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.

翻译：在体育领域，老化曲线描述了运动员职业生涯中平均表现与年龄之间的关系。本文研究了美国职业棒球大联盟进攻球员的老化曲线。我们在缺失数据背景下探讨该问题，并考虑了棒球运动员职业生涯中不同类型的退出机制。具体而言，针对缺失赛季的表现指标，采用适用于多层次数据的多重插补模型进行填补，并基于插补后的数据集构建老化曲线。首先通过模拟研究评估不同退出机制对老化曲线估计的影响，随后利用过去赛季的MLB球员数据进行实证分析。结果表明，未对未观测赛季进行插补时构建的老化曲线存在高估现象，而本文提出的方法能实现更优的估计效果。