An application of the matching law to evaluate the allocation of two- and three-point shots by college basketball players

We applied the matching equation to evaluate the allocation of two- and thr ee-point shea by male and female college basketball players from a large Di vision 1 university. The matching law predicts that the proportion of shots taken from three-point range should match the proportional reinforcement r ate produced by such shots. Thus, we compared the proportion of three-point shots taken relative to all show to the proportion of three-point shots sc ored relative to all shots scored. However, the matching equation was adjus ted to account for the greater reinforcer magnitude of the three-point bask et (i.e., 1.5 times greater than the two-point basket reinforcer magnitude) . For players with substantial playing rime, results showed that the overal l distribution of two- and three-point shots was predicted by the matching equation. Game-by-game shot distribution was variable, but the cumulative p roportion of shots taken from three-point range as the season progressed wa s predicted almost perfectly on a player-by-player basis for both male and female basketball players.