Although we are able to identify optimal competition structures evaluated in terms of our six efficiency measures, we find that the cost of deviating from optimal structure appears to be small. This finding suggests that the costs of the implicit constraints associated with the objectives listed above may not be high. 5Although confusing, we adopt the convention used throughout sports competition that a “low” seeding or finishing position is a higher number than a “high” position. For example, in a 10-player competition, the “highest” seed is seeding position 1, while the lowest seed is position 10. 3 Measures of Efficiency In order to measure the selection efficiency of various FedExCup competition struc- tures, we simulate entire seasons of regular PGA TOUR competition followed by four Playoffs rounds. In each simulation trial, we begin with a set of “true” player skills, or expected 18-hole scores. Throughout the regular season and Playoffs com- petition, each simulated score for a given player equals his expected score, as given by his true skill level, plus a residual random noise component.
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