IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/9024.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    Note: IO
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w9024.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    5. Clark Nardinelli & Curtis Simon, 1990. "Customer Racial Discrimination in the Market for Memorabilia: The Case of Baseball," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(3), pages 575-595.
    6. Rodney Fort & James Quirk, 1995. "Cross-subsidization, Incentives, and Outcomes in Professional Team Sports Leagues," Journal of Economic Literature, American Economic Association, vol. 33(3), pages 1265-1299, September.
    7. 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..
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bhaskar, V, 2004. "Rational Adversaries? Evidence from Randomized Trials in the Game of Cricket," Economics Discussion Papers 8875, University of Essex, Department of Economics.
    2. Ryan Elmore & Andrew Urbaczewski, 2021. "Loss Aversion in Professional Golf," Journal of Sports Economics, , vol. 22(2), pages 202-217, February.
    3. Timothy C. Y. Chan & Craig Fernandes & Martin L. Puterman, 2021. "Points Gained in Football: Using Markov Process-Based Value Functions to Assess Team Performance," Operations Research, INFORMS, vol. 69(3), pages 877-894, May.
    4. Alamar Benjamin C, 2010. "Measuring Risk in NFL Playcalling," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-9, April.
    5. 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.
    6. Michael Carter & Graeme Guthrie, 2002. "Cricket interruptus: Fairness and incentive in interruped cricket matches," Discussion Papers 02-07, Indian Statistical Institute, Delhi.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Klaassen, F.J.G.M. & Magnus, J.R., 2006. "Are Economic Agents Successful Optimizers? An Analysis Through Strategy in Tennis," Other publications TiSEM 73e12d86-8fe4-4a87-9181-7, Tilburg University, School of Economics and Management.
    2. Franc J.G.M. Klaasen & Jan R. Magnus, 2006. "Are Economic Agents Successful Optimizers? An Analysis through Service Strategy in Tennis," Tinbergen Institute Discussion Papers 06-048/2, Tinbergen Institute.
    3. Klaassen, Franc J.G.M. & Magnus, Jan R., 2009. "The efficiency of top agents: An analysis through service strategy in tennis," Journal of Econometrics, Elsevier, vol. 148(1), pages 72-85, January.
    4. Sebastian Bervoets & Bruno Decreuse & Mathieu Faure, 2014. "A Renewed Analysis of Cheating in Contests: Theory and Evidence from Recovery Doping," AMSE Working Papers 1441, Aix-Marseille School of Economics, France, revised Jun 2015.
    5. Marios Michaelides, 2010. "A New Test of Compensating Differences: Evidence on the Importance of Unobserved Heterogeneity," Journal of Sports Economics, , vol. 11(5), pages 475-495, October.
    6. V. Bhaskar, 2009. "Rational Adversaries? Evidence from Randomised Trials in One Day Cricket," Economic Journal, Royal Economic Society, vol. 119(534), pages 1-23, January.
    7. Vincenzo Scoppa, 2008. "Are subjective evaluations biased by social factors or connections? An econometric analysis of soccer referee decisions," Empirical Economics, Springer, vol. 35(1), pages 123-140, August.
    8. Helmut Dietl, 2010. "Besonderheiten des Sports ‐ Was rechtfertigt eine "eigene Ökonomik"?," Working Papers 0137, University of Zurich, Institute for Strategy and Business Economics (ISU).
    9. Garicano, Luis & Palacios-Huerta, Ignacio, 2005. "Sabotage in Tournaments: Making the Beautiful Game a Bit Less Beautiful," CEPR Discussion Papers 5231, C.E.P.R. Discussion Papers.
    10. Joseph P. McGarrity & Brian Linnen, 2010. "Pass or Run: An Empirical Test of the Matching Pennies Game Using Data from the National Football League," Southern Economic Journal, John Wiley & Sons, vol. 76(3), pages 791-810, January.
    11. Rosen, Sherwin & Sanderson, Allen, 2001. "Labour Markets in Professional Sports," Economic Journal, Royal Economic Society, vol. 111(469), pages 47-68, February.
    12. Schläpfer, Alain, 2024. "Cross-cultural differences in retaliation: Evidence from the soccer field," Journal of Economic Behavior & Organization, Elsevier, vol. 223(C), pages 216-233.
    13. V. Bhaskar, 2004. "Rational Adversaries? Evidence from Randomized Trials in the Game of Cricket," Levine's Working Paper Archive 122247000000000163, David K. Levine.
    14. Alexander W. Salter, 2017. "Strategic Offsetting Behavior in the NBA," Journal of Sports Economics, , vol. 18(2), pages 126-139, February.
    15. Pedro Garcia-del-Barrio & Stefan Szymanski, 2009. "Goal! Profit Maximization Versus Win Maximization in Soccer," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 34(1), pages 45-68, February.
    16. Lenten, Liam J.A. & Geerling, Wayne & Kónya, László, 2012. "A hedonic model of player wage determination from the Indian Premier League auction: Further evidence," Sport Management Review, Elsevier, vol. 15(1), pages 60-71.
    17. Isabelle Brocas & Juan D. Carrillo, 2004. "Do the “Three-Point Victory†and “Golden Goal†Rules Make Soccer More Exciting?," Journal of Sports Economics, , vol. 5(2), pages 169-185, May.
    18. Isabelle Brocas & Juan D. Carrillo, 2022. "The development of randomization and deceptive behavior in mixed strategy games," Quantitative Economics, Econometric Society, vol. 13(2), pages 825-862, May.
    19. Klein Teeselink, Bouke & Potter van Loon, Rogier J.D. & van den Assem, Martijn J. & van Dolder, Dennie, 2020. "Incentives, performance and choking in darts," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 38-52.
    20. Emara, Noha & Owens, David & Smith, John & Wilmer, Lisa, 2017. "Serial correlation in National Football League play calling and its effects on outcomes," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 125-132.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:9024. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.