Volume 17, Issue 3

The Saint Louis Blues were hot at the end of the 2018–2019 National Hockey League season, winning eleven games in a row in January and February, and eight of their last ten. They parlayed this momentum to their first Stanley Cup Championship in franchise history. Or did they? Did the series of wins at the end of the season give the Blues the momentum needed to reach the pinnacle of the sport on June 12th, or was the Blues’ path to victory the confluence of a series of random events that fell in their favor? In this paper we apply entropy as an unbiased measure to further refute the idea of momentum in sports. We show that game outcomes are not dependent on previous games’ outcomes and conclude that the theory of momentum, across the season, is a fallacy that should not affect behavior.

Previously published statistical analyses of NCAA Division I Men’s Tournament (“March Madness”) game outcomes have revealed that the relationship between tournament seed and the time-aggregated number of third-round (“Sweet 16”) appearances for the middle half of the seeds exhibits a statistically and practically significant departure from monotonicity. In particular, the 8- and 9-seeds combined appear less often than any one of seeds 10–12. In this article, we show that a similar “middle-seed anomaly” also occurs in the NCAA Division I Women’s Tournament but does not occur in two other major sports tournaments that are similar in structure to March Madness. We offer explanations for the presence of a middle-seed anomaly in the NCAA basketball tournaments, and its absence in the others, that are based on the combined effects of the functional form of the relationship between team strength and seed specific to each tournament, the degree of parity among teams, and certain elements of tournament structure. Although these explanations account for the existence of middle-seed anomalies in the NCAA basketball tournaments, their larger-than-expected magnitudes, which arise mainly from the overperformance of seeds 10–12 in the second round, remain enigmatic.

Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players’ performance. Metrics applied successfully in other sports, such as the (adjusted) +/− that allows for division of credit among a basketball team’s players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framework that can estimate the expected contribution of a soccer player to his team’s winning chances using publicly available data. In particular, using data from (i) approximately 20,000 games from 11 European leagues over eight seasons, and, (ii) player ratings from the FIFA video game, we estimate through a Skellam regression model the importance of every line (attackers, midfielders, defenders and goalkeeping) in winning a soccer game. We consequently translate the model to expected league points added above a replacement player (eLPAR). This model can further be used as a guide for allocating a team’s salary budget to players based on their expected contributions on the pitch. We showcase similar applications using annual salary data from the English Premier League and identify evidence that in our dataset the market appears to under-value defensive line players relative to goalkeepers.

The Elo rating system, originally designed for rating chess players, has since become a popular way to estimate competitors’ time-varying skills in many sports. Though the self-correcting Elo algorithm is simple and intuitive, it lacks a probabilistic justification which can make it hard to extend. In this paper, we present a simple connection between approximate Bayesian posterior mode estimation and Elo. We provide a novel justification of the approximations made by linking Elo to steady-state Kalman filtering. Our second key contribution is to observe that the derivation suggests a straightforward procedure for extending Elo. We use the procedure to derive versions of Elo incorporating margins of victory, correlated skills across different playing surfaces, and differing skills by tournament level in tennis. Combining all these extensions results in the most complete version of Elo presented for the sport yet. We evaluate the derived models on two seasons of men’s professional tennis matches (2018 and 2019). The best-performing model was able to predict matches with higher accuracy than both Elo and Glicko (65.8% compared to 63.7 and 63.5%, respectively) and a higher mean log-likelihood (−0.615 compared to −0.632 and −0.633, respectively), demonstrating the proposed model’s ability to improve predictions.

Prediction of player performance is a key component in the construction of baseball team rosters. As a result, most prediction models are the proprietary property of team or industrial sports entities, and little is known about them. Of those models that have been published, the main focus has been to separately model each outcome with nearly no emphasis on uncertainty quantification. This research introduces a joint modeling approach to predict seasonal plate appearance outcome vectors using a mixed-effects multinomial logistic-normal model. This model accounts for positive and negative correlations between outcomes, both across and within player seasons, and provides a joint posterior predictive outcome distribution from which uncertainty can be quantified. It is applied to the important, yet unaddressed, problem of predicting performance for players moving between the Japanese (NPB) and American (MLB) major leagues.

Subjective wellness data can provide important information on the well-being of athletes and be used to maximize player performance and detect and prevent against injury. Wellness data, which are often ordinal and multivariate, include metrics relating to the physical, mental, and emotional status of the athlete. Training and recovery can have significant short- and long-term effects on athlete wellness, and these effects can vary across individual. We develop a joint multivariate latent factor model for ordinal response data to investigate the effects of training and recovery on athlete wellness. We use a latent factor distributed lag model to capture the cumulative effects of training and recovery through time. Current efforts using subjective wellness data have averaged over these metrics to create a univariate summary of wellness, however this approach can mask important information in the data. Our multivariate model leverages each ordinal variable and can be used to identify the relative importance of each in monitoring athlete wellness. The model is applied to professional referee daily wellness, training, and recovery data collected across two Major League Soccer seasons.