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Pythagorean Expected Wins Calculator

Estimate a team's expected win% and record from points/runs scored vs allowed using Pythagorean expectation, with MLB, NBA and NFL presets.

Enter points/runs for and against plus games played. Pick a sport preset or set your own exponent.

About this tool

The Pythagorean Expected Wins Calculator estimates how many games a team “should” have won based on how many points or runs it scored versus how many it allowed. It applies Bill James's Pythagorean expectation, ExpWin% = PF^x / (PF^x + PA^x), where PF is points/runs for, PA is points/runs against, and x is a sport-specific exponent. Expected wins are then ExpWin% multiplied by the number of games played.

The right exponent varies by sport because scoring dynamics differ. This tool ships presets of x = 1.83 for baseball (the value James refined from the original 2), x = 13.91 for basketball (the Daryl Morey figure), and x = 2.37 for American football. You can also type any custom exponent to experiment; the sport selector simply fills the exponent field, which remains the source of truth for the math.

Everything runs locally in your browser, so nothing you enter is uploaded. If you also enter the team's actual won–lost record, the calculator reports the “luck” delta — actual wins minus expected wins. A large positive delta suggests a team outperformed its scoring margin (often unsustainable), while a negative delta hints a team was unlucky and may improve. Win percentages are shown as a percentage alongside the expected win and loss totals.

Frequently asked questions

What is the Pythagorean expectation formula?
Expected win percentage is PF^x / (PF^x + PA^x), where PF is points or runs scored, PA is points or runs allowed, and x is a sport-specific exponent. Multiplying by games played gives expected wins.
Which exponent should I use?
Common values are 1.83 for baseball, 13.91 for basketball, and 2.37 for American football. These reflect how scoring margin translates to wins in each sport. You can override the exponent with any positive value.
What does the luck delta mean?
It is actual wins minus expected wins. A positive number means the team won more than its scoring margin predicted (possibly lucky or clutch); a negative number means it underperformed and may be due for improvement.
Why is baseball's exponent 1.83 instead of 2?
Bill James originally used 2 (hence “Pythagorean”), but analysts found that an exponent near 1.83 fits historical MLB results more accurately. Basketball and football need much larger exponents because of their different scoring scales.

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