Abstract
In mixed strategy games, the ability to randomize decisions is a critical strategic necessity, yet studies show that such rational behavior is sometimes elusive. This paper examines mixed strategy play in a natural setting, by looking at a pitcher’s decision to throw the ball to home plate or to throw it to first base in a pickoff play. In the absence of significant pressure, we find that pitchers can effectively randomize their sequence of choices to remain unpredictable, as mixed strategy Nash equilibriums require. However, in the face of pressure, some pitchers are less able to randomize their choices. Our paper is the first empirical study in the English language literature to find that decision makers are unable to randomize their strategic decisions when they face an increased cognitive load due to pressure.
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Notes
See Oskarsson et al. (2009) for a review of the literature that documents how people have a hard time producing or recognizing random sequences.
This study only examines the situation in which a runner is on first base and no other base.
Thanks to an anonymous reviewer for pointing this out.
The dataset was also limited to games played in American League parks only. The National League teams bunt quite a bit more than they do in the American League, which can confound the data. A bunt is another option to move a runner to second base besides stealing the base. It is probably easier to bunt on a left-handed pitcher since a batter is most likely going to bunt down the first base line. The left-handed pitcher will have his back to first base when he finishes his throw. Therefore it is more difficult for him to field the ball. This gives batters an incentive to bunt more against left-handed pitchers compared to their incentive to bunt against right-handed pitchers. Excluding National League parks eliminates this situation to some extent.
For an easy to read discussion of dynamic probit models see Miranda (2007).
One-tailed tests were used to evaluate the significance of the lagged dependent variable since the literature has found that strategic decisions which are not random have a negative serial correlation pattern. Using the existing literature to inform our approach, the null hypothesis for the estimated coefficients is specified to be greater than or equal to zero, leaving the alternative hypothesis (the sign of the coefficient that we expect) to be negative. See chapter 5 of Studenmund (2011) for a discussion of one-tailed versus two-tailed tests.
It is an interesting question for further research whether the mixed results, concerning whether athletes in different professional sports randomize their decisions, would provide more of a consensus result if the level of pressure were added to the empirical models.
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Downey, J., McGarrity, J. Pressure and the ability to randomize decision-making: The case of the pickoff play in Major League Baseball. Atl Econ J 47, 261–274 (2019). https://doi.org/10.1007/s11293-019-09631-8
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DOI: https://doi.org/10.1007/s11293-019-09631-8