American Journal of Sports Science
Volume 5, Issue 6, November 2017, Pages: 45-49
Received: Sep. 9, 2017;
Accepted: Oct. 12, 2017;
Published: Dec. 25, 2017
Views 2029 Downloads 264
Stephen Clarke, Department of Mathematics, Swinburne University of Technology, Melbourne, Australia
Stephanie Kovalchik, Tennis Australia, Melbourne Park, Melbourne, Australia; Institute of Sport Exercise and Active Living, Victoria University, Footscray, Australia
Martin Ingram, Division of Machine Learning, Silverpond, Melbourne, Australia
Several methods have been proposed to adjust bookmakers’ implied probabilities, including an additive model, a normalization model, and an iterative method proposed by Shin. These approaches have one or more defects: the additive model can give negative adjusted probabilities, normalization does not account for favorite long-shot bias, and both the normalization and Shin approaches can produce bookmaker probabilities greater than 1 when applied in reverse. Moreover, it is shown that the Shin and additive methods are equivalent for races with two competitors. Vovk and Zhadanov (2009) and Clarke (2016) suggested a power method, where the implied probabilities are raised to a fixed power, which never produces bookmaker or fair probabilities outside the 0-1 range and allows for the favorite long-shot bias. This paper describes and applies the methods to three large bookmaker datasets, each in a different sport, and shows that the power method universally outperforms the multiplicative method and outperforms or is comparable to the Shin method.
Adjusting Bookmaker’s Odds to Allow for Overround, American Journal of Sports Science.
Vol. 5, No. 6,
2017, pp. 45-49.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
C. Leitner, A. Zeileis, and K. Hornik, "Forecasting sports tournaments by ratings of (prob) abilities: A comparison for the EURO 2008." International Journal of Forecasting 26, no. 3, 2010, pp. 471-481.
S. Kovalchik, "Searching for the GOAT of tennis win prediction." Journal of Quantitative Analysis in Sports 12, no. 3, 2016, pp. 127-138.
L. Robinson, "The business of sport" in Sport & Society: A Student Introduction, Houlihan, B. Eds. London: SAGE, 2003, pp. 165-183.
M. Viney A. Bedford, and E. Kondo, “Incorporating over-round into in-play Markov Chain models in tennis”. 15th International Conference on Gambling & Risk-Taking, Las Vegas, USA, 2013.
S. R. Clarke, “Successful applications of statistical modeling to betting markets”. In IMA Sport 2007: First International conference on Mathematics in Sport. D. Percy, P Scarf & C Robinson, Eds., The Institute of Mathematics and its Applications: Salford, United Kingdom, 2007, pp. 35-43.
H. S. Shin, “Prices of State Contingent Claims with Insider traders, and the Favorite-Longshot Bias”. The Economic Journal, 1992, 102, pp. 426-435.
H. S. Shin, “Measuring the Incidence of Insider Trading in a Market for State-Contingent Claims”. The Economic Journal, 1993, 103(420), pp. 1141-1153.
E. J. Strumbelj, "On Determining Probability Forecasts from Betting Odds." International Journal of Forecasting, 2014, 30(4), pp. 934-943.
M. Cain, D. Law, and D. Peel, “The favorite-longshot bias, bookmaker margins and insider trading in a variety of betting markets”. Bulletin of Economic Research, 2003, 55, pp. 263–273.
M. A. Smith, D. Paton, and L. V. Williams, “Do bookmakers possess superior skills to bettors in predicting outcomes?” Journal of Economic Behavior & Organization, 2009, 71, 539 – 549.
S. R. Clarke, “Adjusting true odds to allow for vigorish”. In Proceedings of the 13th Australasian Conference on Mathematics and Computers in Sport. R. Stefani and A. Shembri, Eds., 2016: Melbourne, pp. 111-115.
V. Vovk, and F. Zhdanov, “Prediction with Expert Advice for the Brier Game”. Journal of Machine Learning Research, 2009, 10, pp. 2445-2471.
L. H. Yuan, A. Liu, A., Yeh, A. et al. “A mixture-of-modelers approach to forecasting NCAA tournament outcomes”. Journal of Quantitative Analysis in Sports, 2015, 11(1), pp. 13-27.