Creating space to shoot: quantifying spatial relative field goal efficiency in basketball

Abstract

Every basketball player takes and makes a unique spatial array of shots. In recent years, technology to measure the coordinates of these constellations has made analysis of them possible, and the possibility exists for distinguishing between different shooters at a level of spatial detail finer than the entire basketball court. This paper addresses the challenge of characterizing and visualizing relative spatial shooting effectiveness in basketball by developing metrics to assess spatial variability in shooting. Several global and local measures are introduced and formal tests are proposed to enable the comparison of shooting effectiveness between players, groups of players, or other collections of shots. We propose an empirical Bayesian smoothing rate estimate that uses a novel local spatial neighborhood tailored for basketball shooting. These measures are evaluated using data from the 2011 to 2012 NBA basketball season in three distinct ways. First we contrast nonspatial and spatial shooting metrics for two players from that season and then extend the comparison to all players attempting at least 250 shots in that season, rating them in terms of shooting effectiveness. Second, we identify players shooting significantly better than the NBA average for their shot constellation, and formally compare shooting effectiveness of different players. Third, we demonstrate an approach to map spatial shooting effectiveness. In general, we conclude that these measures are relatively straightforward to calculate with the right input data, and they provide distinctive and useful information about relative shooting ability in basketball. We expect that spatially explicit basketball metrics will be useful additions to the sports analysis toolbox.