Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies
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Brian Skinner
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.
©2012 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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- Letter from the Editor
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- Rule of Tangent for Win-By-Two Games
- Effect of Differences in Kicking Legs, Kick Directions, and Kick Skill on Kicking Accuracy in Soccer Players
- The Methodology of Officially Recognized International Sports Rating Systems
- Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies
- Using Tree Ensembles to Analyze National Baseball Hall of Fame Voting Patterns: An Application to Discrimination in BBWAA Voting
- An Estimate of How Hitting, Pitching, Fielding, and Basestealing Impact Team Winning Percentages in Baseball
Articles in the same Issue
- Letter from the Editor
- The Next Step
- Article
- A Hierarchical Bayesian Variable Selection Approach to Major League Baseball Hitting Metrics
- Ups and Downs: Team Performance in Best-of-Seven Playoff Series
- The Penalty Shot/Optional Minor Choice in Ice Hockey
- Using Local Correlation to Explain Success in Baseball
- Exploring Competition Performance in Decathlon Using Semi-Parametric Latent Variable Models
- Going for the Green: A Simulation Study of Qualifying Success Probabilities in Professional Golf
- Rule of Tangent for Win-By-Two Games
- Effect of Differences in Kicking Legs, Kick Directions, and Kick Skill on Kicking Accuracy in Soccer Players
- The Methodology of Officially Recognized International Sports Rating Systems
- Scoring Strategies for the Underdog: A General, Quantitative Method for Determining Optimal Sports Strategies
- Using Tree Ensembles to Analyze National Baseball Hall of Fame Voting Patterns: An Application to Discrimination in BBWAA Voting
- An Estimate of How Hitting, Pitching, Fielding, and Basestealing Impact Team Winning Percentages in Baseball
