Pythagorean Win Loss Calculator

Pythagorean Expectation Formula:

\[ \text{Expected Wins} = \frac{\text{Scored}^{\text{exp}}}{\text{Scored}^{\text{exp}} + \text{Allowed}^{\text{exp}}} \times \text{Games} \]

Runs Scored:

runs

Runs Allowed:

runs

Exponent:

Games Played:

games

Expected Wins:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Pythagorean Expectation?

The Pythagorean expectation is a sports analytics formula originally developed by Bill James to estimate how many games a baseball team "should" have won based on runs scored and allowed. It has since been adapted for other sports with different exponents.

2. How Does the Calculator Work?

The calculator uses the Pythagorean expectation formula:

\[ \text{Expected Wins} = \frac{\text{Scored}^{\text{exp}}}{\text{Scored}^{\text{exp}} + \text{Allowed}^{\text{exp}}} \times \text{Games} \]

Where:

\( Scored \) — Total runs scored by the team
\( Allowed \) — Total runs allowed by the team
\( exp \) — Exponent (typically 1.83 for baseball)
\( Games \) — Total number of games played

Explanation: The formula estimates what percentage of games a team should win based on their run differential, then applies this to the actual number of games played.

3. Importance of Pythagorean Wins

Details: Comparing actual wins to Pythagorean expected wins helps identify teams that may have been lucky or unlucky during a season. Consistently outperforming the expectation may indicate superior bullpen or clutch performance.

4. Using the Calculator

Tips: Enter runs scored and allowed (must be positive numbers), select an appropriate exponent (1.83 for baseball, other sports use different values), and enter total games played.

5. Frequently Asked Questions (FAQ)

Q1: What's the standard exponent for baseball?
A: The original exponent was 2, but 1.83 has been found to be more accurate for modern baseball.

Q2: How is this used in other sports?
A: Basketball typically uses 14, football 2.37, and hockey 2. Different exponents account for scoring variance between sports.

Q3: What does it mean if actual wins exceed expected wins?
A: The team may have been "lucky" or particularly good in close games. The opposite suggests "unluckiness" or poor performance in close games.

Q4: Can this predict future performance?
A: Teams that significantly outperform their Pythagorean expectation often regress toward it in future seasons.

Q5: What are limitations of this formula?
A: It doesn't account for game-by-game variance, strength of schedule, or roster changes during the season.