Volume 9, Issue 4

Recreational golf events differ from professional events in that the primary goal is not simply to identify the best golfer, but rather for all golfers to enjoy and participate meaningfully in the competition. For this reason, it can be beneficial in recreational events to employ “handicapping” systems which enable players of varying skill levels to compete on a level playing field. In this paper we use a stochastic model of the most common recreational event format, the scramble competition, to develop a formula for handicapping scramble tournaments. The formula involves only simple arithmetic, enabling its implementation by tournament organizers in a spreadsheet or other user-friendly platform. In theory, the proposed handicapping system provides all scramble teams with an equal expectation of winning the tournament. Data from actual scramble tournaments are used to assess how well this objective is met, using a scramble handicapping system recommended by the USGA as a basis for comparison. We show that the handicap developed in this paper achieves its goal of providing a more equitable tournament.

The convex payoff structure in professional golf rewards scoring volatility, giving rise to player types who succeed in spite of higher average scoring. The same risk incentives should influence all players to adjust risk strategies at key moments in tournaments when payoffs either crystallize or become particularly convex. This paper develops a simple theoretical framework, then explores the empirical evidence for strategic risk adjustment by players over the 2003–2012 PGA Tour seasons. Findings suggest that players respond measurably on average to risk incentives around the cutline, but much less so (if at all) to leaderboard position on the closing holes of a tournament. Both the payoff to risk and the technical capacity of players to add or subtract risk are estimated. Analysis of individual players indicates that some elite players are more risk responsive. Bias (e.g., loss aversion) is discussed along with other possible explanations for the apparent lack of risk response over the closing holes of a tournament.

A double-elimination tournament is a competition where no participant is eliminated until they have lost two matches. It is structured as two single-elimination tournaments: the winner bracket and the loser bracket. Players who lose once in the winner bracket are mapped to positions in the loser bracket, according to a mapping called the link function. Surprisingly, although the same structure of the winner and loser brackets is used universally, there is no standard definition of the link function. By investigating several design goals, we show that the functions used in practice are not optimal. We propose a similar function that is optimal with respect to our design goals. In order to demonstrate some of the possible research questions about double-elimination tournaments, we address the manipulability of the outcome of a double-elimination tournament. We show that they are vulnerable to manipulation by a coalition of players who can improve their chance of winning by throwing matches, a phenomenon recently observed in Olympic Badminton. We also discuss the computational complexity of manipulation by a tournament organizer (agenda control) in two settings: by changing the player seeding in the winner bracket, or by picking the mapping of losers to the loser bracket. We provide algorithms, hardness proofs, and we formulate open problems for future research.

In this paper, we model a basketball player’s on-court production as a function of the percentiles corresponding to the number of games played. A player’s production curve is flexibly estimated using Gaussian process regression. The hierarchical structure of the model allows us to borrow strength across players who play the same position and have similar usage rates and play a similar number of minutes per game. From the results of the modeling, we discuss questions regarding the relative deterioration of production for each of the different player positions. Learning how minutes played and usage rate affect a player’s career production curve should prove to be useful to NBA decision makers.

Player selection is one of the great challenges of professional soccer clubs. Despite extensive use of performance data, a large number of player transfers at the highest level of club soccer have less than satisfactory outcome. This study uses player performance and decision making data to estimate team performance in terms of goal differential and model the effects of team compatibility on player and team performance. In this methodology, players’ attributes are assessed with respect to the potential contribution to team performance, given the attributes of surrounding players. The study is using a semi-Markov decision process to model game flow. Performance data from the English Premier League between seasons 2008/2009 and 2011/2012 is used to predict the outcome of 69 transfers. The model provides an average error of 7.86 in predicting teams’ goal differential in a season with current squad and 18.91 in estimating the effect of a future transfer on team performance.

Paired-comparison models have been previously used in the literature to assess the relative performance of tennis players over a given period of time. In this paper, I discuss how the rankings of tennis players can be modified to address variations in the importance of tennis tournaments, and concerns about under-participation over the tennis season. The methods are applied to the 2011 WTA season, where the WTA-ranked number one player Caroline Wozniacki was often criticized for not being the true top player. The alternative rankings proposed here indicate that Petra Kvitova was the top player in 2011, with Serena Williams a close second. These rankings do appear to perform better in predicting match probabilities in early 2012 than methods based on the official rankings.