Volume 19, Issue 4

As a baseball game progresses, batters appear to perform better the more times they face a particular pitcher. The apparent drop-off in pitcher performance from one time through the order to the next, known as the Time Through the Order Penalty (TTOP), is often attributed to within-game batter learning. Although the TTOP has largely been accepted within baseball and influences many managers’ in-game decision making, we argue that existing approaches of estimating the size of the TTOP cannot disentangle continuous evolution in pitcher performance over the course of the game from discontinuities between successive times through the order. Using a Bayesian multinomial regression model, we find that, after adjusting for confounders like batter and pitcher quality, handedness, and home field advantage, there is little evidence of strong discontinuity in pitcher performance between times through the order. Our analysis suggests that the start of the third time through the order should not be viewed as a special cutoff point in deciding whether to pull a starting pitcher.

This paper explores defensive play in soccer. The analysis is predicated on the assumption that the area of the convex hull formed by the players on a team provides a proxy for defensive style where small areas coincide with a greater defensive focus. With the availability of tracking data, the massive dataset considered in this paper consists of areas of convex hulls, related covariates and shots taken during matches. Whereas the pre-processing of the data is an exercise in data science, the statistical analysis is carried out using linear models. The resultant messages are nuanced but the primary message suggests that an extreme defensive style (defined by a small convex hull) is negatively associated with generating shots.

Successful performance in Formula One is determined by combination of both the driver’s skill and race-car constructor advantage. This makes key performance questions in the sport difficult to answer. For example, who is the best Formula One driver, which is the best constructor, and what is their relative contribution to success? In this paper, we answer these questions based on data from the hybrid era in Formula One (2014–2021 seasons). We present a novel Bayesian multilevel rank-ordered logit regression method to model individual race finishing positions. We show that our modelling approach describes our data well, which allows for precise inferences about driver skill and constructor advantage. We conclude that Hamilton and Verstappen are the best drivers in the hybrid era, the top-three teams (Mercedes, Ferrari, and Red Bull) clearly outperform other constructors, and approximately 88 % of the variance in race results is explained by the constructor. We argue that this modelling approach may prove useful for sports beyond Formula One, as it creates performance ratings for independent components contributing to success.

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the on-line rating algorithms that estimate skills after each new game by exploiting the probabilistic models that (i) relate the skills to the outcome of the game and (ii) describe how the skills evolve in time. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual as well as in the group sports. We show how the well-known Elo, Glicko, and TrueSkill algorithms may be seen as instances of the one-fits-all approach we propose. To clarify the conditions under which the gains of the Bayesian approach over simpler solutions can actually materialize, we critically compare the known and new algorithms by means of numerical examples using synthetic and empirical data.

The FIFA Men’s World Cup tournament is the most popular sporting event in the world. Scholars have identified several flaws in the organization of the World Cup causing competitive imbalance. We empirically assess competitive imbalance between groups for the World Cup tournaments from 1954 through 2022. We average the Elo ratings of a team’s opponents in the group stage to calculate their group opponents rating. In every World Cup, the range in group opponents rating exceeds 118 Elo rating points – the difference between an average participant and an average semifinalist. Using logistic regression, we find that for an average participant in a 32-team World Cup, an increase in group opponents rating of only 88 Elo rating points can reduce the probability of reaching the quarterfinal from 0.174 to 0.081, which is a decrease of more than 50 %. None of the five seeding systems used by FIFA during 1954–2022 lessened the negative impact of group opponents rating on the probability of reaching the quarterfinal. We close with seven policy recommendations to restore competitive balance at the World Cup.