Editing Pythagorean expectation (section)

==Use in the National Football League==
The formula has also been used in the [[National Football League]] by football stat website and publisher [[Football Outsiders]], where it is known as '''Pythagorean projection'''.

The formula is used with an exponent of 2.37 and gives a projected winning percentage. That winning percentage is then multiplied by 17 (for the number of games played in an NFL season from 2021), to give a projected number of wins. This projected number given by the equation is referred to as Pythagorean wins.

:<math>\text{Pythagorean wins} = \frac{\text{points for}^{2.37}}{\text{points for}^{2.37} + \text{points against}^{2.37}}\times 17.</math>

The 2011 edition of ''Football Outsiders Almanac''<ref>''Football Outsiders Almanac 2011'' ({{ISBN|978-1-4662-4613-3}}), p.xviii</ref> states, "From 1988 through 2004, 11 of 16 [[Super Bowl]]s were won by the team that led the [[National Football League|NFL]] in Pythagorean wins, while only seven were won by the team with the most actual victories. Super Bowl champions that led the league in Pythagorean wins but not actual wins include the [[2004 New England Patriots season|2004 Patriots]], [[2000 Baltimore Ravens season|2000 Ravens]], [[1999 St. Louis Rams season|1999 Rams]] and [[1997 Denver Broncos season|1997 Broncos]]."

Although ''Football Outsiders Almanac'' acknowledges that the formula had been less-successful in picking Super Bowl participants from 2005–2008, it reasserted itself in 2009 and 2010. Furthermore, "[t]he Pythagorean projection is also still a valuable predictor of year-to-year improvement. Teams that win a minimum of one full game more than their Pythagorean projection tend to regress the following year; teams that win a minimum of one full game less than their Pythagorean projection tend to improve the following year, particularly if they were at or above .500 despite their underachieving.

For example, the [[2008 New Orleans Saints season|2008 New Orleans Saints]] went 8–8 despite 9.5 Pythagorean wins, hinting at the improvement that came with the [[2009 New Orleans Saints season|following year's]] [[2009 NFL season|championship season]]."

The [[2022 Minnesota Vikings season|2022 Minnesota Vikings]] were a great outlier in this regard, going 13-4 despite having 8.4 Pythagorean wins.<ref>{{Cite web |title=2022 Minnesota Vikings Advanced Stats |url=https://www.pro-football-reference.com/teams/min/2022_advanced.htm |access-date=2023-11-02 |website=Pro-Football-Reference.com |language=en}}</ref> Two years later, the [[2024 Kansas City Chiefs]] surpassed this discrepancy by going 15-2 with a Pythagorean win total of 10.2 wins.<ref>{{Cite web |title=2024 Kansas City Chiefs Advanced Stats |url=https://www.pro-football-reference.com/teams/kan/2024_advanced.htm |access-date=2025-01-17|website=Pro-Football-Reference.com |language=en}}</ref>