Volume 7, Issue 4

I started the Journal of Quantitative Sports eight years ago with the hope that it would become an outlet for academics looking to develop a research program in sports statistics. At the time, the field of sports statistics was clearly in its infancy. There were no venues for academics looking to spend substantial time on the field, precious few professional teams were experimenting with how statistical analysis could provide a competitive edge, and there were zero major motion pictures dedicated to the profession.

Numerous statistics have been proposed to measure offensive ability in Major League Baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are the most reliable or consistent. We address this issue by using a hierarchical Bayesian variable selection model to determine which offensive metrics are most predictive within players across time. Our sophisticated methodology allows for full estimation of the posterior distributions for our parameters and automatically adjusts for multiple testing, providing a distinct advantage over alternative approaches. We implement our model on a set of fifty different offensive metrics and discuss our results in the context of comparison to other variable selection techniques. We find that a large number of metrics demonstrate signal. However, these metrics are (i) highly correlated with one another, (ii) can be reduced to about five without much loss of information, and (iii) these five relate to traditional notions of performance (e.g., plate discipline, power, and ability to make contact).

This paper explores the impact of the status of a playoff series on team performance in a best-of-seven playoff format. Betting line data are collected on more than 1200 playoff matches from the National Basketball Association (NBA) and the National Hockey League (NHL) from 2003 through 2011. Regression methodology is used to suggest that teams in desperate situations (i.e., those teams close to elimination in a series) tend to have better results than when they are not in desperate situations. However, there also seem to exist situations where the mountain is too steep to climb, and desperation leads to capitulation. In comparing the two leagues, it appears that the effects due to the status of a series are less prominent in the NHL than in the NBA.

Under the rules of NCAA Hockey and USA hockey, when a penalty shot is awarded, the nonoffending team has the choice of taking the penalty shot or having a minor penalty assessed to the offending team. Since the chance of scoring on a penalty shot normally exceeds the chance of scoring during the minor penalty, most teams will accept the penalty shot. We show, however, that there are times when selecting the minor penalty in lieu of the penalty shot is optimal. We show that when the nonoffending team is ahead near the end of the game, the optimal choice is the minor penalty.

Statisticians have long employed linear regression models in a variety of circumstances, including the analysis of sports data, because of their flexibility, ease of interpretation, and computational tractability. However, advances in computing technology have made it possible to develop and employ more complicated, nonlinear, and nonparametric procedures. We propose a fully nonparametric nonlinear regression model that is associated to a local correlation function instead of the usual Pearson correlation coefficient. The proposed nonlinear regression model serves the same role as a traditional linear model, but generates deeper and more detailed information about the relationships between the variables being analyzed. We show how nonlinear regression and the local correlation function can be used to analyze sports data by presenting three examples from the game of baseball. In the first and second examples, we demonstrate use of nonlinear regression and the local correlation function as descriptive and inferential tools, respectively. In the third example, we show that nonlinear regression modeling can reveal that traditional linear models are, in fact, quite adequate. Finally, we provide a guide to software for implementing nonlinear regression. The purpose of this paper is to make nonlinear regression and local correlation analysis available as investigative tools for sports data enthusiasts.

In this paper, we explore competition performance in decathlon based on competition, training and personal data. Our data set comprises 3103 competition results from the decathlon world's best performance lists from 1998 to 2009. The aim of our analysis is to estimate latent factors describing the performance results and—at the same time—to model effects of age, season, and year of the competition on the results. Thus, we apply a new statistical method, semi-parametric latent variable models (LVMs), which can be seen as a synthesis between classical factor analysis and semi-parametric regression. LVMs are especially well-suited for modeling decathlon data, because (i) they permit the assumption of latent factors and therefore take the correlation structure between the ten performance results into account, and (ii) they enable us to model (potentially non-linear) relationships between response variables and covariates—contrary to classical factor analysis. In our analysis, we apply LVMs with a semi-parametric predictor allowing for non-linear covariate effects on the latent factors. Thereby, we obtain well interpretable results: four latent factors standing for sprint, jumping, throwing, and endurance abilities, as well as interesting non-linear effects of age and season on these latent factors. We also compare our results from LVMs to those obtained from classical factor analysis.

Each year, over 1,300 golfers attempt to qualify for the PGA TOUR through Q-School. Using simulation, we estimate the probabilities that Q-School correctly identifies high-skill golfers. We show that players with skill equivalent to the very best on the PGA TOUR would have high probabilities of qualifying, but others, equal in skill to many active PGA TOUR members, would have low odds of qualifying. We explore the impact of variations in Q-school structure on qualifying probabilities for players with different skill levels, but most of the variations that improve tournament efficiency are largely impractical.

