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.

What are we doing when we translate from quantitative models?

“…Using a laboratory choice task, Kollins, Lane, and Shapiro (1997) found that sensitivity often was lower for children with attention deficit hyperactivity disorder than for typically developing controls ( Figure 6A). Alferink et al (2009) found that the sensitivity of basketball shot selection was higher for regular college players than for substitutes ( Figure 6B). …”

“…Applications of the generalized matching law (Figure 2) suggest that in many of these situations behavior allocation is a common function of relative reinforcement. Figure 3 shows the core matching relation as it describes conversation (Panel A; Borrero et al, 2007), basketball shot selection (Panel B; Alferink et al, 2009), and academic behavior (Panel C; Mace, Neef, Shade, & Mauro, 1994).…”

Explanatory Flexibility of the Matching Law: Situational Bias Interactions in Football Play Selection

“…Quite often they are. For example, the GML has accounted for a large proportion of variance in basketball shot selection (two-point versus three-point field goals) when shot-making was considered as the reinforcer (e.g., Alferink et al 2009;Vollmer and Bourret 2000). It is convenient to refer to this kind of outcome as demonstrating the GML's reliability of fit.…”

“…Reed et al (2011) found that emphasis on passing versus rushing (as measured through the GML's bias parameter) varied with the quality of defense played by opposing teams. In applying the GML to preference for two-point versus three-point basketball shots, Alferink et al (2009) found that the GML's sensitivity parameter differed for players on successful versus unsuccessful teams and for regular players versus substitutes. McDowell and Caron (2010) used the GML to describe verbal interactions between pairs of boys, with the relative frequency of two kinds of behaviors (statements that endorsed either rule-breaking or rule-following) considered as a function of the relative frequency of social reinforcement.…”

On applying the matching law to between-subject data

“…A misunderstanding of this fundamental assumption has led several authors (i.e. Schroeder & Holland 1969;Conger & Killeen 1974;Schmitt 1974;Vollmer & Bourret 2000;Borrero & Vollmer 2002;Alferink et al 2009;McDowell & Caron 2010a, b) to conduct their analyses incorrectly. For instance, they used a small number of levels of the independent variable and pooled their subjects' data, which combined idiosyncratic dependent variables into a single analysis and did not account for within-subject and within-level variances.…”