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Adjusting Bookmaker’s Odds to Allow for Overround

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 Forecasts, Betting, Sports Forecasting, Probability Forecasting

APA Style

Stephen Clarke, Stephanie Kovalchik, Martin Ingram. (2017). Adjusting Bookmaker’s Odds to Allow for Overround. American Journal of Sports Science, 5(6), 45-49.

ACS Style

Stephen Clarke; Stephanie Kovalchik; Martin Ingram. Adjusting Bookmaker’s Odds to Allow for Overround. Am. J. Sports Sci. 2017, 5(6), 45-49. doi: 10.11648/j.ajss.20170506.12

AMA Style

Stephen Clarke, Stephanie Kovalchik, Martin Ingram. Adjusting Bookmaker’s Odds to Allow for Overround. Am J Sports Sci. 2017;5(6):45-49. doi: 10.11648/j.ajss.20170506.12

Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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