Volume 14, Issue 2

Offensive performance in baseball depends on a number of correlated factors: the pitches the batter faces, the batter’s choice to swing, and the batter’s hitting ability. Recently a renewed focus on the effect of plate discipline on batter performance has emerged. Plate discipline has traditionally been summarized as the proportion of pitches inside and outside of the strike zone a player swings at; however, there have been few metrics proposed to assess the effect of plate discipline directly on batters’ outcomes. In this paper, we focus on estimating a batter’s performance if he were able to adopt a different plate discipline. Because we wish to assess the effect of a counterfactual plate discipline, we use a potential outcome framework and show how the G-computation algorithm can be used to isolate the effect of plate discipline separately from a batter’s hitting ability or the types of pitches the batter faces. As an example, we implement our approach using data collected with the PITCHf/x system over the 2012–2014 seasons to identify the improvement Starlin Castro would expect to see in offensive performance were he able to adopt Andrew McCutchen’s plate discipline. We estimate that had Castro adopted McCutchen’s discipline his batting average, on-base percentage, and slugging percentage would have increased 0.017 (se = 0.004), 0.040 (se = 0.006), and 0.028 (se = 0.008), respectively.

As relief pitcher usage in Major League Baseball has spiked in recent years, optimal bullpen decision-making has become increasingly vital for team managers. Throughout the season, managers must be mindful to avoid overusing their most talented relievers, due to the risks of injury and ineffectiveness. Despite the substantial amount of attention given to pitcher arm health and injury prevention, the effect of workload on pitcher fatigue is poorly understood. As a result, many of these overuse decisions are driven by feel and intuition. In this paper, we borrow ideas from toxicology to provide a framework for estimating the effect of recent workload on short-term reliever effectiveness, as measured by fastball velocity. Treating a thrown pitch as a fatigue-inducing “toxin” administered to a player’s arm, we develop a Bayesian hierarchical model to estimate the pitcher-level dose-response relationship, the rate of recovery, and the relationship between pitch count and fatigue. Based on the model, we find that the rate of reliever fatigue rises with increasing pitch count. When relief pitchers throw more than 15 pitches in an appearance, they are expected to suffer small, short-term velocity decreases in future games; upon crossing the 20 pitch threshold, this dip is further amplified. For each day that passes after the appearance, we estimate that the effect on a player’s velocity is cut roughly in half. Finally, we identify the relievers most affected by fatigue, along with those most resilient to its effects.

When analyzing and modeling the results of soccer matches, one important aspect is to account for the correct dependence of the scores of two competing teams. Several studies have found that, marginally, these scores are moderately negatively correlated. Even though many approaches that analyze the results of soccer matches are based on two (conditionally) independent pairwise Poisson distributions, a certain amount of (mostly negative) dependence between the scores of the competing teams can simply be induced by the inclusion of covariate information of both teams in a suitably structured linear predictor. One objective of this article is to analyze if this type of modeling is appropriate or if additional explicit modeling of the dependence structure for the joint score of a soccer match needs to be taken into account. Therefore, a specific bivariate Poisson model for the two numbers of goals scored by national teams competing in UEFA European football championship matches is fitted to all matches from the three previous European championships, including covariate information of both competing teams. A boosting approach is then used to select the relevant covariates. Based on the estimates, the tournament is simulated 1,000,000 times to obtain winning probabilities for all participating national teams.

A time-varying predictor in a longitudinal model can be separated into between- and within-subject components. This is important if a researcher is specifically interested in differences between subjects or changes within subjects. If no separation is made, then the effect associated with the time-varying predictor is a combination of the between- and within-subject effects. In this article, running race performances are considered as a nonlinear function of age, for which both absolute and relative difference terms are used to separate between- and within-subject components. Longitudinal data were obtained from 12 consecutive years of the 10-km Bolder Boulder for analysis, for the class of competitive recreational runners. Mixed models were used to fit the data after log transforming the nonlinear model. Results of model fits demonstrated that between-subject differences between ages were somewhat similar to within-subject changes, although the latter tended to change somewhat more slowly, especially after the peak racing ages. For example, the between-subject rate of change for 43 year-old runners was about 1% per year on average (increase in race time), while the within-subject change for a runner of the same age averaged between 0.6 and 0.8% per year.