# Predicting Overtime with the Pythagorean Formula

## Author Info

• Rosenfeld Jason W.

(Harvard University)

• Fisher Jake I

(Harvard University)

(Harvard University)

• Morris Carl

(Harvard University)

Registered author(s):

## 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.degruyter.com/view/j/jqas.2010.6.2/jqas.2010.6.2.1244/jqas.2010.6.2.1244.xml?format=INT

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

## Bibliographic Info

Article provided by De Gruyter in its journal Journal of Quantitative Analysis in Sports.

Volume (Year): 6 (2010)
Issue (Month): 2 (April)
Pages: 1-19

as in new window
Handle: RePEc:bpj:jqsprt:v:6:y:2010:i:2:n:1

Contact details of provider:
Web page: http://www.degruyter.com

Order Information:
Web: http://www.degruyter.com/view/j/jqas

Keywords:

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:bpj:jqsprt:v:6:y:2010:i:2:n:1. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.