Volume 9, Issue 3

Golf is a popular form of competition, and it is traditional for amateur players to use a handicapping system when competing against one another in order to make the competition more interesting and perhaps more equitable. Additionally, the scramble, where each player plays a ball and the better/best of the shots is selected and played (by all players) until the ball is holed, is a popular format for team competition. However, an official handicapping system for scrambles has yet to be developed. This paper develops a model that could provide a rationale for assigning handicaps to multi-person scramble teams with the objective of yielding equitable matches, i.e., equal win probabilities for both/all teams. Probabilistic analysis is used to derive the distributions of team scores and winning probabilities, which can then be use as a mechanism for optimally assigning teams. This paper relaxes many strict assumptions of previous work; results show that equal handicaps are not the best measure of fairness and that player inconsistency may be desirable in scramble formats.

In this paper, we develop a Markov decision process (MDP) model to determine when a player should challenge a line call in a game of tennis, if the objective is to maximize the probability of winning the game. The parameters in the model include the relative strength of the players and the fallibility of the officials. The player’s decision depends on the the current score, the number of challenges remaining, the outcome of a successful challenge, and his confidence that the line call is incorrect. The model developed is a multi-chain MDP operating under the long-run average cost criterion. We also performed extensive numerical studies when the player has one challenge remaining, varying the player strengths and the fallibility levels. These studies imply some general intuitive challenge strategies but also exhibit unusual strategic behavior in some game states. For example, in some states it is not optimal for very weak or very strong players to challenge calls. Furthermore, we demonstrate that the challenge decision is not “unimodal” as a function of the player’s strength, i.e., there may be multiple decision thresholds with respect to this parameter.

Using ShotLink data that records information on every stroke taken on the PGA Tour, this paper introduces a new metric to assess putting. The methodology is based on ideas from spatial statistics where a spatial map of each green is constructed. The spatial map provides estimates of the expected number of putts from various green locations. The difficulty of a putt is a function of both its distance to the hole and its direction. A golfer’s actual performance can then be assessed against the expected number of putts.

The UEFA Champions League Round of 16 is characterized by restrictions that prevent teams from the same preliminary group and the same nations from matches against each other. Together with the draw procedure currently employed by UEFA, this leads to odd probabilities: in 2012/2013, there were more outcomes of the draw with German Schalke 04 facing Ukrainian Shakhtar Donetsk than there were results where they were matched with Galatasaray Istanbul. In contrast, the probability of Schalke being drawn against Galatasaray exceeded that of playing Shakhtar. We show that this strange effect is due to the group restriction and the mechanism used by UEFA for the draw. Additionally, we provide procedures with which UEFA could produce adequate probabilities for the draw.

This paper develops a simulator for matches in Major League Baseball (MLB). Aspects of the approach that are studied include the introduction of base-running probabilities which were obtained through a large data set, and the simulation of nine possible outcomes for each at-bat. Various applications to the simulator are investigated, such as the definition of a measure of the ability of a batter/pitcher, in-play strategy and the determination of the optimal batting order for a given team.