Predict your next football game with the Generalized Matching Equation!

By Todd A. Ward, PhD, BCBA-D

Founding Editor,

Stilling and Critchfield, in a study published in the Journal of the Experimental Analysis of Behaviortested the degree to which the Generalized Matching Equation (GME) predicted the selection of passing vs. rushing plays in the National Football League.

In short, the GME is an equation that predicts how behaviors are allocated across concurrent choices relative to differential rates of reinforcement across the choices.  The model, which traces its origins to Baum (1974) also provides a measure of bias, which refers to “a preference for one behavior beyond what the r terms predict.”  For “r terms” read reinforcement rates for competing behaviors.

The authors note that theirs is not the first to apply the GME to naturalistic settings.  In fact, the GME has been shown to predict the course of conversations, teen pregnancy, and a variety of sports events.  Stilling and Critchfield built on the previous work of Reed et al. (2006), who found that the GME predicted a bias for rushing plays on first downs and passing plays on third downs, with yards gained as reinforcers.  They sought to extend Reed et al.’s work to further examine the ability of the GME to tease out situational elements in play selection to better predict the course of the game.

Through an analysis of archived statistics from 192 football games, the authors examined season-aggregate data for each team across an entire season, as well as a random selection of six games from each team in order to examine play-by-play data.  Results suggest that “the GME accounted for about 40% to 70% of the variance in play selection across the various game-situation categories.”  For example, the GME showed that passing was most often selected in five specific cases: “second down, 5-1 yards needed for a first down; 2:01-15:00 remaining in the half, score tied, and ball positioned 9-82 yards from the goal.”

The authors recognized the descriptive, non experimental, nature of the study.  In doing so, they made an assumption that yards gained functioned as a reinforcer for play selection.  Even so, the authors suggest that their study lends a degree of “explanatory flexibility” to the GME by specifying how parameters of the model relate to specific situational factors in play selection. They assert that, if the football elite are to become interested in an operant account of play selection, it must address “the rich play-selection variance that is part of the sport’s appeal.”

Do you think the GME is the way to get others interested in behavior analysis?  Let us know in the comments below, and be sure to check out the full article for many more details not mentioned here.  Also don’t forget to subscribe to bSci21 via email to receive the latest articles directly to your inbox!


Todd A. Ward, PhD, BCBA-D is President of bSci21 Media, LLC, which owns and  Todd serves as an Associate Editor of the Journal of Organizational Behavior Management and as an editorial board member for Behavior and Social Issues.  He has worked as a behavior analyst in day centers, residential providers, homes, and schools, and served as the director of Behavior Analysis Online at the University of North Texas.  Todd’s areas of expertise include writing, entrepreneurship, Acceptance & Commitment Therapy, Instructional Design, Organizational Behavior Management, and ABA therapy. Todd can be reached at

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