Pythagorean win expectations

Everything is Bill James’ fault. Bill James is the nerd who began the trend toward baseball analytics (James coined the term “sabrmetrics”) as a household term.

Baseball analytics works, because baseball performance is usually an individual thing: one guy throws it, another guy hits it 500 feet or swings and misses. You can chart that with some basis in reality.

After the application of baseball analytics began saving and making major league baseball teams billions of dollars, basketball people naturally wanted to participate. But I don’t think basketball performance can soundly be quantified as an individual thing; even when Chamberlain scored 100, it was a cooperative effort of 10 players. Chamberlain’s teammates had to give him the ball, and their opponents had to give Chamberlain’s team the ball; the other team was committing turnovers on purpose at the end of that game.

Team-based analytics have a better shot at genuine usefulness. Take the Pythagorean Winning Percentage, which James concocted as a method for determining an expected winning percentage based on runs scored:

pwp = (runs_scored^2) / (runs_scored^2 + runs_allowed^2)

The 2021 San Francisco Giants won 107 regular season games (107-55, .660). The Giants scored 804 runs, and allowed 594, for a Pythagorean projection of .647, or 105 wins.

For reasons that escape me, Daryl Morey (NBA Philadelphia) and John Hollinger (NBA Memphis) use exponents of 13.91 and 16.5, respectively. Look at what this does to the 2022 Utah Utes women.

pwp = (points_scored^some_exponent) / (points_scored^some_exponent + points_allowed^some_exponent)

The Utes scored 2505 points, and allowed 2251, and went 21-12 (.636).

Using Morey’s exponent 13.91, Utah’s Pythagorean expectation was .816, or 27-6. Using Hollinger’s exponent 16.5, the Utes’ expectation was .854, or 28-5. I tried a range of exponents until landing on 5, which returned .631.

TeamScoredAllowedactual winsPythagorean expected
Oregon St.193218661716
Arizona St.164515571215
Washington St.180218001915
Southern Cal180118111214