Daniel F. Stone, Associate Professor of Economics, Bowdoin College
Brian Mills, Associate Professor, Department of Kinesiology & Health Education, University of Texas at Austin
Duncan Finigan, Associate Product Manager, Toast/ Bowdoin College, 2018
We address a fundamental baseball decision: when to make the “call to the bullpen” and pull the starting pitcher. The limited prior literature on this topic found that pulling starters earlier tends to reduce runs allowed in the current inning. We use a simple theoretical model to show that this result is consistent with win maximization and does not necessarily imply managerial bias.
We then use data from the 2008-2017 seasons to estimate the effects of pulling the starter on both runs allowed in the current inning and win probability. We argue that the pulling starter decision is plausibly quasi-random conditional on the large set of included covariates, but we acknowledge the lack of true randomization.
Our estimated effect of pulling the starter on runs allowed in the inning is indeed negative, but the effect on win probability is a precise zero. We examine how these effects vary by game situation, including a measure of lucky hitting performance, and use an alternative measure of managerial quality (a moving average of “Manager of the Year” votes), and find only scattered and highly limited evidence of biases.
We interpret the results to imply that call to the bullpen decisions are approximately Bayesian-optimal. However, there was a steady downward trend in the mean inning that starters were pulled over a period of decades prior to our sample time-frame. Thus, managers appear to have learned to optimize, but at a very slow pace.