The Predictive Power of Pythagorean Records

Pythagoras was an interesting guy, but he was no Bill James. Starting in 1977, James wrote a very interesting series of “abstracts” filled with baseball stats and analysis. Although James wasn’t the first person to do this, his work was so groundbreaking, he’s now considered the father of baseball analytics. He even gave it a name: sabermetrics.

One of the more important things James talked about was how a team’s run differential (the number of runs scored, minus the number of runs allowed) was a better indicator of performance level than actual wins and losses. The higher the differential, the more likely the team will continue to perform well. James came up with a formula that translated run differential into what he called the Pythagorean Winning Percentage. Betting on sports has never been the same.

Square Dancing

The original formula itself is simple enough:

W% = RS2/(RS2 + RA2)

It does look a bit like the Pythagorean Theorem we learned in school, with Runs Scored and Runs Allowed instead of the sides of a triangle. It’s also not entirely accurate; using this formula will give you an expected win-loss record that’s about three games away from a team’s actual record, on average. Statheads have tweaked the formula in different ways, like using 1.83 instead of 2 for the exponent.

You don’t have to worry about these details too much when you’re betting on sports. Leading websites like ESPN list the run differentials and even the expected win-loss records for every team when they publish their standings. You can see which teams are winning and losing more games than they “should” be; at press time, the Texas Rangers lead the AL West at 72-50, but their plus-7 run differential translates to a Pythagorean record of 62-60.

Orange Fizz

When you see a considerable gap like this between the actual and Pythagorean records, you may have found a good team to either fade or follow – fade in the case of Texas. Recreational bettors are more likely to focus on those 72 wins, without thinking much about that tiny run differential. They’ll bet too heavily on the Rangers, the odds will move to compensate, and whichever team Texas is playing will be available at a bargain price.

Other sports have their versions of the Pythagorean record, using point differentials (for football and basketball) and goal differentials (for hockey) to calculate expected win-loss records. Are the Denver Broncos a good fade candidate this year after winning the Super Bowl? Possibly; they went 12-4 during the 2015 regular season, but Denver’s plus-59 point differential translates to just 9.7 Pythagorean Wins. The Broncos could easily miss the playoffs if they don’t improve their performance level.

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