Analyzing NBA player positions and interactions with density-functional fluctuation theory.

The increasing availability of high-precision player-tracking data in sports-centimeter-precision positional information of athletes captured dozens of times per second-has the potential to improve the quantification of player abilities and overall team strategies. Working toward achieving this quantification, we adapt density-functional fluctuation theory (DFFT) to infer spatial preferences and player-to-player interactions in National Basketball Association (NBA) basketball. We first demonstrate several foundational results, including the ability of DFFT to predict the location of a player to within 3% of the half-court area roughly half the time, and to provide a team-position-based metric that correlates strongly with play outcomes. Building on these results, we demonstrate that it is possible to improve player positioning and identify player-specific tendencies, such as the consistency with which a player positions himself to help his team collectively defend against 2-point or 3-point shots. Finally, we quantify how particular players attract the opposing team, with and without the ball, constituting the first advanced quantification of 'player gravity' that explicitly deconfounds the influence of teammate positioning.