A team's real strength is written in how many points it scores and allows — not its win-loss record. The Pythagorean expectation reveals who is lucky and who is good.
Pythagorean ExpectationLive
wins from points
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Bill James discovered that a team's win percentage tracks the ratio of points scored to points allowed, raised to a sport-specific exponent — the Pythagorean expectation. It predicts records better than actual wins early in a season, exposing teams that are lucky or unlucky and due to regress. The exponent varies from ~1.8 in baseball to ~14 in basketball.
Reading this result: A near-even scoring ratio lands close to .500 (53.2%); with an exponent of 1.83, Baseball win % swings sharply once the ratio tilts.
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How it works
Bill James found that win percentage closely follows the ratio of points scored to points allowed, raised to a sport-specific exponent. It often predicts future records better than current standings, flagging teams whose luck is about to turn. The exponent ranges from about 1.8 in baseball to nearly 14 in basketball, reflecting how much scoring separates teams.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.