The relationship between players’ average marginal contributions and salaries: an application to NBA basketball using the generalized Shapley value

Abstract

Measuring players’ importance in basketball is allowed by many proposed advanced measures based on play-by-play data, such as the adjusted plus-minus, the wins above replacement, and the generalized Shapley value. In this paper we focus on the latter one in order to study whether, for a player, obtaining a large salary can be explained by its average marginal contribution to the team win. In order to explore this issue, a linear regression model strategy where the logarithm of salaries (Y) depends on the generalized Shapley value (X) is proposed and applied to players of selected National Basketball Association (NBA) teams over selected seasons. A validation based on confusion matrices and on the Hit-Rate index shows that the accuracy in predicting whether free-agent players will obtain a more profi table contract solely basing on their generalized Shapley value is fairly good.