Pythagorean Win Expectation Calculator
See the record a team's scoring margin deserves, and whether it has been lucky or unlucky.
How Pythagorean expectation works
Expected win % = scored^x ÷ (scored^x + allowed^x). An MLB team that scores 800 runs and allows 700 has an expected win % of .561 with the 1.83 exponent, or about 90.8 wins over 162 games.
If that team actually won 96, it beat its expectation by about 5 wins, often a sign of a strong record in one-run games that may not last.
FAQ
What is Pythagorean expectation?
An estimate of the win percentage a team's scoring deserves: scored^x ÷ (scored^x + allowed^x). Teams far above it have often been lucky in close games, and tend to drift back toward it.
Which exponent should I use?
Commonly used values are about 1.83 for MLB runs, 13.91 for NBA points, 2.37 for NFL points and 2 for NHL goals. None is official, so you can change it above.
Why is the NBA exponent so high?
Basketball has many scoring possessions, so a small points margin is a strong sign of a better team. The higher exponent turns small margins into bigger win % differences.
Who created it?
Baseball writer Bill James, who used an exponent of 2 for runs. It is called Pythagorean because the formula looks like the Pythagorean theorem.