The impact of player age on performance has received attention across sport. Most research has focused on the performance of players at each age, ignoring the reality that age likewise influences which players receive opportunities to perform. Our manuscript makes two contributions. First, we highlight how selection bias is linked to both (i) which players receive opportunity to perform in sport, and (ii) at which ages we observe these players perform. This approach is used to generate underlying distributions of how players move in and out of sport organizations. Second, motivated by methods for missing data, we propose novel estimation methods of age curves by using both observed and unobserved (imputed) data. We use simulations to compare several comparative approaches for estimating aging curves. Imputation-based methods, as well as models that account for individual player skill, tend to generate lower RMSE and age curve shapes that better match the truth. We implement our approach using data from the National Hockey League.
翻译:球员年龄对球员表现的影响在整个体育中引起了关注。大多数研究都侧重于球员在每一年龄的表现,忽视了年龄同样影响球员获得表演机会的现实。我们的手稿做出了两项贡献。首先,我们强调选择偏见如何与以下两方面联系在一起:(一)球员在体育中获得表演机会,以及(二)我们观察这些球员所表现的年龄。这个方法被用来产生球员在体育组织中进出球员如何移动的基本分布。第二,由于缺少数据的方法,我们提出新的年龄曲线估计方法,我们使用观测到的数据和未观测到的(模拟)数据。我们使用模拟来比较几种比较方法来估计老化曲线。基于光学法的方法,以及计算个人球员技能的模式,往往产生更符合事实的更低的皇家骑兵队和年龄曲线形状。我们使用来自国家曲棍联盟的数据来实施我们的方法。