Quantifying NBA Player and Lineup Contributions Using Shapley Values and Convex Optimization

Abstract

It is commonly assumed that in a league like the National Basketball Association (NBA), where statistics

are well maintained and broadly reported, the best contributors are clear-cut. The player who gets the most

points, rebounds, and assists is typically assumed to be the biggest contributor to team success. While in most

cases, these statistics can be indicative of a great player, the four other players are also doing their part to

contribute to team success. To obtain a complete picture of player contribution, this study must look beyond

traditional statistics to evaluate the offensive and defensive contributions of specific lineups and players using

novel frameworks. These frameworks must remain agnostic to the traditional statistics mentioned above,

producing data by exclusively observing outcomes. Although this has been attempted previously, many

mathematical subtleties have been overlooked. The goal of this project is to provide specific formulas and

mathematical rigor to commonly used algorithms for estimating player contribution. This study starts with

an exploration of how Shapley Values can be applied to extract individual player contributions from team

outcomes. It then presents a novel closed-form solution for ranking teams through convex optimization by

drawing on observed results from team matchups. Finally, it explores the contributions of lineups through

the same process, equating each lineup to a team and each possession to a game. Beyond basketball, these

frameworks provide concrete methods to quantify contribution in any competitive setting