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Professionals Do Not Play Minimax: Evidence from Major League Baseball and the National Football League

  • Kenneth Kovash
  • Steven D. Levitt

Game theory makes strong predictions about how individuals should behave in two player, zero sum games. When players follow a mixed strategy, equilibrium payoffs should be equalized across actions, and choices should be serially uncorrelated. Laboratory experiments have generated large and systematic deviations from the minimax predictions. Data gleaned from real-world settings have been more consistent with minimax, but these latter studies have often been based on small samples with low power to reject. In this paper, we explore minimax play in two high stakes, real world settings that are data rich: choice of pitch type in Major League Baseball and whether to run or pass in the National Football League. We observe more than three million pitches in baseball and 125,000 play choices for football. We find systematic deviations from minimax play in both data sets. Pitchers appear to throw too many fastballs; football teams pass less than they should. In both sports, there is negative serial correlation in play calling. Back of the envelope calculations suggest that correcting these decision making errors could be worth as many as two additional victories a year to a Major League Baseball franchise, and more than a half win per season for a professional football team.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 15347.

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Date of creation: Sep 2009
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Handle: RePEc:nbr:nberwo:15347
Note: LE PE
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  1. Ignacio Palacios-Huerta & Oscar Volij, 2008. "Experientia Docet: Professionals Play Minimax in Laboratory Experiments," Econometrica, Econometric Society, vol. 76(1), pages 71-115, 01.
  2. P.-A. Chiappori, 2002. "Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer," American Economic Review, American Economic Association, vol. 92(4), pages 1138-1151, September.
  3. Steven D. Levitt, 2006. "An Economist Sells Bagels: A Case Study in Profit Maximization," NBER Working Papers 12152, National Bureau of Economic Research, Inc.
  4. repec:spr:compst:v:59:y:2004:i:3:p:359-373 is not listed on IDEAS
  5. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
  6. Jason Shachat & J. Todd Swarthout, 2003. "Do We Detect and Exploit Mixed Strategy Play by Opponents?," Experimental 0310001, EconWPA.
  7. Spiliopoulos, Leonidas, 2008. "Do repeated game players detect patterns in opponents? Revisiting the Nyarko & Schotter belief elicitation experiment," MPRA Paper 6666, University Library of Munich, Germany.
  8. Robert W. Rosenthal & Jason Shachat & Mark Walker, 2003. "Hide and Seek in Arizona," Experimental 0312001, EconWPA.
  9. Steven D. Levitt & John A. List, 2007. "What Do Laboratory Experiments Measuring Social Preferences Reveal About the Real World?," Journal of Economic Perspectives, American Economic Association, vol. 21(2), pages 153-174, Spring.
  10. Ignacio Palacios-Huerta, 2003. "Professionals Play Minimax," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 395-415.
  11. O'Neill, Barry, 1991. "Comments on Brown and Rosenthal's Reexamination [Testing the Minimax Hypothesis, A Reexamination of O'Neill's Game Experiment]," Econometrica, Econometric Society, vol. 59(2), pages 503-07, March.
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