Physics – Physics and Society
Scientific paper
2011-11-02
Journal of Quantitative Analysis in Sports: Vol. 7: Iss. 4, Article 11 (2011)
Physics
Physics and Society
6+ pages, 6 figures
Scientific paper
10.2202/1559-0410.1364
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 description 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 American football, and the correct use of Hack-a-Shaq.
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