  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.
