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It's Fourth Down and What Does the Bellman Equation Say? A Dynamic Programming Analysis of Football Strategy

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  • David Romer

Abstract

This paper uses play-by-play accounts of virtually all regular season National Football League games for 1998-2000 to analyze teams' choices on fourth down between trying for a first down and kicking. Dynamic programming is used to estimate the values of possessing the ball at different points on the field. These estimates are combined with data on the results of kicks and conventional plays to estimate the average payoffs to kicking and going for it under different circumstances. Examination of teams' actual decisions shows systematic, overwhelmingly statistically significant, and quantitatively large departures from the decisions the dynamic-programming analysis implies are preferable.

Suggested Citation

  • David Romer, 2002. "It's Fourth Down and What Does the Bellman Equation Say? A Dynamic Programming Analysis of Football Strategy," NBER Working Papers 9024, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:9024
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    References listed on IDEAS

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    1. Mark Walker & John Wooders, 2001. "Minimax Play at Wimbledon," American Economic Review, American Economic Association, vol. 91(5), pages 1521-1538, December.
    2. McCormick, Robert E & Tollison, Robert D, 1984. "Crime on the Court," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 223-235, April.
    3. Ehrenberg, Ronald G & Bognanno, Michael L, 1990. "Do Tournaments Have Incentive Effects?," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1307-1324, December.
    4. Clark Nardinelli & Curtis Simon, 1990. "Customer Racial Discrimination in the Market for Memorabilia: The Case of Baseball," The Quarterly Journal of Economics, Oxford University Press, vol. 105(3), pages 575-595.
    5. Gwartney, James & Haworth, Charles, 1974. "Employer Costs and Discrimination: The Case of Baseball," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 873-881, July/Aug..
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    Cited by:

    1. Eric Zitzewitz, 2006. "Nationalism in Winter Sports Judging and Its Lessons for Organizational Decision Making," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(1), pages 67-99, March.
    2. Bhaskar, V, 2004. "Rational Adversaries? Evidence from Randomized Trials in the Game of Cricket," Economics Discussion Papers 8875, University of Essex, Department of Economics.
    3. Michael Carter & Graeme Guthrie, 2002. "Cricket interruptus: Fairness and incentive in interruped cricket matches," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 02-07, Indian Statistical Institute, New Delhi, India.
    4. James M. Poterba, 2005. "Steven D. Levitt: 2003 John Bates Clark Medalist," Journal of Economic Perspectives, American Economic Association, vol. 19(3), pages 181-198, Summer.

    More about this item

    JEL classification:

    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory

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