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Abstract:
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The “Time Through the Order Penalty” (TTOP), first identified by Tango et al. in 2007, quantifies the notion that as a baseball game goes on, batters appear to perform better the more times they face a particular pitcher. Unfortunately, Tango et al.'s analysis is incomplete: it fails to describe how it adjusts for confounders like batter and pitcher quality and, importantly, it fails to quantify the uncertainty in the estimated effect of the penalty, making it difficult to assess its significance. In response, we conduct a rigorous statistical analysis of the trajectory of pitcher performance over the course of a baseball game. Specifically, we fit a Bayesian multinomial logistic regression model to estimate how time through the order affects the probability of each outcome of a plate appearance, after adjusting for confounders. We find that the TTOP is essentially negligible. Somewhat unsurprisingly, we find that pitcher and batter quality have a much larger impact on the outcome of a plate appearance than the TTOP. This suggests that when deciding to pull a starting pitcher, managers should focus more on assessing the pitcher's quality that day than simply appealing to the TTOP.
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