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

TL;DR

This paper introduces novel methods for estimating player age-performance curves by accounting for selection bias and using data imputation, leading to more accurate and realistic age-related performance assessments.

Contribution

It highlights the role of selection bias in age-performance analysis and proposes new imputation-based estimation methods that improve accuracy over existing approaches.

Findings

Imputation methods reduce RMSE in age curve estimation

Models accounting for individual skill produce more accurate age curves

Simulation results favor imputation-based approaches over traditional methods

Abstract

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.