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AN APPLICATION OF THE MATCHING LAW TO EVALUATE THE ALLOCATION OF TWO‐ AND THREE‐POINT SHOTS BY COLLEGE BASKETBALL PLAYERS
Author(s) -
Vollmer Timothy R.,
Bourret Jason
Publication year - 2000
Publication title -
journal of applied behavior analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.1
H-Index - 76
eISSN - 1938-3703
pISSN - 0021-8855
DOI - 10.1901/jaba.2000.33-137
Subject(s) - basketball , matching (statistics) , reinforcement , point (geometry) , psychology , statistics , range (aeronautics) , matching law , mathematics , social psychology , engineering , history , geometry , archaeology , aerospace engineering
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.