Predicting Overtime with the Pythagorean Formula
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Jason W. Rosenfeld
In 1980, Bill James created the Pythagorean win expectation formula with a somewhat counterintuitive idea in mind. James believed, and his formula proved, that a baseball team's current runs scored to runs allowed ratio was better than a team's current record at predicting a team's future winning percentage. The rationale was that the outcomes of close games, which factor prominently in a record but not in a runs ratio, are subject to luck and randomness. The win expectation formula was referred to as Pythagorean because the exponents of two made it resemble the Pythagorean Theorem. James' idea has been extended to other major sports through a generalized Pythagorean win expectation formula, with different exponents—which we call "alphas"—emerging for each sport. In this paper, we estimate the alphas for the win expectation formulas for both full-length and overtime games in the National Basketball Association (NBA), National Football League (NFL), and Major League Baseball (MLB), based on games over the past 10-20 seasons. While our results for full-length games are similar to the generally-accepted win expectation formulas, we believe this is the first attempt to measure how teams' runs scored to runs allowed ratios—which we term "strength"—influence overtime games. We find through logistic regression that the overtime alphas for the NBA, NFL, and MLB are 9.22, 1.11, and .94, respectively. Comparing the full-length game win expectation formulas to the overtime formulas allows one to see how the impact of strength changes from full-length games to overtime games. It is discovered that the impact of strength on win probability decreases least in NBA overtime and most in NFL overtime. Therefore, NBA overtime games are most likely to be won by the team that would win a full-length game and NFL overtime games are most random relative to full-length games. If a team has a 75 percent chance of winning a full-length game, its chances of winning an overtime game are 67.28, 63.00, and 61.56 percent for the NBA, MLB, and NFL, respectively.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Artikel in diesem Heft
- Conference Paper
- Predicting Overtime with the Pythagorean Formula
- Using Game Theory to Optimize Performance in a Best-of-N Set Match
- A Spatial Multidimensional Unfolding Choice Model for Examining the Heterogeneous Expressions of Sports Fan Avidity
- Anomalies in Tournament Design: The Madness of March Madness
- Skill Importance in Women's Volleyball
- Quantifying the Effect of Performance-Enhancing Drug Use on Fastball Velocity in Major League Baseball
- A New Iterative Method for Ranking College Football Teams
- Receiver Operating Characteristic (ROC) Curves for Measuring the Quality of Decisions in Cricket
- Visualization of Crew Race Performance: Drives and Duels
- Valuations of Soccer Players from Statistical Performance Data
- Measuring Risk in NFL Playcalling
- Using Random Forests and Simulated Annealing to Predict Probabilities of Election to the Baseball Hall of Fame
- The 2009 New England Symposium on Statistics in Sports
