B0334
Title: Players' importance in basketball and the generalized Shapley value
Authors: Rodolfo Metulini - University of Salerno (Italy) [presenting]
Giorgio Gnecco - IMT School for Advanced Studies Lucca (Italy)
Abstract: The issue of how to measure players' importance in team sports is gaining more and more relevance, mainly because of the advent of new data and advanced technologies, in order to help professional coaches and staff with the final aim of winning the game. Each player's importance has been evaluated, for the first time in basketball, by computing his average marginal contribution to the utility of an ordered subset of players, through a generalized version of the Shapley value. A peculiarity is that the value assumed by the generalized characteristic function of the generalized coalitional game is represented by the probability a certain lineup has to win the game. This probability is estimated by applying a logistic regression model, where the response is represented by the game outcome, and the so-called four Dean's factors are used as explanatory features. By applying the proposed approach to play-by-play data covering fourteen full NBA seasons (from 2004/2005 to 2017/18), we obtain generalized Shapley values for the players of selected teams. It is, in such a way, possible to find those players whose average marginal contribution is higher than expected, by comparing each player's generalized Shapley value with his income.
