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A Markov Chain Approach to Baseball

Author

Listed:
  • Bruce Bukiet

    (New Jersey Institute of Technology, Newark, New Jersey)

  • Elliotte Rusty Harold

    (New Jersey Institute of Technology, Newark, New Jersey)

  • José Luis Palacios

    (Universidad Simón Bolívar, Caracas, Venezuela)

Abstract

Most earlier mathematical studies of baseball required particular models for advancing runners based on a small set of offensive possibilities. Other efforts considered only teams with players of identical ability. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a given model for runner advancement. Our method is limited only by the available data and can use any reasonable deterministic model for runner advancement when sufficiently detailed data are not available. Furthermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method to find optimal batting orders, run distributions per half inning and per game, and the expected number of games a team should win. We also describe the application of our method to test whether a particular trade would benefit a team.

Suggested Citation

  • Bruce Bukiet & Elliotte Rusty Harold & José Luis Palacios, 1997. "A Markov Chain Approach to Baseball," Operations Research, INFORMS, vol. 45(1), pages 14-23, February.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:1:p:14-23
    DOI: 10.1287/opre.45.1.14
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    Citations

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    Cited by:

    1. M Wright & N Hirotsu, 2003. "The professional foul in football: Tactics and deterrents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 213-221, March.
    2. Srinivas K. Reddy & Antonie Stam & Per J. Agrell, 2015. "Brand Equity, Efficiency and Valuation of Professional Sports Franchises: The Case of Major League Baseball," International Journal of Business and Social Research, MIR Center for Socio-Economic Research, vol. 5(1), pages 63-89, January.
    3. Woojin Doo & Heeyoung Kim, 2018. "Modeling the probability of a batter/pitcher matchup event: A Bayesian approach," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-11, October.
    4. Daniel Cervone & Alex D’Amour & Luke Bornn & Kirk Goldsberry, 2016. "A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 585-599, April.
    5. Stekler, H.O. & Sendor, David & Verlander, Richard, 2010. "Issues in sports forecasting," International Journal of Forecasting, Elsevier, vol. 26(3), pages 606-621, July.
      • Herman O. Stekler & David Sendor & Richard Verlander, 2009. "Issues in Sports Forecasting," Working Papers 2009-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    6. Baumer Ben S, 2009. "Using Simulation to Estimate the Impact of Baserunning Ability in Baseball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(2), pages 1-18, May.
    7. Holmes, Benjamin & McHale, Ian G. & Żychaluk, Kamila, 2023. "A Markov chain model for forecasting results of mixed martial arts contests," International Journal of Forecasting, Elsevier, vol. 39(2), pages 623-640.
    8. Davis Donald M, 2011. "Markov Analysis of APBA, a Baseball Simulation Game," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(3), pages 1-14, July.
    9. Damásio, Bruno & Nicolau, João, 2024. "Time inhomogeneous multivariate Markov chains: Detecting and testing multiple structural breaks occurring at unknown dates," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    10. Young William A & Holland William S & Weckman Gary R, 2008. "Determining Hall of Fame Status for Major League Baseball Using an Artificial Neural Network," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(4), pages 1-46, October.
    11. Chia-Hao Chang, 2021. "Construction of a Predictive Model for MLB Matches," Forecasting, MDPI, vol. 3(1), pages 1-11, February.
    12. Hirotsu Nobuyoshi, 2011. "Reconsideration of the Best Batting Order in Baseball: Is the Order to Maximize the Expected Number of Runs Really the Best?," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(2), pages 1-12, May.
    13. Bruno Damásio & João Nicolau, 2020. "Time Inhomogeneous Multivariate Markov Chains: Detecting and Testing Multiple Structural Breaks Occurring at Unknown," Working Papers REM 2020/0136, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    14. Sueyoshi, Toshiyuki & Ohnishi, Kenji & Kinase, Youichi, 1999. "A benchmark approach for baseball evaluation," European Journal of Operational Research, Elsevier, vol. 115(3), pages 429-448, June.
    15. J M Norman & S R Clarke, 2010. "Optimal batting orders in cricket," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(6), pages 980-986, June.
    16. Kostuk, Kent J. & Willoughby, Keith A. & Saedt, Anton P. H., 2001. "Modelling curling as a Markov process," European Journal of Operational Research, Elsevier, vol. 133(3), pages 557-565, September.
    17. Akifumi Kira & Keisuke Inakawa, 2014. "On Markov perfect equilibria in baseball," TMARG Discussion Papers 115, Graduate School of Economics and Management, Tohoku University.

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