Hot or Not? A Nonparametric Formulation of the Hot Hand in Baseball

Abstract

A nonparametric analysis of player plate appearances (PA) in the 2018 Major League Baseball (MLB) season provides no evidence of a batter hot hand. Players with more than 100 PAs in the 2018 season are analyzed using one-sided permutation tests stratified by player. Based on recent literature, we use the correlation between lagged on-base percentage (OBP)and a binary indicator of on-base performance. We discuss the strengths and weaknesses of this test statistic as well as others in the literature. A common criticism of no-hot-hand findings for individual players is low power, and a frequently proposed remedy is pooling data across players. Through simulation, we show that pooling data conflates long-term ability and recent performance. Another common criticism of no-hot-hand findings is emphasis on recent performance. We show that long lags, which de-emphasize recent performance, can lead to counter intuitive results. In contrast to much of the recent literature, which uses parametric methods, we argue that our nonparametric method is the most appropriate way to analyze the existence of the hot hand in baseball as well as numerous other inference questions.