Evaluating Basketball Player Performance via Statistical Network Modeling

The major difficulty in evaluating individual player performance in basketball is adjusting for interaction effects by teammates. With the advent of play-by-play data, the plus-minus statistic was created to address this issue [5]. While variations on this statistic (ex: adjusted plusminus [11]) do correct for some existing confounders, they struggle to gauge two aspects: the importance of a player’s contribution to his units or squads, and whether that contribution came as unexpected (i.e. overor under-performed) as defined by a statistical model. We quantify both in this paper by adapting a network-based algorithm to estimate centrality scores and their corresponding statistical significances [10]. Using four seasons of data [9], we construct a single network where the nodes are players and an edge exists between two players if they played in the same five-man unit. These edges are assigned weights that correspond to an aggregate sum of the two players’ performance during the time they played together. We determine the statistical contribution of a player in this network by the frequency with which that player is visited in a random walk on the network, and we implement bootstrap techniques on these original weights to produce reference distributions for testing significance.