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For K-12 Students · Pythagorean Expectation

Pythagorean Expectation for a high jump

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a high jump live below — adjust the inputs and watch it respond, right in your browser.

Pythagorean ExpectationLive

wins from points

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Points/runs scored

Points/runs allowed

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.

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Data Inspector

Expected win %53.2%

Projected wins86 of 162

Exponent1.83

Governing equation

Win% = \frac{75 0 ^{1.83}}{75 0 ^{1.83} + 70 0 ^{1.83}} = 53.2%

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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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Pythagorean Expectation for a high jump" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.