Order Statistics of Horse Racing and the Randomly Broken Stick

6 Pages Posted: 9 Dec 2016

See all articles by Peter Bebbington

Peter Bebbington

University College London, Department of Physics and Astronomy, Students

Julius Bonart

Capital Fund Management

Date Written: December 7, 2016

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.

Keywords: Order Statistics, Sports Betting, Horse Racing, Division of an Interval, Odds

Suggested Citation

Bebbington, Peter and Bonart, Julius, Order Statistics of Horse Racing and the Randomly Broken Stick (December 7, 2016). Available at SSRN: https://ssrn.com/abstract=2882062 or http://dx.doi.org/10.2139/ssrn.2882062

Peter Bebbington (Contact Author)

University College London, Department of Physics and Astronomy, Students ( email )

Gower Street
London
United Kingdom

Julius Bonart

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

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