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We introduce a three-step framework to determine at which pitches Major League batters should swing. Unlike traditional plate discipline metrics, which implicitly assume that all batters should always swing at (resp. take) pitches inside (resp. outside) the strike zone, our approach explicitly accounts not only for the players and umpires involved in the pitch but also in-game contextual information like the number of outs, the count, baserunners, and score. We first fit flexible Bayesian nonparametric models to estimate (i) the probability that the pitch is called a strike if the batter takes the pitch; (ii) the probability that the batter makes contact if he swings; and (iii) the number of runs the batting team is expected to score following each pitch outcome (e.g. swing and miss, take a called strike, etc.). We then combine these intermediate estimates to determine whether swinging increases the batting team’s run expectancy. Our approach enables natural uncertainty propagation so that we can not only determine the optimal swing/take decision but also quantify our confidence in that decision. We illustrate our framework using a case study of pitches faced by Mike Trout in 2019.

It is often the goal of sports analysts, coaches, and fans to predict athlete performance over time. Models such as Bradley–Terry and Plackett–Luce measure athlete skill based on results of competitions over time, but have limited predictive strength without making assumptions about the nature of the evolution of athletic skill. Growth curves are often applied in the context of sports to predict future ability, but these curves are too simple to account for complex career trajectories. We propose a non-linear, mixed-effects trajectory to model the ratings as a function of time and other athlete-specific covariates. The mixture of trajectories allows for flexibility in the estimated shape of career trajectories between athletes as well as between sports. We use the fitted trajectories to make predictions of an athlete’s career trajectory through a model of how athlete performance progresses over time in a multi-competitor scenario as an extension to the Plackett–Luce model. We show how this model is useful for predicting the outcome of women’s luge races, as well as show how we can use the model to compare athletes to one another by clustering career trajectories.

Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics which better cope with these challenges. Specifically, metrics such as expected goals added, goals above expectation, and post-shot expected goals all use advanced data to offer an improvement over the classical conversion rate. However, all metrics developed to date assign a value of zero to off-target shots, which account for almost two-thirds of all shots, since these shots have no probability of scoring. We posit that there is non-negligible shooting skill signal contained in the trajectories of off-target shots and propose two shooting skill metrics that incorporate the signal contained in off-target shots. Specifically, we develop a player-specific generative model for shot trajectories based on a mixture of truncated bivariate Gaussian distributions. We use this generative model to compute metrics that allow us to attach non-zero value to off-target shots. We demonstrate that our proposed metrics are more stable than current state-of-the-art metrics and have increased predictive power.

Every season, the international football calendar contains periods reserved for a series of so-called special matches including international friendly or official matches played by national teams. All these periods are called “FIFA reserved dates” in the calendar and generally cause domestic competitions to shut down for some days. Such interruptions of leagues might generate different effects or externalities on the performance of players, clubs or even on the competition itself. While a number of studies focus on the effect of players’ absence on teams performance, this paper contributes to the literature by specifically evaluating the effect of the “FIFA reserved dates” on football outcomes. Using data for four seasons from the “big five” European leagues, I find evidence that the outcomes distribution in those matches played after a “FIFA reserved date” becomes more balanced, thus increasing the uncertainty of outcome. The results of this paper contribute to the ongoing debate about the management and design of the international match calendar.

Carl Morris 1938–2023 was well-known for his pioneering research in Bayesian multiparameter inference and prediction. Morris was also known for his development of statistical thinking and methodology in sports. This paper provides an overview of Morris’ contributions in sports. This includes Morris’ experience in sports as a youth, summaries of some of Morris’ best-known contributions using sports data, his influence working with students, and some of Morris’ thinking about the interplay of statistics and sports.