Measuring Spatial Allocative Efficiency in Basketball

TL;DR

This paper introduces a new spatial allocative efficiency metric in basketball that assesses how well shot attempts are distributed among players based on court location, aiming to optimize team offensive performance.

Contribution

The paper develops a Bayesian hierarchical model to estimate player FG% at every court location and introduces a spatial efficiency metric to identify sub-optimal shot allocation within lineups.

Findings

Inefficient shot allocation correlates with lower team scoring.

The new metric identifies specific court areas with sub-optimal shot distribution.

Optimizing shot allocation can enhance overall offensive potential.

Abstract

Every shot in basketball has an opportunity cost; one player's shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency---the optimal way to allocate shots within a lineup---is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player's field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup's estimated FG%s and pairing these rankings with the lineup's empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team's overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.