The matching law to evaluate the allocation of two-and three-point shots by college basketball
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2000) AN APPLICATION OF THE MATCHING LAW TO EVALUATE THE ALLOCATION OF
TWO- AND THREE-POINT SHOTS BY COLLEGE BASKETBALL PLAYERS
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JOURNAL OF APPLIED BEHAVIOR ANALYSIS 2000, 33, 137–150 NUMBER 2 (SUMMER 2000) AN APPLICATION OF THE MATCHING LAW TO EVALUATE THE ALLOCATION OF TWO- AND THREE-POINT SHOTS BY COLLEGE BASKETBALL PLAYERS TIMOTHY R. VOLLMER AND JASON BOURRET UNIVERSITY OF FLORIDA We applied the matching equation to evaluate the allocation of two- and three-point shots by male and female college basketball players from a large Division 1 university. The matching law predicts that the proportion of shots taken from three-point range should match the proportional reinforcement rate produced by such shots. Thus, we compared the proportion of three-point shots taken relative to all shots to the proportion of three-point shots scored relative to all shots scored. However, the matching equation was adjusted to account for the greater reinforcer magnitude of the three-point basket (i.e., 1.5 times greater than the two-point basket reinforcer magnitude). For players with substantial playing time, results showed that the overall distribution of two- and three- point shots was predicted by the matching equation. Game-by-game shot distribution was variable, but the cumulative proportion of shots taken from three-point range as the season progressed was predicted almost perfectly on a player-by-player basis for both male and female basketball players. DESCRIPTORS: athletic performance, basketball, matching law, sports, quantitative analysis The matching law is a quantitative for- where R1 represents the rate of responding mulation stating that the relative rates of re- on one response alternative and R2 repre- sponding across two concurrently available sents the rate of responding on a second al- alternatives tend to equal the relative rein- ternative; r1 and r2 represent the respective forcement rates they produce (Catania, rates of reinforcement for those alternatives. 1992). For example, if an animal receives A large body of empirical research with hu- food reinforcement for pressing Lever A on mans and nonhumans has shown the robust a variable-interval (VI) 30-s schedule and descriptive validity of the matching equa- pressing Lever B on a VI 60-s schedule, the tion. Further, the basic formulation is flexi- animal is likely to press Lever A twice as ble enough to incorporate variables such as often as it presses Lever B (e.g., Herrnstein, reinforcer delay, reinforcer magnitude, and 1961). This phenomenon is called matching response bias (Baum, 1974b; McDowell, (Herrnstein, 1961, 1970), and an equation 1989). In this study, we applied the equation representing the formulation can be ex- to the allocation of two- and three-point pressed as follows: basket shooting in college basketball players. Several studies have involved experimental R1 r1 , (1) manipulations of reinforcement rates to eval- R1 R2 r1 r2 uate matching with human behavior in ap- plied settings (Fisher & Mazur, 1997). For We thank Tony Nevin and the anonymous review- example, Conger and Killeen (1974) showed ers for their detailed recommendations about data pre- that allocation of conversation in college stu- sentation and analysis. dents was distributed in a manner propor- Reprint requests can be sent to Timothy R. Vollmer, Psychology Department, University of Florida, tional to the rate of reinforcement (positive Gainesville, Florida 32611. vollmer@psych.ufl.edu reply statements) delivered by a confederate. 137
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