Assessing pitcher and catcher influences on base stealing in Major League Baseball

Abstract

A formal statistical analysis is performed to determine the extent to which pitchers and catchers can influence stolen-base attempts and successes. Two response proportions, attempt/opportunity and success/attempt, are modelled separately using mixed-effects logistic regression models applied to situations with a runner on first and other bases empty. Data include the first innings of all Major League Baseball games played between 1978 and 1990, which encompasses over 48,000 opportunities and 9000 attempts. Pitchers and catchers are entered as random effects and various other factors thought to influence stolen-base attempts and successes are entered as fixed effects. Variance components are estimated and hypotheses tests indicate that the population variance components for both pitchers and catchers are significant for both response proportions. The presence of variation among players at the respective positions is interpreted as evidence that stolen-base defence is a real skill exhibited to varying extents by different players. Furthermore, the variance component for pitchers is greater than that for catchers for both response proportions, indicating that pitchers have greater potential to affect stolen-base attempts and successes. Under usual conditions, it is estimated that 95% of pitchers have first-inning stolen-base success/attempt probabilities between 0.50 and 0.84, while 95% of catchers have probabilities between 0.59 and 0.79.

Keywords:

• Logistic regression
• generalized linear mixed model
• variance component
• stolen base
• sports

Acknowledgements

We thank Bill James for several helpful suggestions for fixed effects, and John Boyer and George Milliken for interesting discussions and encouragement. An anonymous reviewer offered several suggestions that improved the manuscript.