Out of gas: quantifying fatigue in MLB relievers

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.