Volume 15, Issue 1

Left-handers comprise approximately 15% of professional tennis players, but only 11% of the general population. In boxing, baseball, fencing, table-tennis and specialist batting positions in cricket the contrast is even starker, with 30% or more of top players often being left-handed. In this paper we propose a model for identifying the advantage of being left-handed in one-on-one interactive sports (as well as the inherent skill of each player). We construct a Bayesian latent ability model in the spirit of the classic Glicko model but with the additional complication of having a latent factor, i.e. the advantage of left-handedness, that we need to estimate. Inference is further complicated by the truncated nature of data-sets that arise from only having data of the top players. We show how to infer the advantage of left-handedness when only the proportion of top left-handed players is available. We use this result to develop a simple dynamic model for inferring how the advantage of left-handedness varies through time. We also extend the model to cases where we have ranking or match-play data. We test these models on 2014 match-play data from top male professional tennis players, and the dynamic model on data from 1985 to 2016.

In this paper, we present and analyze a mathematical programming approach to expansion draft optimization in the context of the 2017 NHL expansion draft involving the Vegas Golden Knights, noting that this approach can be generalized to future NHL expansions and to those in other sports leagues. In particular, we present a novel mathematical optimization approach, consisting of two models, to optimize expansion draft protection and selection decisions made by the various teams. We use this approach to investigate a number of expansion draft scenarios, including the impact of “collaboration” between existing teams, the trade-off between team performance and salary cap flexibility, as well as opportunities for Vegas to take advantage of side agreements in a “leverage” experiment. Finally, we compare the output of our approach to what actually happened in the expansion draft, noting both similarities and discrepancies between our solutions and the actual outcomes. Overall, we believe our framework serves as a promising foundation for future expansion draft research and decision-making in hockey and in other sports.

The Traveling Umpire Problem (TUP) is a combinatorial optimization problem concerning the assignment of umpires to the games of a fixed double round-robin tournament. The TUP draws inspiration from the real world multi-objective Major League Baseball (MLB) umpire scheduling problem, but is, however, restricted to the single objective of minimizing total travel distance of the umpires. Several hard constraints are employed to enforce fairness when assigning umpires, making it a challenging optimization problem. The present work concerns a constructive matheuristic approach which focuses primarily on large benchmark instances. A decomposition-based approach is employed which sequentially solves Integer Programming (IP) formulations of the subproblems to arrive at a feasible solution for the entire problem. This constructive matheuristic efficiently generates feasible solutions and improves the best known solutions of large benchmark instances of 26, 28, 30 and 32 teams well within the benchmark time limit. In addition, the algorithm is capable of producing feasible solutions for various small and medium benchmark instances competitive with those produced by other heuristic algorithms. The paper also details experiments conducted to evaluate various algorithmic design parameters such as subproblem size, overlap and objective functions.

The deployment of sensors that characterize the trajectory of pitches and batted balls in three dimensions provides the opportunity to assign an intrinsic value to a pitch that depends on its physical properties and not on its observed outcome. We exploit this opportunity by using a Bayesian framework to learn a set of mappings from five-dimensional velocity, movement, and location vectors to intrinsic pitch values. A kernel method generates nonparametric estimates for the component probability density functions in Bayes theorem while nonparametric regression is used to derive a batted ball weight function that is invariant to the defense, ballpark, and atmospheric conditions. Cross-validation is used to determine the parameters of the model. We use Cronbach’s alpha to show that intrinsic pitch values have a significantly higher reliability than outcome-based pitch values. We also develop a method to combine intrinsic values at the individual pitch level into a statistic that captures the value of a pitcher’s collection of pitches over a period of time. We use this statistic to show that pitchers who outperform their intrinsic values during a season tend to perform worse the following year. We also show that this statistic provides better predictive value for future Earned Run Average (ERA) than either current ERA or Fielding Independent Pitching (FIP).

We explore the probabilities of winning a best-of-three doubles racquetball match given the probabilities that each of the participants wins a point while serving. We restrict our attention to the cases where these probabilities are between 0.4 and 0.6 for all participants; in other words, the cases where all of the players are moderately evenly matched. In doing so, we find it sensible to suggest changes to the side-out scoring schemes in singles and in team events. These changes would cause each game played to be more fair while preserving the fairness of a match, for which there seems to be adequate impetus.