Derek D. Reed, Thomas S. Critchfield, & Brian K. Martens. (2006)
The generalized matching law in elite sport competition:
Football play calling as operant choice.
Journal of Applied Behavior Analysis,
39, 281-297.
A mathematical model of operant choice, the generalized matching law
was used to analyze play-calling data from the 2004 National Football
League season. In all analyses, the relative ratio of passing to rushing
plays was examined as a function of the relative ratio of reinforcement,
defined as yards gained, from passing versus rushing. Different analyses
focused on season-aggregate data for the league as a whole, game-by-game
data for the league as a whole, and game-by-game data for individual teams.
In all analyses except those for a few individual teams, the generalized
matching law accounted for a majority of variance in play calling. The typical
play-calling pattern reflected undermatching (suggesting imperfect sensitivity
of play calling to yardage-gained reinforcers) and a bias for calling
rushing plays. Bias was found to be a function of both the relative risk
of turnovers and the relative variability in yards gained associated with
passing versus rushing plays. The external validity of the matching analyses
was supported by significant correlations between parameters of the generalized
matching law and team success on offense and season winning percentage. These
results illustrate the broad applicability of the generalized matching law to
problems outside of the laboratory.
DESCRIPTORS: choice, generalized matching law, football, sport, play calling