Volume 8, Issue 4

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 reasonable deviations from the present FedExCup structure do not yield large differences in the various measures of efficiency.

The purpose of this study is to develop a new method for ranking driving ability amongst PGA Tour players. Currently the PGA Tour ranks golfers from first to last place in both driving distance and driving accuracy, and then adds the two ranks together for an overall measure of driving performance. The best drivers are the players with the lowest combined rank. While this measure accounts for both driving skills, information is lost by converting driving distance and driving accuracy to ordinal measurements.Thanks to the generosity of the PGA Tour, data from the PGA Tour Shot Link database has been made available. In this study, hole-by-hole level data is recorded for each player. Variables include: driving distance; distance to the hole after the drive; whether the drive was in the fairway, left rough, right rough, water, etc.; par for the hole; score on the hole; and others. With the level of detail now available in the data, a much more accurate measure can be made of the driving skill of each player.A linear mixed effects model was used to determine the actual value of driving the ball a certain distance and in a certain location. The predicted score on a hole, given the distance and location of the tee shot, was used to assess this value. Player was modeled as a random effect, to account for the correlation among the multiple measurements for each player. The Total Driving Performance measure developed in this study not only provides a more precise ranking method, but also quantifies the difference in driving skill from one player to another in terms of strokes gained or lost per round and per tournament.

We present an analysis of a time-dependent stochastic model of the real-time progress of the difference between the home and the away team's scores in sports contests. The model was originally proposed by Stern (1994) and treats the evolution of the home team lead (or deficit) as a Wiener diffusion process. We derive the distribution, the mean, and the variance, of the maximum home team lead during one match, both unconditionally, and also conditional on the final score. We present estimates of the model's parameters, and apply the model to the joint distribution of the maximum home team lead and the final results of one complete season (2010/2011) of the top German basketball league. The diffusion model predicts the maximum home team lead from the final results fairly accurately which suggests that static result-oriented accounts may profitably be complemented by dynamic accounts which model the real-time events leading up to the final score.

We consider the problem of projecting future success of Minor League baseball players at each level of the farm system. Using tree based methods, in particular random forests, we consider which statistics are most correlated with Major League success, how Major League teams use these statistics differently in handling prospects, and how prior belief in a players ability, measured through draft position, is used throughout a players Minor League career. We show that roughly the 18th round prospect corresponds to being draft neutral for a team, whereas teams essentially make decisions based strictly on performance. We use for our data all position players drafted between 1999 and 2002.

Route choice through mountainous terrain requires a knowledge of how pace (the reciprocal of speed) varies with gradient of ascent or descent. To model this variation for runners, we analyse record times for 91 uphill and 15 downhill races or race stages. The pace is modelled as a nonlinear function of gradient and a linear function of race duration, using ordinary least squares to obtain a best fit. For the gradient-dependence, six functional forms are compared, of which a quartic is found to fit the data best; however, at steep gradients the quartic model is unrealistic and it may be argued that a linear model is more appropriate. Critical gradients, at which a runner's vertical speed (uphill or downhill) is maximised, may be calculated from a nonlinear model, although it appears that there is no uphill critical gradient within the range of our dataset.