Pulling starters

We theoretically and empirically study a fundamental strategic decision in baseball: when to make the “call to the bullpen” and pull th=e starting pitcher. The limited previous literature on this topic found that pulling starters tends to reduce runs allowed in the current inning. We show with a simple model that this result is consistent with win maximization, and does not necessarily imply that starters should typically be pulled sooner. We then use detailed pitch-level data from the 2008–2017 seasons to estimate the effects of pulling the starter on both runs allowed in the current inning and on win probability. We argue that whether or not the starter is pulled is plausibly “as good as random” conditional on the large set of included covariates, but acknowledge the lack of true randomization. We find that the estimated effect of pulling the starter on runs allowed in the current inning is indeed negative, but the effect on win probability is a precise zero. We examine a variety of game situations and recent events, and find only scattered and limited evidence of biases, but note that statistical power is limited for these analyses. We interpret the results to imply that, at least on average, decisions for when to pull starters were approximately Bayesian-optimal in between plate appearances due to a period of institutional learning that occurred over decades. However, starters were very rarely pulled within-plate appearances, so we cannot analyze the optimality of these decisions.