Application of the matching law to Mixed Martial Arts

In the contemporary behavior-analytic literature, athletic performance (e.g.,choice of shot or movement) across multiple team sports has been found to correspond with predictions of the generalized matching equation. However, the research in this area has focused primarily on team sports. In the current study the Generalized Matching Equation (GME) was applied to Mixed Martial Arts (MMA) performance by examining strike selection as a function of landing significant strikes among fighters from various weight classes in the Ultimate Fighting Championship. The results suggest that the GME is a good descriptor of strike selection in MMA, an individual sport that is dynamic and fast paced where responding results in immediate feedback from an opponent.

Choice in transition: Replication and extension to preschool children in a naturalistic setting

This study replicated previous basic research into the dynamics of choice and extended this analysis to children's behavior in a naturalistic setting. Two preschoolers with disabilities were observed interacting with their teachers at baseline and during an experimental analysis involving four pairs of concurrent variable-interval schedules of adult attention implemented by an experimenter. Each child was exposed to four experimental phases in which the relative reinforcer rates for on- and off-task behavior were 10:1, 1:1, 1:10, and reversed back to 10:1. The 10:1 phase was designed to mimic the same schedules and types of adult attention observed at baseline. We used the generalized matching equation to model steady-state behavior at the end of the transition phases and to evaluate changes in sensitivity at various points throughout the phases. Choice in transition was evaluated by plotting log behavior ratios by session, cumulated time on- and off-task and cumulated attention for on- and off-task behavior by session, and interreinforcer behavior ratios following different sequences of the first four reinforcer deliveries. The generalized matching equation accounted for a large proportion of variance in steady-state responding, sensitivity values increased steadily throughout the phases, patterns of choice in transition were similar to those reported in basic research, and interreinforcer preference generally shifted toward the just-reinforced alternative. These findings are consistent with previous basic research and support the generality of the dynamics of choice to children's on- and off-task behavior reinforced by adult attention.

Switch hitting in baseball: apparent rule-following, not matching

Many studies, including some dealing with shot selection in basketball and play selection in football, demonstrate that the generalized matching equation provides a good description of the allocation of time and effort to alternative responses as a function of the consequences of those alternatives. We examined whether it did so with respect to left- and right-handed at bats (alternative responses) and left- and right-handed total bases earned, runs batted in, and home runs (three consequences) for the outstanding baseball switch-hitters Mickey Mantle, Eddie Murray, and Pete Rose. With all hitters, undermatching, suggesting insensitivity to the consequences of behavior (reinforcement), was evident and there was substantial bias towards left-handed at bats. These players apparently chose handedness based on the rule "bat opposite the pitcher," not on differential consequences obtained in major league games. The present findings are significant in representing a counter-instance of demonstrations of a matching relationship in sports in particular and in human behavior in general and in calling attention to the need for further study of the variables that affect choice.

Using Microsoft Office Excel 2007 to conduct generalized matching analyses

The generalized matching equation is a robust and empirically supported means of analyzing relations between reinforcement and behavior. Unfortunately, no simple task analysis is available to behavior analysts interested in using the matching equation to evaluate data in clinical or applied settings. This technical article presents a task analysis for the use of Microsoft Excel to analyze and plot the generalized matching equation. Using a data-based case example and a step-by-step guide for completing the analysis, these instructions are intended to promote the use of quantitative analyses by researchers with little to no experience in quantitative analyses or the matching law.

Quantification of ethanol's antipunishment effect in humans using the generalized matching equation

Increases in rates of punished behavior by the administration of anxiolytic drugs (called antipunishment effects) are well established in animals but not humans. The present study examined antipunishment effects of ethanol in humans using a choice procedure. The behavior of 5 participants was placed under six concurrent variable-interval schedules of monetary reinforcement. In three of the six concurrent schedules, punishment, in the form of monetary loss, was superimposed on one alternative. Data were analyzed according to the generalized matching equation which distinguishes between bias (allocation of behavior beyond what matching to relative reinforcer densities would predict) and sensitivity to reinforcement (how well behavior tracks relative reinforcer densities). In addition, participants completed a pencil-tapping test. Under placebo punishment conditions, all participants demonstrated low response rates and a bias against the alternative associated with punishment, despite a resultant loss of available reinforcers. Bias against the punished alternative was dose-dependently reduced in participants shown to be most sensitive to ethanol (0.6, 1.2, and 1.8 g/kg) in measures of overall responding and on the pencil-tapping test. No ethanol-induced change in bias was noted when punishment was not imposed. Sensitivity to reinforcement also decreased for participants shown to be sensitive to ethanol. In addition to extending antipunishment effects to humans, these results also show that antipunishment effects can be quantified via the matching equation.

The matching relation and situation-specific bias modulation in professional football play selection

The utility of a quantitative model depends on the extent to which its fitted parameters vary systematically with environmental events of interest. Professional football statistics were analyzed to determine whether play selection (passing versus rushing plays) could be accounted for with the generalized matching equation, and in particular whether variations in play selection across game situations would manifest as changes in the equation's fitted parameters. Statistically significant changes in bias were found for each of five types of game situations; no systematic changes in sensitivity were observed. Further analyses suggested relationships between play selection bias and both turnover probability (which can be described in terms of punishment) and yards-gained variance (which can be described in terms of variable-magnitude reinforcement schedules). The present investigation provides a useful demonstration of association between face-valid, situation-specific effects in a domain of everyday interest, and a theoretically important term of a quantitative model of behavior. Such associations, we argue, are an essential focus in translational extensions of quantitative models.