Pythagorean Win Expectation Calculator — Baseball
Estimate a run-based win percentage and season record using exponent 2, 1.83 or your chosen value, with explicit model limits.
Estimate a baseball team’s win percentage from its runs scored and runs allowed. Choose the original squared-runs formula, the commonly used 1.83 exponent, or a custom exponent for a sensitivity check. The expected record summarizes run balance over a period; it is not a live game probability or a certainty about the next season.
How to use this tool
- Enter runs scored and allowed for the same team and period.
- Enter the number of games to use for the expected record.
- Choose exponent 2, 1.83, or a custom scenario from 0.1 to 10.
- Read the fractional expectation before using the rounded whole-win record.
Formula
Expected win share = RSᵉ / (RSᵉ + RAᵉ); expected wins = games × win share
RS and RA are run totals and e is the selected exponent. Equal positive totals produce one-half; two zero totals are undefined. Scaling preserves tiny positive outcomes. Whole wins round exact halves upward; unusually precise custom exponents too close to a numerical rounding boundary show a range.
Example
With 800 runs scored, 600 allowed and exponent 2, the share is 640,000 / 1,000,000 = 64%. Across 162 games, that gives 103.68 expected wins and 58.32 expected losses, summarized as 104–58 when rounded.
Frequently asked questions
Why offer different exponents?
The original model squares the totals; 1.83 is a common baseball modification. A custom exponent changes sensitivity to run imbalance and should not be mistaken for an empirically fitted value.
Why does the expected record differ from actual wins?
The formula uses run totals and ignores their game-by-game timing. Teams with the same aggregate runs can have different actual records, schedules and underlying circumstances.
Do zero allowed runs guarantee an unbeaten future?
No. The formula returns its mathematical endpoint for the supplied sample. That endpoint is not a claim that future opponents cannot score or that outcomes are certain.
Sources
Last updated: 2026-10-30