Slowly Back Away from the Pythag Expectation

Updated: Thanks to the commentors, especially Evan, for double checking my work. I had an issue in Excel that messed up the results for May and June. Charts have been updated.

For most of 2012, the Baltimore Orioles have been playing over their heads. Well, at least when it comes to their expected win-loss record.

Based on the run differential the team has generated, the O’s have amassed 10 more wins than we would expect based on their Pythagorean winning percentage. The team has outplayed its cumulative expected winning percentage throughout the year and — since April — picked up two additional wins at the end of each month. If they sustain this performance and finish August with at least 10 more wins then their Pythagorean winning percentage would predict, they would be just the third team to do so since 2001 (the 2004 Yankees and the 2007 Diamondbacks are the other two).

Some might point to this glaring discrepancy between Baltimore’s actual winning percentage and Pythagorean winning percentage as evidence that the Orioles cannot sustain their winning ways. Of course, this raises the question of whether we really gain anything from a predictive standpoint heading into September if we focus on a team’s expected winning percentage rather than their actual performance.

The answer based on a review of the past decade seems to be no.

Using Baseball-Reference’s historical standings tool, I looked at cumulative team winning percentage at the end of May, June, July and August — between 2001 and 2011 — and how well their winning percentage and Pythagorean winning percentage* correlated with the actual rest-of-season winning percentage (n=330 individual seasons). Basically: How well did a team’s winning percentage through the end of July correlate with the team’s winning percentage from Aug. 1, through the end of the season?

Here are the results:

For the first few months, Pythagorean winning percentage holds a slight edge over actual winning percentage. In July, the advantage flips to actual winning percentage, but here we are still only talking about a .01 advantage. That changes in August. That’s where winning percentage has about a 3% advantage in terms of explanatory power.  It would appear that once a team manages to navigate to August, focusing on a team’s expected winning percentage — with an eye toward predicting September — is less helpful than simply looking at real performance.**

But what about significantly overachieving teams, like this year’s Orioles? Surely, a team that’s five or more wins above their expected winning percentage is expected to fade down the stretch, right?

Turns out, not so much.

First, let’s simply isolate the data to teams that outperformed their Pythagorean expectation by five or more wins through the end of each month:

As you see, the results are similar to what we found with the full sample: Actual winning percentage is just as good, or better, at predicting ROS winning percentage in July and August. And it gives about 4% better explanatory power at the end of August.

For underperforming teams, though, the story is much different:

The predictive power of both types of winning percentage increase each month, but in this case, Pythagorean winning percentage has a higher correlation to ROS winning percentage in each month.

So why the difference? Here’s one theory: It’s somewhat of a self-fulfilling prophecy. For example, teams that are over performing are more likely to see themselves as contenders and make moves to reinforce that status. By the time you get to August, they may have counteracted any kind of natural regression by altering the team. Conversely, underachieving teams might do the opposite, thereby securing a disappointing season.

There probably are a bunch of other theories for this finding (i.e. superior performance in one-run games based on bullpen strength, which isn’t captured by the calculation for expected winning percentage, etc.), but the bottom line is that simply relying on expected winning percentage to discount a team’s chances for sustaining their performance through September isn’t a great idea. Especially since their actual winning percentage generally predicts their September record better. The better way to approach it would be to look at whether the composition of the team has changed (for better or worse) and whether there are trends their more recent performance that foretell a change in either direction (e.g. injuries, pitcher fatigue).


*I also used Baseball-Reference’s Pythagorean Winning Percentage: For details on the equation used, see here.

**These findings differ from Clay Davenport’s, who looked at the difference between actual and Pythagorean winning percentages through various games played increments. Why that’s the case, I’m not sure. But his overall results that Pythagorean becomes less useful relative to actual winning percentage as the end of the season draws closer is consistent with the findings here.

Bill leads Predictive Modeling and Data Science consulting at Gallup. In his free time, he writes for The Hardball Times, speaks about baseball research and analytics, has consulted for a Major League Baseball team, and has appeared on MLB Network's Clubhouse Confidential as well as several MLB-produced documentaries. He is also the creator of the baseballr package for the R programming language. Along with Jeff Zimmerman, he won the 2013 SABR Analytics Research Award for Contemporary Analysis. Follow him on Twitter @BillPetti.

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11 years ago

How about using PWs as a predictor for the playoffs? (Team A won 87 games and made the playoffs, but only had 79 PWs, so they’re toast against Team B who had 90.)