Madness is Match(ing) Madness!
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
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.
Critchfield, & Hitt (2009), Journal
of Applied Behavior Analysis
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.
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,
J. & Vollmer, T. (2003). Basketball and the matching law. Behavioral
Technology Today, 3, 2-6. (PDF)
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)