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

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 performance. In order to explore this issue, a linear regression model strategy where the logarithm of salary (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 leave-one-out cross validation shows that the accuracy in predicting whether free-agent players will obtain a more profitable contract solely basing on their generalized Shapley value is generally fairly good.