Filling in the Gaps: A Multiple Imputation Approach to Estimating Aging Curves in Baseball

In sports, an aging curve depicts the relationship between average performance and age in athletes' careers. This paper investigates the aging curves for offensive players in the Major League Baseball. We study this problem in a missing data context and account for different types of dropouts of baseball players during their careers. In particular, the performance metric associated with the missing seasons is imputed using a multiple imputation model for multilevel data, and the aging curves are constructed based on the imputed datasets. We first perform a simulation study to evaluate the effects of different dropout mechanisms on the estimation of aging curves. Our method is then illustrated with analyses of MLB player data from past seasons. Results suggest an overestimation of the aging curves constructed without imputing the unobserved seasons, whereas a better estimate is achieved with our approach.