Pythagorean Expectation (Sport Exponent) Calculator
Project expected wins from points for and against for basketball, football or hockey using each sport’s tuned Pythagorean exponent.
How it works
Expected win % = PF^exp ÷ (PF^exp + PA^exp) · Expected wins = win % × games
The Pythagorean idea generalises to any sport by changing the exponent that links scoring margin to wins. Basketball uses a high exponent near 13.9 (Daryl Morey’s fit) because scores are large and blowouts are common, while football sits near 2.37 and hockey near 2. A higher exponent means the same points ratio maps to a more lopsided win percentage.
Worked example
An NBA team with 9,000 points for and 8,800 against, using exponent 13.91, has an expected win % of 1 ÷ (1 + (8,800 ÷ 9,000)^13.91) ≈ 0.578 — roughly 47 wins in 82 games.
Sources: Pythagorean expectation — Wikipedia
Frequently asked questions
Why does basketball use such a big exponent?
NBA games routinely produce hundreds of points, so a small percentage edge in scoring reflects a large real advantage. The high exponent (~13.9) rescales that ratio into a realistic spread of win totals.
Where do these exponents come from?
They are empirical best-fits found by minimising prediction error against historical seasons — Morey’s 13.91 for the NBA, and roughly 2.37 for the NFL, are the widely cited values.
Can I use my own exponent?
This calculator offers the common sport presets. For a fully custom exponent or the classic baseball case, use the baseball Pythagorean calculator, which fixes the exponent at 2.
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This calculator is for educational purposes. Double-check important results before acting on them.