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The Matching Law in Nature


March Madness is Match(ing) Madness!

While waiting for the next game in the NCAA Basketball Tournament, you should read the articles cited below showing the near perfection of the Matching Law for predicting 2- and 3-point shots in basketball. A simple principle accounts for over 90% of the variance in a complex, multiply-determined human behavior.

The Matching Law says that behavior is distributed in proportion to the relative rates of obtained reinforcement. A 3-point shot is worth 50% more than a 2-point shot. This suggests double the preference for 3-pointers over 2-pointers. Why do we not see mostly 3-point shots? Because it's not the reinforcement we assign that makes the difference. It's the reinforcement the person actually earns: the obtained reinforcement. When the relative accuracies for 2- and 3-point shots are factored in to determine the actual points obtained for each type of shot, we see almost perfect matching.

Graphs showing matching law applied to basketball
From: Alferink, Critchfield, & Hitt (2009), Journal of Applied Behavior Analysis


Alferink, L.A., Critchfield, T. S. & Hitt, J.L. (2009). Generality of the matching law as a descriptor of shot selection in basketball. Journal of Applied Behavior Analysis, 42, 595–608. (PDF)

Bourret, J. & Vollmer, T. (2000). An application of the matching law to evaluate the allocation of two- and three-point shots by college basketball players. Journal of Applied Behavior Analysis, 33, 137-150. (PDF)

Bourret, J. & Vollmer, T. (2003). Basketball and the matching law. Behavioral Technology Today, 3, 2-6. (PDF)

Romanowich, P., Bourret, J. & Vollmer, T. (2007). Further analysis of the matching law to describe two-and three-point shot allocation by professional basketball players. Journal of Applied Behavior Analysis, 40, 311–315. (PDF)