TY - JOUR
T1 - The generalized matching law in elite sport competition
T2 - Football play calling as operant choice
AU - Reed, Derek D.
AU - Critchfield, Thomas S.
AU - Martens, Brian K.
PY - 2006/9
Y1 - 2006/9
N2 - A mathematical model of operant choice, the generalized matching law was used to analyze playcalling 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 yardagegained 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.
AB - A mathematical model of operant choice, the generalized matching law was used to analyze playcalling 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 yardagegained 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.
KW - Choice
KW - Football
KW - Generalized matching law
KW - Play calling
KW - Sport
UR - http://www.scopus.com/inward/record.url?scp=33748933076&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33748933076&partnerID=8YFLogxK
U2 - 10.1901/jaba.2006.146-05
DO - 10.1901/jaba.2006.146-05
M3 - Article
C2 - 17020210
AN - SCOPUS:33748933076
SN - 0021-8855
VL - 39
SP - 281
EP - 297
JO - Journal of Applied Behavior Analysis
JF - Journal of Applied Behavior Analysis
IS - 3
ER -