The Baseball Exchange


The Pythagorean Calculus (Part I) by The Fallen Phoenix
June 20, 2007, 1:12 am
Filed under: Baseball Statistics

The Fallen Phoenix here, and it’s time for my first blog post–which is either going to be rather exciting or rather anticlimactic, depending on your point of view.

I’m opting for the latter.

In any event, I don’t really have much of an excuse for not posting anything yet, other than I’ve been somewhat busy. That and I had all of my wisdom teeth pulled a few weeks ago, which really did nothing except make me feel less wise. And I suppose it’s better for my teeth in the long run.

Right, on to baseball.

I have been working on something the past few days, something which I hope to be at least somewhat illuminating, and not something that is only going to confirm what sabermetricians everywhere already know. As most of you probably know, there is a very, very nifty sabermetric out there called the Pythagorean Record (or Pythagorean Win-Loss Expectation), an equation initially developed by Bill James to estimate what a team’s record ought to be based on runs scored and allowed. It tends to be a pretty accurate estimation, give or take three or four games (that tends to be the accepted mean, at least).

Generally, this deviation is attributed to luck. Still, there have been some very odd deviations over the years–two of the largest ones over the last few years have belonged to the 2006 Cleveland Indians and the 2004 New York Yankees. Both teams were at least ten wins shy of their Pythagorean Record–the Cleveland Indians on the wrong side of that (roughly ten additional losses), the New York Yankees on the right side (roughly ten additional wins).

Over the last few days, I have begun tabulating the records of every team in both leagues over the last six years. I am including their actual records, their pythagorean records*, their records in one-run games, their records in blowout** games, and their records in all other games.

My goal is to find some trend, something–other than luck–that might provide some indicator for why some teams outperform their pythagorean records, and why some teams don’t. Do I expect to find anything? Honestly, I don’t–I think the variations will, undoubtedly, be tied to luck. But I think there will be some loose correlations. For example, it is generally assumed that teams that underperform (or outperform) their Pythagorean record will have particularly good records in one-run games: my studies up until this point seem to agree. I will ultimately move even deeper than this: I will look into bullpen performance, offensive performance, starting pitching performance, even average age of teams, to see if there is anything that might suggest whether a team is more or less likely to outperform its Pythagorean record.

I’m hoping to have solid statistics to post by the end of the week. So far, I’ve tabulated most of the records from the playoff teams and the last place teams from the last three years (all in the American League), and I’ve been taking most of my statistics from baseball-reference.com. So, hopefully I’ll have my initial findings posted Thursday evening; if not, it’ll likely be pushed back to Sunday or Monday evening, at the very earliest.

*For Pythagorean record, I’m using the following equation (courtesy of baseball-reference.com): [(runs scored)^1.83] / [(runs scored)^1.83 + (runs allowed)^1.83]

**For blowout games, I am borrowing the same definition used at baseball-reference.com: a run-differential between the two games equal to or exceeding five runs.

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