SoSH Glossary: Pythagorean Theorem Winning Percentage

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Pyhagorean Theorem Winning Percentage

The Pythagorean theorem winning percentage is a formula that predicts the expected winning percentage of a team based only on its runs scored and runs allowed. The resulting percentage is often converted into a record which is sometimes referred to as a Pythagorean, or Pythag, win-loss record.

If a team exceed its Pythag record, then it is sometimes considered “lucky,” while teams that underperform theirs are often called “unlucky.” However, these teams may simply need to be looked at more closely, as the Pythagorean theorem is a means of finding teams that may be playing above or below their heads. An excellent or poor bullpen can positively or negatively affect a team’s performance in tight games respectively, and therefore skew their Pythag record.

How Does It Work In Real Life?

A good example of the Pythagorean theorem in action is the 2005 Washington Nationals. At the halfway point, the Nats were 50-31 with 335 runs scored and 333 runs allowed! After plugging those numbers into the formula, their Pythag winning percentage is .503 for an expected record of 41-41. So, the Nationals were playing nine games over their heads according to the theorem. In the second half, Washington would win only 31 more games to finish .500 on the season (81-81). They finished with 639 runs scored and 673 runs allowed for a final Pythag winning percentage of .474, or a predicted record of 77-85. In the second half, they scored 304 runs and allowed 340 runs, so it is not surprising they played significantly below .500 in the second half.

What to Watch For

It’s important to remember that the Pythagorean theorem is meant as a rule of thumb and that teams should be expected to play around that winning percentage going forward assuming there are no major trades or injuries. The Pythagorean theorem winning percentage is a simple calculation that tends to be reasonably accurate and should be treated as such.


Pete Hodges has written about the call up of a top prospect, an odd tradition, and Leo the Lip.

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