Measuring individual worker output in a complementary team setting: Does regularized adjusted plus minus isolate individual NBA player contributions?

Abstract

Adjusted plus minus (APM) measures have redefined our understanding of player value in basketball and hockey, where both are team games featuring player productivity spillovers. APM measures use seasonal play-by-play data to estimate individual player contributions. If a team's overall score margin success is figuratively represented by a pie, APM measures are well-designed to slice the pie and attribute individual contributions accordingly. However, they do not account for the possibility that better players can increase the overall size of the pie and thus increase the size of the slice (overall APM value) for teammates. Herein, we use data from NBA player-season Real Plus Minus (RPM)-a leading APM measure-for all recorded player-seasons from 2013-19 and player lineup data to test whether RPM is related to teammate quality. We run sets of linear fixed effect regression models to explain variation in RPM across player-seasons. We also employ a two-stage least square (2-SLS) method for robustness check. Both empirical approaches address potential endogeneity in the relationship of interest. We find strong evidence that RPM is related to on-court teammate quality. Despite adjusting for teammate and opponent quality, RPM does not control for complementarity effects. As such, RPM is not suited for out-of-sample prediction.