Explanatory Flexibility of the Matching Law: Situational Bias Interactions in Football Play Selection

Abstract

The generalized matching law was used to evaluate play selection (passing versus rushing) in professional football game situations defined by combinations of football-specific factors. Archival statistics were analyzed to determine whether play selection covaried with yards gained from passing and rushing plays, and whether the details of this relationship, as measured by the matching law's fitted parameters, varied systematically across game situations. The matching law accounted for substantial variance in play selection for several combinations of game situations, and statistically significant situation-interaction effects were found for bias, but not sensitivity. Follow up analyses revealed that, across game situations, play-selection bias effects were closely related to relative probability of a turnover (can be described in terms of punishment) and the relative yards-gained variance (which can be described in terms of variable-magnitude reinforcement schedules). These results bolster an operant-choice interpretation of football play selection; they reveal two separate aspects of play preference (generic matching versus bias); and provide a rare example of how face-valid effects in a domain of everyday interest may relate to a theoretically-important term of a laboratory-based quantitative model of choice.

Experimental evaluation of matching via a commercially available basketball video game

“…While other behavioral scientists have employed video games to answer behavior analytic questions related to concepts such as matching (e.g., Kollins, Lane, & Shapiro, 1997; Neuringer, Deiss, & Imig, ) and discounting (e.g., Scheres et al, ; Young & McCoy, ), the games were developed specifically for those experiments and lacked many of the features used in commercial video game design. Our findings open the door for extensions of this work to model how situational factors during gameplay impact sensitivity to reinforcement (e.g., Critchfield, Meeks, & Stilling, ). Beyond matching, this videogame preparation could be useful for human operant experiments of other behavioral phenomena involving basic schedule performance (e.g., resurgence).…”

A matching law analysis of risk tolerance and gain–loss framing in football play selection.

“…Figure 1 does not bear directly on risk aversion or game score, but it demonstrates empirically that NFL play selection can vary across game situations in terms of whether rushing plays occur more or less than "expected." Stilling and Critchfield's (2010; see also Critchfield, Meeks, & Stilling, 2014) evaluation of play selection in several kinds of game situations suggested that the third-down bias for passing shown in Figure 1 (and also described previously by Reed et al, 2006) is a bit of an aberration. In most game situations that have been examined, such as those defined by field position, the number of yards needed to earn a new set of downs, and time remaining to play in the game, play selection tends to reflect a rushing bias.…”

“…For each of the score categories, each team’s plays from the six targeted games were pooled to allow the team to count as one “observation.” Consistent with the approach of previous studies (Critchfield et al, 2014; Reed et al, 2006; Stilling & Critchfield, 2010), for each score category least-squares linear regression was used to fit the GML (Equation 2) to a function involving one data point for each NFL team. Seven teams that had fewer than 15 offensive opportunities in one of the score categories were dropped from the analysis (on the grounds that ratio measures are volatile when based on a small number of cases), leaving n = 25 teams.…”

“…For present purposes game score is worthy of emphasis because of its obvious relevance to gain–loss framing, which has been widely shown to relate to risk tolerance. For information on how play selection varies under game situations that are not defined by the score, we refer the reader to Critchfield et al (2014); Reed et al, (2006); Reed et al, (2011); and Stilling and Critchfield (2010).…”

Matching theory applied to MLB team-fan social media interactions: An opportunity for behavior analysis.

“…Recent applications either go beyond simple demonstrations and offer additional insight into the explanatory flexibility of matching theory to account for situational modulators of matching (Critchfield, Meeks, & Stilling, 2014; Critchfield & Stilling, 2015; Reed, Skoch, Kaplan, & Brozyna, 2011; Stilling & Critchfield, 2010) or they demonstrate that matching predicts athletic success in other ways (Alferink, Critchfield, Hitt, & Higgins, 2009; Seniuk, Williams, Reed, & Wright, 2015). A yet-to-be explored avenue of translational interest is fan behavior in sport.…”