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An Extension of the Pythagorean Expectation for Association Football

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  • Hamilton Howard H

    (Soccermetrics Research & Consulting, LLC)

Abstract

This publication presents a formulation of an extension to the Pythagorean expectation for association football and other sports in which a draw result is a nontrivial event. Instead of estimating win percentage as in baseball, the extended Pythagorean estimates points won per game. A least-squares algorithm is used to fit offensive and defensive goal distributions to a three-parameter Weibull distribution, of which the parameter of interest is the Pythagorean exponent. Further analysis reveals that the league Pythagorean exponent remains stable across multiple leagues in the same calendar year and within a single league over multiple seasons, which gives support to the notion of a "universal" Pythagorean exponent. Application of the extended Pythagorean to results of domestic soccer leagues in Europe, Asia, and the Americas shows excellent agreement between goal statistics and league records for a majority of teams, and it indicates the teams that strongly overperform or underperform with respect to their expected performance.

Suggested Citation

  • Hamilton Howard H, 2011. "An Extension of the Pythagorean Expectation for Association Football," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(2), pages 1-18, May.
    • Handle: RePEc:bpj:jqsprt:v:7:y:2011:i:2:n:15
    DOI: 10.2202/1559-0410.1335
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    References listed on IDEAS

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    1. Cochran James J & Blackstock Rob, 2009. "Pythagoras and the National Hockey League," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(2), pages 1-13, May.
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    Cited by:

    1. Heiner Matthew & Fellingham Gilbert W. & Thomas Camille, 2014. "Skill importance in women’s soccer," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 1-16, June.
    2. Kovalchik Stephanie Ann, 2016. "Is there a Pythagorean theorem for winning in tennis?," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(1), pages 43-49, March.
    3. Yuan Lo-Hua & Liu Anthony & Yeh Alec & Franks Alex & Wang Sherrie & Illushin Dmitri & Bornn Luke & Kaufman Aaron & Reece Andrew & Bull Peter, 2015. "A mixture-of-modelers approach to forecasting NCAA tournament outcomes," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 11(1), pages 13-27, March.

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