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Order statistics of horse racing and the randomly broken stick

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  • Peter A. Bebbington
  • Julius Bonart

Abstract

We find a remarkable agreement between the statistics of a randomly divided interval and the observed statistical patterns and distributions found in horse racing betting markets. We compare the distribution of implied winning odds, the average true winning probabilities, the implied odds conditional on a win, and the average implied odds of the winning horse with the corresponding quantities from the "randomly broken stick problem". We observe that the market is at least to some degree informationally efficient. From the mapping between exponential random variables and the statistics of the random division we conclude that horses' true winning abilities are exponentially distributed.

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  • Peter A. Bebbington & Julius Bonart, 2016. "Order statistics of horse racing and the randomly broken stick," Papers 1612.02567, arXiv.org.
    • Handle: RePEc:arx:papers:1612.02567
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    References listed on IDEAS

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    1. Bouchaud,Jean-Philippe & Potters,Marc, 2009. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521741866.
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    3. Jonathan Donier & Julius Bonart & Iacopo Mastromatteo & Jean-Philippe Bouchaud, 2014. "A fully consistent, minimal model for non-linear market impact," Papers 1412.0141, arXiv.org, revised Mar 2015.
    4. Vaughan Williams, Leighton, 1999. "Information Efficiency in Betting Markets: A Survey," Bulletin of Economic Research, Wiley Blackwell, vol. 51(1), pages 1-30, January.
    5. Figlewski, Stephen, 1979. "Subjective Information and Market Efficiency in a Betting Market," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 75-88, February.
    6. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
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