Our study of win-by-two tie games is motivated by a famous 2010 Wimbledon tennis match whose final set was decided by the improbable score of 70-68. We introduce a trigonometric interpretation of the odds of winning points and games in tennis when serving from deuce. We place this result in the more general setting of a gambler’s ruin problem and also propose a performance measure to quantify the serving and receiving skill of one player relative to another. Then we extend the analysis to table tennis and volleyball. These latter games are similar to tennis in that the winner must obtain a certain minimum score while leading by two points, but they differ in their determination of which player serves a given rally and in whether a point is awarded to the receiver for winning a rally. We quantify the impact of these differences on the outcomes of games, assuming that the probability for a player to win a single point does not change during a game. We also apply a Markov chain analysis to arrive at our earlier results for tennis and to calculate the expected length of a game after reaching deuce. Finally, we develop the idea of “equivalent games” so that the analysis can be carried out using only the probability of winning a point (that is, without regard for the question of which player is serving).

Purpose: It is important for soccer players to accurately kick a ball in various directions with both legs. This study aimed to examine the accuracy of the kick in soccer players in terms of kick direction, kicking legs (dominant and non-dominant legs), and experience. Methods: Seventeen male soccer players (age: 20.1 ± 1.1 yr) and fourteen male university students without soccer experience (age: 19.8 ± 1.2 yr) participated in the experiment. They kicked a ball from the penalty spot to the targets set at four corners of the goal and the accuracy of each kick was measured. Results: The soccer group’s score was significantly higher than that of the control group regardless of the kick direction or kicking legs. The score of the upper position targets was significantly lower than that of the lower position targets in both groups. There was no significant difference between the scores of the lower position targets of dominant and non-dominant legs in the soccer group. In addition, the score of reverse cross directions (kicking towards the right side of the goal with the right-leg) was significantly higher than that of cross directions (kicking towards the left side of the goal with the right-leg) in soccer players. Conclusion: Soccer players differ non-significantly between the dominant and non-dominant legs in the accuracy of inside kick with low trajectory and have high accuracy when kicking in the reverse cross direction.

A comprehensive comparative survey is presented, covering official rating systems as published by internationally recognized sports federations. Mind sports and physical sports are both included. As of November 2010, competitions in 159 international sports are organized by sports federations recognized by the IOC, Sport Accord and by Wikipedia identified under “List of International Sport Federations.” Of the 159 sports, 18 are combat sports in which opponents are in direct physical contact as in boxing and wrestling, 74 are independent sports in which significant contact is not allowed as in swimming and archery and 67 are object sports in which indirect contact is allowed while opponents attempt to control an object as in basketball and chess. Of the 159 sports, 60 sports have no rating system, two combat sports have a subjective rating system, 84 sports have an accumulative system in which points accrue non-decreasingly over some window of time, and 13 sports have an adjustive system in which a rating self adjusts based on the difference between some observed result and a prediction of that result based on past performance. For accumulative rating systems, features include converting results to points, ageing results more than one year old, and possibly adjusting points using other performance measures. Such systems are favored by tournament organizers who want to encourage many top competitors to enter as for skiing and tennis. The adjustive systems include Elo, probit and averaging methods. These systems are favored for their technical sophistication by sports such as chess, draughts, go, cricket, and women’s soccer. This study thus identifies the observed successful methodology used by the various sports federations to publish comparative ratings. Predictive success of certain rating systems are tabulated for FIBA world championship basketball, Grand Slam tennis and FIFA men’s world cup soccer.

When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average variance. The difficult question is how much risk a team should be willing to accept. This is equivalent to asking how much the team should be willing to sacrifice from its mean score in order to increase the score’s variance. In this paper a general analytical method is developed for addressing this question quantitatively. Under the assumption that every play in a game is statistically independent, both the mean and the variance of a team’s offensive output can be described using the binomial distribution. This allows for direct calculations of the winning probability when a particular strategy is employed, and therefore allows one to calculate optimal offensive strategies. This paper develops this method for calculating optimal strategies exactly and then presents a simple heuristic for determining whether a given strategy should be adopted. A number of interesting and counterintuitive examples are then explored, including the merits of stalling for time, the run/pass/Hail Mary choice in football, and the correct use of Hack-a-Shaq.

We predict the induction of Major League Baseball hitters and pitchers into the National Baseball Hall of Fame by the Baseball Writers’ Association of America. We employ a Random Forest algorithm for binary classification, improving upon past models with a simplistic input approach. Our results suggest that the random forest technique is a fruitful line of research with prediction in the sports world. We find an error rate as low as 0.91% in our most accurate forest, with no out-of-bag Error higher than 2.6% in any tree ensemble. We extend the results to an examination of the possibility of discrimination with respect to BBWAA voting, finding little evidence for exclusions based on race.

Past research attempting estimates of the relative impact of hitting, pitching, fielding, and basestealing on team winning percentage in baseball has been marked by a number of problems, mostly in terms of poor choice of performance measures. The current analysis attempts to perform this task using readily available measures for the years 1951 through 1998. The analysis method is based on a conceptual decomposition of offense and defense into its component parts and then recombinations of the parts in intuitively meaningful ways. The findings imply that offense and defense have about the same impact on team performance than defense, the former is based almost totally on hitting, and the latter divided about equally between pitching and fielding. Division of the sample into time periods with low, medium, and high levels of offense did not substantially change these conclusions.