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Pythagorean Winning Percentage


Pythagorean winning percentage is a formula developed by renowned statistician Bill James. The concept strives to determine the number of games that a team *should* have won -- based its total number of runs scored versus its number of runs allowed -- in an effort to better forecast that team's future outlook.

The initial formula for pythagorean winning percentage was as follows: (runs scored ^ 2) / [(runs scored ^ 2) + (runs allowed ^ 2)] That formula proved more predictive than basic winning percentage when trying to predict a team's future performance, although in the years since pythagorean winning percentage was popularized, other analysts have attempted to find an even more accurate formula., for instance, uses 1.83 as its exponent of choice -- a modification that has successfully narrowed the formula's margin of error.


The 2018 Seattle Mariners finished the season with an 89-73 record that looked impressive upon first glance. However, as a team, the Mariners allowed 34 more runs than they scored. Their pythagorean win-loss record, as calculated by Baseball-Reference, was a mere 77-85, suggesting that the Seattle club vastly overperformed in 2018 and should not have been expected to repeat its success. General manager Jerry Dipoto and the rest of the Mariners front office clearly agreed. The Mariners dramatically reshaped their roster in the ensuing offseason, trading away the likes of Robinson Cano, Edwin Diaz, Jean Segura, Alex Colome, Mike Zunino and others.

Why it's useful

Pythagorean winning percentage can help to identify teams that have either overachieved or underachieved. When looking at a club with a surprisingly poor or surprisingly strong record early in the season, using the theory to determine a team's "expected" winning percentage for the remainder of the year can paint a more accurate picture of how things will play out than merely looking at actual winning percentage.