Pythagorean Wins for Managers

Pythagorean Wins is a very real concept developed by Bill James to attempt to measure how well a team did using the runs scored. Since it compares very well with actual results, it’s used as a marker to measure “luck” or other supposedly intangible elements of the game. After much consideration, I will contend it isn’t luck as much as something else far more basic.

The Pythagorean Wins formula is:

Runs²/(Runs² + Runs Allowed²)

Using the 2012 Chicago Cubs as an example, we see that they scored 613 runs and gave up 799. Using the formula, we would expect their Win-Loss record to be:

613²/(613² + 799²)                 375,769/(375,769 + 638,401)                .371 * 162 games ≈ 60-102

The Cubs finished 61-101, so somehow the team “exceeded” its expectations, if such a term can be used on a 100-loss team. These numbers fluctuate from year to year, which is why it is common to hear Pythagorean Wins referred to as the “luck factor.” If Pythagorean Wins can be applied to a team (and it appears to work well, and not just in baseball), can we then apply it to managers and see how much better or worse they did than expected?

This chart shows the top 40 managers whose careers began after 1950 (Hall of Famers highlighted in yellow), with the following column explanations:

R=Runs RA=Runs Against PW% the Pythagorean Win percent EW extra wins over predicted. For fun, the last columns refer to how the manager did in 1-run games, with the last column being the percentage of games that the team was in first.

The best of the lot appears to be Bruce Bochy, at about 30 wins over his expected win total. However, to attain that total, he had to manage almost 2900 games, making it appear that he (or his teams or a combination of both) were able to outperform in 1 game out of 100. To see how this looks for an individual manager, lets view Tony LaRussa, the man who can recite the alphabet backwards with the best of them:

Up and down and up and down and up and down…There’s no pattern to whether the teams outperformed expectations or not, which is the main reason why no manager has Pythagorean Win totals that are very high, and possibly the main reason why Pythagorean Wins aren’t shown as any kind of manager statistic. It took me awhile, and people smarter than me have probably known this for years, but the seeds to this lie in some simple facts. This table shows the winning percent of teams by runs scored from 1950-2012:

From 1950-2012, the average runs scored is 4.4, and yet teams still manage to win games when they score as few as 1 run—not many, but it’s still 1 in 10. In the end, that’s what Pythagorean Wins ends up measuring—how well a team does when they DON’T score a lot of runs. Should the manager be credited with this? Sure, he deserves some recognition, but no one credits Jim Leyland with being a genius for running Justin Verlander out every fifth day—he’d be an idiot not to. But no matter the era, a low-run or high-run era, how a team does when they score below average runs is what determines whether they’re on the plus or minus side of the Pythagorean Wins ledger.