Should the Pythagorean win-loss be replaced?

>> Thursday

"You make your own luck."

Like most other sports axioms, "you make your own luck" is nonsense--or, at best, good sense bastardized. Yet, frequent misattributions of skill and all-out dismisals of luck have given literal truth to this folxymoron in the minds of many.

That said, "you make your own luck" can be credible defense in the face of hastily ascribed luck. The implication in such cases, however, is not that honest-to-goodness random luck is really within our conscious control but that the thing we're calling "luck" is actually a mixture of luck and some glossed-over causal factors.

Two days ago, Jay Jaffe of the Baseball Prospectus posted this article in which he examines trends among teams that overachieve in the standings, according to their Pythagorean win-loss projection. The question has nagged me for the better part of the past two seasons. Is there a common link among teams that outperform their Pythagorean projections, or is it--as is typically argued--sheer luck?

This explanation never sat well with me, but the performances of the 2007 Diamondbacks and this year's Angels have ratcheted my skepticism up a notch. Intuitively, it would make sense that both the Angels and last year's Snakes--two teams with below-average offensive production, good pitching, and excellent bullpens--would juice a few extra wins out of their run differentials by being proficient at holding small leads and unlikely to notch blowout wins.

Jaffe points to fairly strong evidence that there is, in fact, a discernable correlation between bullpen strength and D3--that is, the difference between a team's actual record and their third-order Pythagorean projection (which takes into account a more refined version of run differential and opponent strength):

Of the 15 teams above who played after 1953 (the boundary of our sortable stat database), 14 of them had bullpens that finished in the top three in the league in Reliever Expected Wins Added (WXRL), and the trend continues if we round out the list of post-1953 third-order overachievers to an even 20...

He goes on to explain that there is also a correlation--though not as strong--between starting pitching and a high D3. That's not surprising, but I wonder if the correlation would be stronger if a certain percentage of "bad" starts were excluded. As an example, consider this 10-game sample of games for my favorite team, the Faketown Invisibles, in which they were outscored 40-25 but managed to go 8-2:

W, 3-2
W, 2-0
W, 4-3
W, 2-1
L, 2-14
W, 5-4
W, 1-0
W, 2-1
W, 3-2
L, 1-13

You see, the Invisibles' 1 through 4 starters are efficient craftsmen who pitch 7+ quality innings every time they take the mound before handing the game to their one-two bullpen combo of flamethrowing studs. Unfortunately, Faketown's fifth starter is the 42 year-old Jim Bullinger, who last pitched in the big leagues in 1998. Every fifth game, Bully trots out there, does his thing, and after 3 2/3 innings of 8-run ball, he gives way to the Invisibles' longman, Bob Scanlan, who typically gets tagged for a few more runs. By the seventh, the game is more or less an extra BP session for the Cityville Otherdudes.

A reasonable version of this scenario could--I think--skew a team's run differential enough to distort their Pythagorean win-loss quite a bit, especially if they're a light-hitting bunch. Unfortunately, my request to Mr. Jaffe that he run some analysis on the Jim Bullinger Factor has so far gone unfulfilled, so I can't know for sure.

All this leads me to wonder: Is Pythagorean winning percentage a useful tool at all? If nothing else, I'd say the predictive powers of run differential are exaggerated and, at times, abused. Isn't the whole point of a predictive tool to account for lurking variables and adjust for drifts? Obviously, creating a predictive method for wins with excellent correlation to a single counting stat and zero correlation to all others would be virtually impossible.

But the link that Jaffe highlights seems a bit too glaring to have tremendous faith in Pytahogorean winning percentage as a baseline level of performance. Nevertheless, observers who accept the predictive power of crude run differential have branded teams who outperform their Pythagorean as "lucky"--often in weirdly resentful way--when the reality may be that the method sells them short.

The appeal of Pythagorean win-loss, of course, is its simplicity, but there must be ways to improve upon it without undermining that simplicity. Why not narrow the sample of a team's games? Instead of counting their entire run output for the season, chop off the single game run differentials that fall at the margins. Doing so should filter out those meaningless runs scored off AAAA tomato cans late in blowouts. Then again, maybe adjustments like this would only move the error from place to another.

Regardless, I think it's a question worth the scrutiny, given how much stock literate baseball minds put into Pythagorean win-loss marks. Jaffe's article is pretty clear evidence that the method has a hitch, and if that's the case, it should be tweaked, lest we wish to acknowledge that good bullpens make their own luck.

8 comments:

Matt 8:19 PM  

Fuck it, I say we scrap the whole Pythagorean Theorem altogether, although it would make the ACT a whole hell of a lot shorter.

Vinnie 10:32 PM  

You just hate it because you suck at math. I bet you only got, like, a 13 on your ACT math section.

Also, Mr. Jaffe was kind enough to send me this email reply (that I'm going to copy here without his permission), which basically says in very gracious and tactful terms, "That would be a big waste of time":

Thanks for your email, which I thought of today when I was putting together this week's Hit List entry on the Rockies, whom I was chastising over the continued presence of Livan Hernandez in their rotation. Anyway, I haven't had a chance to perform any further investigations into the correlation between D3 and various other metrics, but it's certainly something I intend to follow up in the future.

Nor do I know of anyone who's done what you suggest with regards to the Pythagorean model, which works pretty damn well as it is: correlations around .95 across more than a century of play (2100+ teams) for the Pythagenpat versions of D1, D2 and D3. I'm not saying it's not possible to build a better mousetrap, but the granularity of analyzing over 300,000 scores to try to weed out "outlier games" doesn't seem worth the time to me. What happens if a game is within one very consistent team's outlier but not another, more volatile team's? You may well wind up with more runs mattering on one side of the ledger than another across an entire league/season. I'll leave it to somebody else to try and figure out how many more wins can dance on the head of a pin.

Anyway, thanks for reading and for offering some provocative ideas.

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