Hitting is contagious in baseball: evidence from long hitting streaks

Abstract

Data analysis is used to test the hypothesis that "hitting is contagious". A statistical model is described to study the effect of a hot hitter upon his teammates' batting during a consecutive game hitting streak. Box score data for entire seasons comprising [Formula: see text] streaks of length [Formula: see text] games, including a total [Formula: see text] observations were compiled. Treatment and control sample groups ([Formula: see text]) were constructed from core lineups of players on the streaking batter's team. The percentile method bootstrap was used to calculate [Formula: see text] confidence intervals for statistics representing differences in the mean distributions of two batting statistics between groups. Batters in the treatment group (hot streak active) showed statistically significant improvements in hitting performance, as compared against the control. Mean [Formula: see text] for the treatment group was found to be [Formula: see text] to [Formula: see text] percentage points higher during hot streaks (mean difference increased [Formula: see text] points), while the batting heat index [Formula: see text] introduced here was observed to increase by [Formula: see text] points. For each performance statistic, the null hypothesis was rejected at the [Formula: see text] significance level. We conclude that the evidence suggests the potential existence of a "statistical contagion effect". Psychological mechanisms essential to the empirical results are suggested, as several studies from the scientific literature lend credence to contagious phenomena in sports. Causal inference from these results is difficult, but we suggest and discuss several latent variables that may contribute to the observed results, and offer possible directions for future research.

Figure 1. Distribution of BA statistic for sample groups.

Original sample data representing the population from which resampled statistics are drawn, and ultimately used to construct bootstrap distributions and confidence intervals.

Figure 2. Distribution of Q statistic for sample groups.

Original sample data representing the population from which resampled statistics are drawn, and ultimately used to construct bootstrap distributions and confidence intervals.

Figure 3. Bootstrap distribution for for difference in group wise means, T_BA.

Blue lines denote confidence interval around a mean difference , or 11 percentage points. Sample size , replicates.

Figure 4. Bootstrap distribution for difference in group wise means, T_Q.

Blue lines denote confidence interval around mean difference . Sample size , replicates.

Figure 5. Mean BA versus relative lineup position.

Offensive statistics for players in each sample group as a function of batting order. Negative values along the abscissa correspond to batting before the streak hitter.

Figure 6. Mean Q versus relative lineup position.

Offensive statistics for players in each sample group as a function of batting order. Negative values along the abscissa correspond to batting before the streak hitter.