Pythagorean Expectation Calculator

This Pythagorean Expectation Calculator can be used to reveal the predicted winning percentage of a baseball team on the basis of how many runs they score and how many they allow.

How to use the calculator: Choose the Pythagorean exponent for the equation, input the total number of runs your team has scored, the total number of runs they have allowed, and the total number of games they have played, and click "Calculate".

Pythagorean Expectation Calculator

Expected Winning Percentage:
Expected Number of Wins:


The sabermetrician Bill James created the Pythagorean expectation formula, and it is a way that you can predict the number of wins or losses you can expect a baseball team to experience.

This Pythagorean win/loss equation employs the number of games played (G), the number of allowed runs (RA), and the number of runs scored (RS) to make a prediction of the number of games a team ought to have won. Originally the formula for win percentage (Win%) and total number of wins was:

Win% = RS2 / (RS2 + RA2) and

Wins = Win% × G

James named this the Pythagorean formula because of the fact that the denominator contains the sum of squares. A later revision to the equation for the win percentage was made, thus:

Win% = RS1.83 / (RS1.83 + RA1.83)

James realized that using an exponent of 1.83 gave a more accurate prediction of the true number of wins than using an exponent of 2. Because of this, extra sabermetric analysis has been undertaken to reveal the exponent x so that the equation:

RSx / (RSx + RAx)

offers the most accurate possible prediction for win percentage. Up to now, one of the most extensively employed values of x has been:

x = ((RS + RA) / G)0.287

created by David Smyth. In this instance the x value is not a fixed constant, instead it is a function of RS, RA, and G.

x = 1.83 or x = ((RS + RA) / G)0.287 will both provide accurate predictions for the number of games a team should win.

If a team has more real-world wins than predicted by this formula, we may say that they have had a lucky year, and the opposite is true; if they win fewer games than the formula predicts, they have had an unlucky year.

You may also be interested in our Winning Percentage Calculator

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