Abstract and Keywords
This article uses data on hit batsmen from Major League Baseball to illustrate a mixed-strategy, game theoretic approach to the decisions of the pitcher and the batter. The pitcher would like to throw to a batter who stands in the middle of the batter's box. The game theoretic model predicts that the pitcher will throw at fewer batters as velocity increases, while the standard crime model would assume that the pitcher's throw-ats would remain unchanged and the batter would respond by leaning in less often. The Total Effect curves suggest that there will be more throw-ats in the American League for any level of velocity. The number of purposeful inside pitches will decrease at an increasing rate as velocity increases. The game theoretic model predicts that a pitcher who can throw with greater velocity will have to waste fewer inside pitches to keep a batter from leaning into a pitch.
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