Pythagorean Win Theorem

Pythagorean Win Theorem of Sports

This equation was created by Bill James, the creator of baseball’s Sabermetrics. Originally, he made it only for Baseball. But another statistician, Daryl Morey, applied it other sports to see if this Win Theorem equation works for other sports. It does. The difference lies in the sport’s respective exponential.

The Pythagorean Win Theorem is not your geometric Pythagorean Theorem. A Pythagorean Win Theorem is an Expected Win Rate (ratio). A crude and simple exponential value of 2 was utilized in initially calculating the Expected Win Rate. Because of the use of squares in the exponential made it easier to connect to geometric Pythagorean’s Theorem. The more accurate exponential value for baseball is 1.81.

Expected Win Rate

Pythagorean Win Theorem

For football, Morey discovered the sport exponential was 2.37.

The Expected Win Rate is a barometer for the season. It gives a possible description if a team overachieved, underachieved, or fit into the range of expectation. Remember, a theorem is not definitive, but it also cannot be disproven at the moment.

Bucs 2016 and 2017 seasons

2016: Points for = 354, Points Against = 369

2017: Points for = 335, Points Against = 382

Expected Win Rate Applied to 2016 and 2017 seasons

2016 Season

Record for 2016: 9 – 7

Win % = 0.4754

16 games x (Win %) = 16 games x (0.4754) = 7.60 games won.

Since you cannot win partial games, then we will round down for expected wins.

Expected Wins for 2016: 7 games

Conclusion: The team overachieved by winning 9 games.


2017 Season

Record for 2016: 5 – 11

Win % = 0.4228

16 games x (Win %) = 16 games x (0.4228) = 6.76 games won.

Since you cannot win partial games, then we will round down for expected wins.

Expected Wins for 2017: 6 games

Conclusion: The team played close to the expected wins result with 5 wins, a little underachieving by a single game.


According to Football outsiders, the trend is…

Teams that under-perform their point differential tend to get better the following year, and teams that over-perform tend to get worse.

So if the trend holds true, then the Bucs should be performing better this coming season. Enough for a playoff spot remains to be an unknown projection.

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