Pythagorean Expectation Calculator (Baseball)

LAST UPDATE: September 24th, 2020

Pythagorean Expectation Calculator

Definition – What is Pythagorean Expectation?

Pythagorean Expectation is a metric that evaluates a team’s number of runs for and runs against and attempts to use that data to come up with what a team’s win percentage “should” be base on run data alone.
It is assumed that over a longer period of time (for example a baseball season), win/loss percentage should correlate with run data based on the Pythagorean expectation formula.
Pythagorean expectation can be used to determine if a team is ahead or behind where it “should” be based on run data. A team strongly lagging Pythagorean expectation is seen through this filter as due for a win streak, while one strongly ahead of it is seen as due for a losing streak.
In practice, Pythagorean win percentage has shown to be quite accurate – usually being off by 2 – 3 wins over the course of a baseball season. Alternative forms of Pythagorean win percentage use a different exponent than 2.

Formula – How to calculate Pythagorean Expectation

Pythagorean Win = Runs Scored2/(Runs Scored2 + Runs Allowed2)
It can also calculate as:
Pythagorean Win = 1 / (1 + (Runs Allowed / Runs Scored)2)


A team has 570 runs scored compared with 556 runs allowed.
Pythagorean Win = 1 / (1 + (556 / 570)2)
Pythagorean Win = 1 / (1 + (0.975)2)
Pythagorean Win = 1 / (1 + 0.95)
Pythagorean Win = 1 / 1.95
Pythagorean Win = 0.512
This team’s Pythagorean win is 0.512 – using run data, it is expected that this team’s win-loss percentage should be 51.2%.

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