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What did you expect, Pythagoras?

Pythagorean Expectation, the 2013 Tigers, and the trends of World Series winners

By HookSlide Sep 24, 2013, 11:33am EDT

If you spend a good amount of time hanging around with baseball fans who love sabermetrics, you will soon realize you have better things to do. You will also realize that you hear the term "Pythagorean Expectation" (also "run differential," "Pythag," "PE," and "I have never known a woman's touch") being used from time to time, and you may begin to wonder what this term means.

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"Pythagorean Expectation" is a formula that resembles the Pythagorean Theorem, an ancient mathematical proposition named after its famous creator, Jerry Theorem. The "Pythag" formula takes the number of runs scored and the number of runs allowed by a given team, factors in a fixed exponent, performs some fancy multiplication, division, addition, and magic, and produces a result that lets you know exactly why you should be writing angry emails to your local paper, denouncing the team and its manager.

The Tigers in 2013, at the time of this writing, have scored 785 runs and only given up 612 runs (by my best guess, 90 percent of those were given up by Rick Porcello to the Angels, the other 10 percent were given up by Phil Coke while he was sprinting in from the bullpen). Begin by multiplying the 785 runs by a factor of 1.83, then divide that answer by the number of runs allowed (multiplied by the same factor), plus the number of runs scored (having first multiplied by that same factor), then erase your answer and just go to a baseball stats web site to discover that the Tigers' Pythagorean Expected win-loss record should be 95-61 right now instead of 91-65. Next, write that angry letter to the newspaper and demand that Jim Leyland be fired immediately, if not sooner.

What does the Pythagorean Expectation tell us about the Tigers' performance this year? Under-performing against a given run differential could simply point to the fact that the team has gotten unlucky in several games. It can also point to the fact that the team is not winning enough low-scoring games. In the case of the Tigers, their under-performance against their run differential is probably the result of three things: 1) they have had a number of high-scoring, blowout wins that skew the "runs scored" part of the formula, 2) they have not performed well in low-scoring games (their win percentage is .463 in one-run games), and 3) they once employed a closer named Jose Valverde. (But that's another subject for another time.)

Performing well in one-run games seems to be a common trait of World Series Champions. In fact, 12 of the last 15 World Series winners had a better-than .500 win percentage in one-run games, and of those 12 teams, only three of them under-performed against their run differential for the year. (Useless trivia: it was the 2010 Giants, the 2008 Phillies, and the 2002 Angels. Use that information carefully, it's been known to act as an aphrodisiac.) There does seem to be some correlation between out-performing the Pythagorean Expectation and being good at winning one-run games, and that correlation only gets more obvious the more beer you consume.

In fact, out-performing the Pythagorean Expectation is another common trait of World Series Champions: 80 percent of the World Series winners in the last 30 years fall into this category. Only six teams have under-performed their run differential in the last 30 years and gone on to win the World Series. One explanation for this phenomenon may be that 37 percent of the last 100 World Series games played have been decided by one run. Teams that out-perform their Pythagorean Expectation tend to do well in one-run games, and apparently a large number of World Series games come down to that one run of difference.

The reasons behind the Tigers' sub-par performance in one-run games are nothing new for anyone who has been following the team closely this year. There have been problems with late-inning offense, and bullpen issues were a major weakness for the first three months of the season. But there is reason for hope, and evidence that the underlying problems have gotten better in the second half. We've watched the Tigers' offense improve in late innings, and while the bullpen can still be considered something of a problem area, it's difficult to argue that it hasn't improved since the first half of the season, when Jose Valverde was trying to close games via the rather unorthodox method of giving up game-winning home runs, and when the "bullpen by committee" experiment was still in full swing.

When I first crunched these numbers at the end of the first half, the Tigers had a win percentage of .400 in one-run games, and as noted earlier, that has improved to a .463 win percentage. At the end of the first half, the Tigers were under-performing their run differential by -5.7 percent, and at the time of this writing, they are only under-performing by -2.6 percent. Of the six teams that have won a World Series in the last 30 years while still under-performing against their Pythagorean Expectation, the worst of the bunch was the 2007 Red Sox, who were under-performing by -3.1 percent (the other teams ranged from -0.6 to -1.9 percent).

If the 2007 Red Sox can put up a -3.1 Pythagorean performance and still win the World Series in a four game sweep, then the Tigers can certainly put up a -2.6 Pythagorean performance and still have a shot at bringing home the World Series title. (Incidentally, that 2007 Red Sox team also posted a weak win percentage of .440 in one-run games.)

In conclusion, then, I believe that if we take the 2007 Red Sox as our working model, we have every reason to believe that the Tigers, despite some known weaknesses, can win the World Series in 2013.

Just as soon as they bring Mike Lowell out of retirement and get him on the playoff roster.