Measuring players' importance in basketball using the generalized Shapley value

Measuring players' importance in team sports to help coaches and staff with the aim of winning the game is gaining relevance, mainly because of the advent of new data and advanced technologies. In this paper we evaluate each player's importance - for the first time in basketball - as his/her average marginal contribution to the utility of an ordered subset of players, through a generalized version of the Shapley value, where the value assumed by the generalized characteristic function of the generalized coalitional game is expressed in terms of the probability a certain lineup has to win the game. In turn, such probability is estimated by applying a logistic regression model in which the response is represented by the game outcome and the Dean's factors are used as explanatory features. Then, we estimate the generalized Shapley values of the players, with associated bootstrap confidence intervals. A novelty, allowed by explicitly considering single lineups, is represented by the possibility of forming best lineups based on players' estimated generalized Shapley values conditional on specific constraints, such as an injury or an a-priori coach's decision. A comparison of our proposed approach with industry-standard counterparts shows a strong linear relation. We show the application of our proposed method to seventeen full NBA seasons (from 2004/2005 to 2020/21). We eventually estimate generalized Shapley values for Utah Jazz players and we show how our method is allowed to be used to form best lineups.

Automated summary

This paper evaluates the importance of each basketball player using a generalized version of the Shapley value, aiming to help coaches and staff form the best lineups for winning the game. The approach incorporates new data and advanced technologies, estimating the probability of winning based on logistic regression models and Dean's factors. The proposed method demonstrates a strong linear relation with industry-standard counterparts and is applied to multiple NBA seasons.