IDEAS home Printed from https://ideas.repec.org/a/bpj/jqsprt/v17y2021i2p117-127n4.html
   My bibliography  Save this article

An iterative Markov rating method

Author

Listed:
  • Devlin Stephen

    (Mathematics, University of San Francisco, San Francisco, CA, USA)

  • Treloar Thomas

    (Mathematics, Hillsdale College, Hillsdale, MI, USA)

  • Creagar Molly

    (University of San Francisco, San Francisco, CA, USA)

  • Cassels Samuel

    (Hillsdale College, Hillsdale, MI, USA)

Abstract

We introduce a simple and natural iterative version of the well-known and widely studied Markov rating method. We show that this iterative Markov method converges to the usual global Markov rating, and shares a close relationship with the well-known Elo rating. Together with recent results on the relationship between the global Markov method and the maximum likelihood estimate of the rating vector in the Bradley–Terry (BT) model, we connect and explore the global and iterative Markov, Elo, and Bradley–Terry ratings on real and simulated data.

Suggested Citation

  • Devlin Stephen & Treloar Thomas & Creagar Molly & Cassels Samuel, 2021. "An iterative Markov rating method," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 117-127, June.
    • Handle: RePEc:bpj:jqsprt:v:17:y:2021:i:2:p:117-127:n:4
    DOI: 10.1515/jqas-2019-0070
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/jqas-2019-0070
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/jqas-2019-0070?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mark E. Glickman, 1999. "Parameter Estimation in Large Dynamic Paired Comparison Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(3), pages 377-394.
    2. Mark Glickman, 2001. "Dynamic paired comparison models with stochastic variances," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(6), pages 673-689.
    3. Julio González-Díaz & Ruud Hendrickx & Edwin Lohmann, 2014. "Paired comparisons analysis: an axiomatic approach to ranking methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 139-169, January.
    4. Stefani Ray, 2011. "The Methodology of Officially Recognized International Sports Rating Systems," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-22, October.
    Full references (including those not matched with items on IDEAS)

    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. Kovalchik, Stephanie, 2020. "Extension of the Elo rating system to margin of victory," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1329-1341.
    2. Kovalchik Stephanie Ann, 2016. "Searching for the GOAT of tennis win prediction," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(3), pages 127-138, September.
    3. Alexandra Grand & Regina Dittrich & Brian Francis, 2015. "Markov models of dependence in longitudinal paired comparisons: an application to course design," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 237-257, April.
    4. Blaž Krese & Erik Štrumbelj, 2021. "A Bayesian approach to time-varying latent strengths in pairwise comparisons," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-17, May.
    5. Lasek, Jan & Gagolewski, Marek, 2021. "Interpretable sports team rating models based on the gradient descent algorithm," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1061-1071.
    6. Santos-Fernandez Edgar & Wu Paul & Mengersen Kerrie L., 2019. "Bayesian statistics meets sports: a comprehensive review," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(4), pages 289-312, December.
    7. Newton Paul K & Aslam Kamran, 2009. "Monte Carlo Tennis: A Stochastic Markov Chain Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-44, July.
    8. Mitchell J. Lovett & Ron Shachar, 2011. "The Seeds of Negativity: Knowledge and Money," Marketing Science, INFORMS, vol. 30(3), pages 430-446, 05-06.
    9. Collingwood, James A.P. & Wright, Michael & Brooks, Roger J, 2022. "Evaluating the effectiveness of different player rating systems in predicting the results of professional snooker matches," European Journal of Operational Research, Elsevier, vol. 296(3), pages 1025-1035.
    10. Beaudoin, David & Swartz, Tim, 2018. "A computationally intensive ranking system for paired comparison data," Operations Research Perspectives, Elsevier, vol. 5(C), pages 105-112.
    11. Baker, Rose D. & McHale, Ian G., 2014. "A dynamic paired comparisons model: Who is the greatest tennis player?," European Journal of Operational Research, Elsevier, vol. 236(2), pages 677-684.
    12. Csató, László & Tóth, Csaba, 2020. "University rankings from the revealed preferences of the applicants," European Journal of Operational Research, Elsevier, vol. 286(1), pages 309-320.
    13. Angelini, Giovanni & Candila, Vincenzo & De Angelis, Luca, 2022. "Weighted Elo rating for tennis match predictions," European Journal of Operational Research, Elsevier, vol. 297(1), pages 120-132.
    14. Maria Bolsinova & Gunter Maris & Abe D. Hofman & Han L. J. van der Maas & Matthieu J. S. Brinkhuis, 2022. "Urnings: A new method for tracking dynamically changing parameters in paired comparison systems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 91-118, January.
    15. Barrow Daniel & Drayer Ian & Elliott Peter & Gaut Garren & Osting Braxton, 2013. "Ranking rankings: an empirical comparison of the predictive power of sports ranking methods," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 9(2), pages 187-202, June.
    16. Cristiano Varin & Manuela Cattelan & David Firth, 2016. "Statistical modelling of citation exchange between statistics journals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(1), pages 1-63, January.
    17. Owen G. Ward & Jing Wu & Tian Zheng & Anna L. Smith & James P. Curley, 2022. "Network Hawkes process models for exploring latent hierarchy in social animal interactions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1402-1426, November.
    18. Chan Victor, 2011. "Prediction Accuracy of Linear Models for Paired Comparisons in Sports," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(3), pages 1-35, July.
    19. Baker, Rose D. & McHale, Ian G., 2017. "An empirical Bayes model for time-varying paired comparisons ratings: Who is the greatest women’s tennis player?," European Journal of Operational Research, Elsevier, vol. 258(1), pages 328-333.
    20. Subhasis Ray, 2021. "Identification of Research Paradigms for Managing the Cricketing Ecosystem Using Stakeholder Analysis and Text Mining," Management and Labour Studies, XLRI Jamshedpur, School of Business Management & Human Resources, vol. 46(3), pages 289-312, August.

    More about this item

    Keywords

    Elo; Markov; ranking; rating;
    All these keywords.

    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:bpj:jqsprt:v:17:y:2021:i:2:p:117-127:n:4. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.