IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v679y2025ics037843712500634x.html

Ornstein–Uhlenbeck process for horse race betting: A micro–macro analysis of herding and informed bettors

Author

Listed:
  • Sugawara, Tomoya
  • Mori, Shintaro

Abstract

We model the time evolution of single-win odds in Japanese horse racing as a stochastic process, deriving an Ornstein–Uhlenbeck (O–U) process by analyzing the probability dynamics of vote shares and the empirical time series of odds movements. Our framework incorporates two types of bettors: herders, who adjust their bets based on current odds, and informed better (fundamentalist), who wager based on a horse’s true winning probability. Using data from 3450 Japan Racing Association races in 2008, we identify a microscopic probability rule governing individual bets and a mean-reverting macroscopic pattern in odds convergence. This structure parallels financial markets, where traders’ decisions are influenced by market fluctuations, and the interplay between herding and fundamentalist strategies shapes price dynamics. These results highlight the broader applicability of our approach to non-equilibrium financial and betting markets, where mean-reverting dynamics emerge from simple behavioral interactions.

Suggested Citation

  • Sugawara, Tomoya & Mori, Shintaro, 2025. "Ornstein–Uhlenbeck process for horse race betting: A micro–macro analysis of herding and informed bettors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 679(C).
    • Handle: RePEc:eee:phsmap:v:679:y:2025:i:c:s037843712500634x
    DOI: 10.1016/j.physa.2025.130982
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712500634X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2025.130982?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Donald B. Hausch & William T. Ziemba & Mark Rubinstein, 2008. "Efficiency Of The Market For Racetrack Betting," World Scientific Book Chapters, in: Donald B Hausch & Victor SY Lo & William T Ziemba (ed.), Efficiency Of Racetrack Betting Markets, chapter 38, pages 373-390, World Scientific Publishing Co. Pte. Ltd..
    2. Mizuno, Takayuki & Takayasu, Hideki & Takayasu, Misako, 2007. "Analysis of price diffusion in financial markets using PUCK model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 187-192.
    3. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    4. Kiyoshi Kanazawa & Takumi Sueshige & Hideki Takayasu & Misako Takayasu, 2017. "Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders," Papers 1703.06739, arXiv.org, revised Mar 2018.
    5. Donald B. Hausch & Victor S. Y. Lo & William T. Ziemba, 2008. "Introduction to the Efficiency of Racetrack Betting Markets in England," World Scientific Book Chapters, in: Donald B Hausch & Victor SY Lo & William T Ziemba (ed.), Efficiency Of Racetrack Betting Markets, chapter 51, pages 529-531, World Scientific Publishing Co. Pte. Ltd..
    6. Serge Galam, 2008. "Sociophysics: A Review Of Galam Models," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 409-440.
    7. Justin Wolfers & Eric Zitzewitz, 2006. "Prediction Markets in Theory and Practice," NBER Working Papers 12083, National Bureau of Economic Research, Inc.
    8. Takayasu, Misako & Mizuno, Takayuki & Takayasu, Hideki, 2006. "Potential force observed in market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 91-97.
    9. Takayasu, Misako & Mizuno, Takayuki & Takayasu, Hideki, 2007. "Theoretical analysis of potential forces in markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 115-119.
    10. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    11. Manski, Charles F., 2006. "Interpreting the predictions of prediction markets," Economics Letters, Elsevier, vol. 91(3), pages 425-429, June.
    12. Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-896, July.
    13. Ichinomiya, Takashi, 2006. "Power-law distribution in Japanese racetrack betting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 207-213.
    14. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    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. repec:spo:wpmain:info:hdl:2441/f6h8764enu2lskk9p4oq9ig8k is not listed on IDEAS
    2. Yuki Sato & Kiyoshi Kanazawa, 2023. "Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies," Papers 2306.13378, arXiv.org, revised Nov 2023.
    3. Chen, Shu-Heng, 2012. "Varieties of agents in agent-based computational economics: A historical and an interdisciplinary perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 1-25.
    4. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    5. Alexandru Mandes, 2014. "Order Placement in a Continuous Double Auction Agent Based Model," MAGKS Papers on Economics 201443, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    6. Boilard, J.-F. & Kanazawa, K. & Takayasu, H. & Takayasu, M., 2018. "Empirical scaling relations of market event rates in foreign currency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1152-1161.
    7. Donovan Platt & Tim Gebbie, 2016. "The Problem of Calibrating an Agent-Based Model of High-Frequency Trading," Papers 1606.01495, arXiv.org, revised Mar 2017.
    8. Aleksejus Kononovicius & Julius Ruseckas, 2018. "Order book model with herd behavior exhibiting long-range memory," Papers 1809.02772, arXiv.org, revised Apr 2019.
    9. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    10. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    11. Takumi Sueshige & Kiyoshi Kanazawa & Hideki Takayasu & Misako Takayasu, 2018. "Ecology of trading strategies in a forex market for limit and market orders," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-14, December.
    12. Taiki Wakatsuki & Kiyoshi Kanazawa, 2025. "Mean-field theory of the Santa Fe model revisited: a systematic derivation from an exact BBGKY hierarchy for the zero-intelligence limit-order book model," Papers 2510.01814, arXiv.org.
    13. Xu, Hai-Chuan & Zhang, Wei & Xiong, Xiong & Wang, Xue & Zhou, Wei-Xing, 2021. "The double-edged role of social learning: Flash crash and lower total volatility," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 405-420.
    14. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    15. Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters, 2006. "Random walks, liquidity molasses and critical response in financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 115-123.
    16. Juan C. Henao-Londono & Sebastian M. Krause & Thomas Guhr, 2021. "Price response functions and spread impact in correlated financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(4), pages 1-20, April.
    17. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    18. Yi-Fang Liu & Wei Zhang & Chao Xu & Jørgen Vitting Andersen & Hai-Chuan Xu, 2014. "Impact of information cost and switching of trading strategies in an artificial stock market," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01011701, HAL.
    19. Wang, Yougui & Stanley, H.E., 2009. "Statistical approach to partial equilibrium analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1173-1180.
    20. Gaël Giraud & Céline Rochon, 2010. "Transition to Equilibrium in International Trades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00657038, HAL.
    21. V. Alfi & L. Pietronero & A. Zaccaria, 2008. "Minimal Agent Based Model For The Origin And Self-Organization Of Stylized Facts In Financial Markets," Papers 0807.1888, arXiv.org.

    More about this item

    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:eee:phsmap:v:679:y:2025:i:c:s037843712500634x. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.