Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.290
Source Normalized Impact per Paper (SNIP) 2017: 0.853

See all formats and pricing
More options …
Volume 6, Issue 2


Volume 1 (2005)

Predicting Overtime with the Pythagorean Formula

Jason W. Rosenfeld / Jake I Fisher / Daniel Adler / Carl Morris
Published Online: 2010-04-12 | DOI: https://doi.org/10.2202/1559-0410.1244

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.

Keywords: Pythagorean expectation; Pythagorean formula; Bill James; overtime; team strength

About the article

Published Online: 2010-04-12

Citation Information: Journal of Quantitative Analysis in Sports, Volume 6, Issue 2, ISSN (Online) 1559-0410, DOI: https://doi.org/10.2202/1559-0410.1244.

Export Citation

©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Tyler P. Lawler and Frank H. Lawler
Perceptual and Motor Skills, 2011, Volume 113, Number 3, Page 815
C. Soto Valero
International Journal of Computer Science in Sport, 2016, Volume 15, Number 2
Tyler Lawler, Frank Lawler, Jack Gibson, and Rachael Murray
Annals of Epidemiology, 2012, Volume 22, Number 6, Page 406

Comments (0)

Please log in or register to comment.
Log in