Application of the matching law to pitch selection in professional baseball

Abstract

This study applied the generalized matching equation (GME) to pitch selection in professional baseball. The GME was fitted to the relation between pitch selection and hitter outcomes for five professional baseball pitchers during the 2014 Major League Baseball season. The GME described pitch selection well. Pitch allocation varied across different game contexts such as inning, count, and number of outs in a manner consistent with the GME. Finally, within games, bias decreased for four of the five pitchers and the sensitivity parameter increased for three of the five pitchers. The results extend the generality of the GME to multialternative natural sporting contexts, and demonstrate the influence of context on behavior in natural environments.

Application of the matching law to Mixed Martial Arts

“…Additional analyses were conducted based on Cox et al (). The purpose of this analysis was to calculate the minimum and maximum proportions of responses that could potentially occur given the actual responses and reinforcements observed (Herrnstein, ; Equations 2 and 3).…”

“…Typically, wider ranges indicate that the matching equation can provide valuable information about an organism's response allocation and smaller ranges suggest that any observed matching relations lack empirical validity. Similar to Cox et al () the response with the largest number of observed events was selected, thus the proportion of all strikes to the head to all strikes was plotted as a function of the proportion of reinforcement for strikes to the head to all reinforcements obtained. Based on Herrnstein's () Equations 2 and 3 a range of all possible responses was calculated for each of the head strike proportions.…”

“…Given that “perfect” matching (i.e., slope is equal to 1) is rarely observed in research, this allows for an analysis of data that is easier to interpret (Reed & Kaplan, ). Researchers have demonstrated applications of the GME in team sports such as baseball (Cox, Sosine, & Dallery, ; Poling, Weeden, Redner, & Foster, ), basketball (Alferink, Critchfield, & Hitt, ; Romanowich, Bourret, & Vollmer, ; Schenk & Reed, ; Vollmer & Bourret, ), football (Critchfield & Stilling, ; Falligant, Boomhower, & Pence, ; Reed, Critchfield, & Martens, ; Stilling & Critchfield, ), and hockey (Seniuk, Williams, Reed, & Wright, ). These studies have demonstrated that the GME describes choice in athletic competition (Critchfield & Reed, ; Reed & Kaplan, ) and have advanced research on the matching law by focusing on using interpretations of sensitivity (i.e., overmatching, undermatching, and bias) to explain the role of specific contextual variables termed explanatory flexibility (Stilling & Critchfield, ), and how matching may predict athletic success (Alferink et al, ; Seniuk et al, ).…”

Further application of the generalized matching law to multialternative sports contexts

“…In contrast to the GML, the literature on the descriptive utility of the multialternative GML remains relatively scant (e.g., Kangas et al, 2009). In one of the few articles on this topic, Cox et al (2017) successfully used the multialternative GML to describe pitch selection among a sample of Major League Baseball (MLB) pitchers across a variety of game contexts. Such research represents an important demonstration of the generality of the multialternative GML.…”

Experimental evaluation of matching via a commercially available basketball video game

“…Sports are especially conducive to GME evaluations given the (a) abundance of concurrent choice arrangements inherent in athletics and (b) widespread availability of raw choice data in curated databases containing athletes' performance statistics (e.g., league websites such as http://www.nfl.com, sports websites such as http://www.espn.com, statistics‐focused sites such as http://www.retrosheet.org; see Reed, ). To date, the GME has been used to describe performance in football (e.g., Reed, Critchfield, & Martens, ), hockey (Seniuk, Williams, Reed, & Wright, ), baseball (e.g., Cox, Sosine, & Dallery, ), and basketball (e.g., Vollmer & Bourret, ).…”