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Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies

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  • Skinner Brian

    (University of Minnesota, Twin Cities)

Abstract

When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average variance. The difficult question is how much risk a team should be willing to accept. This is equivalent to asking how much the team should be willing to sacrifice from its mean score in order to increase the score's variance. In this paper a general analytical method is developed for addressing this question quantitatively. Under the assumption that every play in a game is statistically independent, both the mean and the variance of a team's offensive output can be described using the binomial distribution. This allows for direct calculations of the winning probability when a particular strategy is employed, and therefore allows one to calculate optimal offensive strategies. This paper develops this method for calculating optimal strategies exactly and then presents a simple heuristic for determining whether a given strategy should be adopted. A number of interesting and counterintuitive examples are then explored, including the merits of stalling for time, the run/pass/Hail Mary choice in football, and the correct use of Hack-a-Shaq.

Suggested Citation

  • Skinner Brian, 2011. "Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(4), pages 1-18, October.
    • Handle: RePEc:bpj:jqsprt:v:7:y:2011:i:4:n:11
    DOI: 10.2202/1559-0410.1364
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    References listed on IDEAS

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    1. Skinner Brian, 2010. "The Price of Anarchy in Basketball," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(1), pages 1-18, January.
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    Cited by:

    1. Justin A. Ehrlich & Shankar Ghimire & Thomas R. Sadler & Shane D. Sanders, 2023. "Policy and Policy Response on the Court: A Theoretical and Empirical Examination of the Three-Point Line Extension in Basketball," Journal of Sports Economics, , vol. 24(2), pages 159-173, February.
    2. Brian Skinner, 2012. "The Problem of Shot Selection in Basketball," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-8, January.

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