Pythagorean Win Calculator Formula

Understand the math behind the pythagorean win calculator. Each variable explained with a worked example.

Use the Pythagorean Win Calculator

Formulas Used

Expected Win %

exp_win_pct = round(expected_win_pct * 1000) / 1000

Expected Wins

expected_wins = round(expected_win_pct * games_played * 10) / 10

Expected Losses

expected_losses = round((1 - expected_win_pct) * games_played * 10) / 10

Avg Point Differential

pts_per_game_diff = round((points_scored - points_allowed) / games_played * 10) / 10

Variables

VariableDescriptionDefault
points_scoredTotal Points Scored750
points_allowedTotal Points Allowed680
games_playedGames Played82
exponentPythagorean Exponent14
expected_win_pctDerived value= pow(points_scored, exponent) / (pow(points_scored, exponent) + pow(points_allowed, exponent))calculated

How It Works

How the Pythagorean Win Formula Works

Formula

Expected Win % = PF^exp / (PF^exp + PA^exp)

Where PF = Points For, PA = Points Against, and exp is the Pythagorean exponent.

Typical Exponents

  • MLB: 1.83
  • NFL: 2.37
  • NBA: 14
  • NHL: 2.05

    • Teams that significantly outperform their Pythagorean expectation often regress toward the expected record in subsequent seasons.

    Worked Example

    NBA team: 750 points scored, 680 allowed through 82 games (exponent 14).

    points_scored = 750points_allowed = 680games_played = 82exponent = 14
    1. 01Win % = 750^14 / (750^14 + 680^14)
    2. 02This evaluates to approximately 0.769
    3. 03Expected wins = 0.769 * 82 = 63.1 wins
    4. 04Expected losses = 82 - 63.1 = 18.9
    5. 05Avg point diff = (750 - 680) / 82 = 0.9 per game

    Ready to run the numbers?

    Open Pythagorean Win Calculator