Estimation of player aging curves using regression and imputation

The impact of age on performance is a fundamental component to models of player valuation and prediction across sport. Age effects are typically measured using age curves, which reflect the expected average performance at each age among all players that are eligible to participate. Most age curve methods, however, ignore the reality that age likewise influences which players receive opportunities to perform. In this paper we begin by highlighting how selection bias is linked to the ages in which we observe players perform. Next, using underlying distributions of how players move in and out of sport organizations, we assess the performance of various methods for age curve estimation under the selection bias of player entry and issues of small samples at younger and older ages. We propose several methods for player age curve estimation, introduce a missing data framework, and compare these new methods to more familiar approaches including both parametric and semi-parametric modeling. We then use simulations to compare several approaches for estimating aging curves. Imputation-based methods, as well as models that account for individual player skill, tend to generate lower root mean squared error (RMSE) and age curve shapes that better match the truth. We implement our approach using data from the National Hockey League. All of the data and code for this paper are available in a Github repository.