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Predicting Overtime with the Pythagorean Formula

Author

Listed:
  • Rosenfeld Jason W.

    (Harvard University)

  • Fisher Jake I

    (Harvard University)

  • Adler Daniel

    (Harvard University)

  • Morris Carl

    (Harvard University)

Abstract

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.

Suggested Citation

  • Rosenfeld Jason W. & Fisher Jake I & Adler Daniel & Morris Carl, 2010. "Predicting Overtime with the Pythagorean Formula," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(2), pages 1-19, April.
    • Handle: RePEc:bpj:jqsprt:v:6:y:2010:i:2:n:1
    DOI: 10.2202/1559-0410.1244
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    Cited by:

    1. Pettigrew Stephen, 2014. "How the West will be won: using Monte Carlo simulations to estimate the effects of NHL realignment," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(3), pages 1-11, September.
    2. Manner Hans, 2016. "Modeling and forecasting the outcomes of NBA basketball games," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(1), pages 31-41, March.
    3. Kaplan Edward H. & Rich Candler, 2017. "Decomposing Pythagoras," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 13(4), pages 141-149, December.

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