Measuring players’ importance in basketball using the generalized Shapley value

Abstract

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.

Modeling the influence of basketball players’ offense roles on team performance

“…Assessing the critical performance indicators of players and teams is an equally important aspect of sports analysis (Sarlis and Tjortjis, 2020). Previously, basketball data expert Dean Oliver presented a pioneering understanding of data analysis (Oliver, 2004), prompting scholars to subsequently develop diverse metrics for evaluating the game from multiple viewpoints (Cooper et al, 2009;Metulini and Gnecco, 2022). Given that the intricacy of match performance stems from the unique contextual setting in which each match takes place, situational elements like location, opponent, and stage of play exert behavioral influences on the performance of athletes and sports teams (McGarry et al, 2013).…”