Pythagorean expectation calculatorHERMES TOOLS · Sports data
Estimate expected win percentage, wins and the gap to the actual record from MLB / NBA runs or points.
Result
How it works: formula and examples
Pythagorean expectation measures a team by what it scores and allows: scoredˣ ÷ (scoredˣ + allowedˣ). The default exponent is 1.83 for MLB and 13.91 for the NBA, and you can change it.
Enter runs or points scored and allowed, games played and actual wins for the same period. Expected wins = expected win % × games played; actual minus expected is the record gap, which isn't all luck.
Example: 100 both scored and allowed over 10 games with 6 actual wins gives an expected win percentage of 50%, 5 expected wins and a gap of +1. Over a 162-game MLB season, the remaining 152 games project to 76 more wins, 82 in total.
Another example: with exponent 2, 200 scored and 100 allowed, expected win percentage is 40000 ÷ 50000 = 80%. It is a rough performance model, not a full forecast of the remaining schedule, injuries or the postseason.
FAQ
Why are the MLB and NBA exponents different?
Scoring distributions and margins differ between the two sports, so each uses its own empirical exponent.
Can it calculate with zero scored and zero allowed?
No. The formula is undefined without any runs or points. If only one side is zero, the result is 0% or 100%.
How are full-season wins projected?
Actual wins plus expected win percentage times the games left. It assumes the same performance for the rest of the way and does not adjust for opponents.
Related tools
All tools ›This tool is for math and data reference only and offers no betting services. Do not buy sports lottery tickets if you are under 18.