Generality of the matching law as a descriptor of shot selection in basketball

Abstract

Based on a small sample of highly successful teams, past studies suggested that shot selection (two- vs. three-point field goals) in basketball corresponds to predictions of the generalized matching law. We examined the generality of this finding by evaluating shot selection of college (Study 1) and professional (Study 3) players. The matching law accounted for the majority of variance in shot selection, with undermatching and a bias for taking three-point shots. Shot-selection matching varied systematically for players who (a) were members of successful versus unsuccessful teams, (b) competed at different levels of collegiate play, and (c) served as regulars versus substitutes (Study 2). These findings suggest that the matching law is a robust descriptor of basketball shot selection, although the mechanism that produces matching is unknown.

Keywords: basketball shot selection; choice; matching law.

Figure 1

Relation between shot-selection and shots-made ratios for six illustrative Division I college teams (2005–2006 season). Each data point represents one player's season-aggregate statistics. See text for details.

Figure 2

Results of fitting the generalized matching law to the shot-selection data of NCAA Division I teams from the 2005–2006 season. Top: variance accounted for by the matching law for 319 teams. Middle: sensitivity estimates (a parameter, or slope) for 315 teams. Bottom: bias estimates (log b parameter or y intercept) for 315 teams.

Figure 3

Distribution of sensitivity estimates (a parameter) derived from fitting the generalized matching law to the behavior-allocation data of individuals in laboratory choice experiments (estimated from Figure 1 of Robinson, 1992) and to the shot-selection data of 315 NCAA Division I teams. Sensitivity estimates were logarithmically transformed to normalize the distributions.

Figure 4

Relation between shot-selection and shots-made ratios for nine iconic professional basketball players. Each data point represents one season. In each panel, dates show the span of a player's career, with the number of seasons that were included in the analysis shown in parentheses. See text and Table 2 for details.