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The impact of player age on performance has received attention across sport.Most research has focused on the performance of players at each age, ignoringthe reality that age likewise influences which players receive opportunities toperform. Our manuscript makes two contributions. First, we highlight howselection bias is linked to both (i) which players receive opportunity toperform in sport, and (ii) at which ages we observe these players perform. Thisapproach is used to generate underlying distributions of how players move inand out of sport organizations. Second, motivated by methods for missing data,we propose novel estimation methods of age curves by using both observed andunobserved (imputed) data. We use simulations to compare several comparativeapproaches for estimating aging curves. Imputation-based methods, as well asmodels that account for individual player skill, tend to generate lower RMSEand age curve shapes that better match the truth. We implement our approachusing data from the National Hockey League.

What does not get observed can be used to make age curves stronger: estimating player age curves using regression and imputation