The Futility Infielder

A Baseball Journal by Jay Jaffe I'm a baseball fan living in New York City. In between long tirades about the New York Yankees and the national pastime in general, I'm a graphic designer.

Wednesday, September 13, 2006


Pythagoras Gets Paid

As I mentioned earlier, this week's Hit List -- the first full one I've done since August 20 -- is up at Baseball Prospectus. For the second week in a row, the Yanks top the list, followed by the Tigers, Mets and surging Twins, who not only look poised to keep the White Sox out of the playoffs but may give the Tigers a run for the AL Central crown.

The Dodgers are running eighth, right between the A's and Angels. I made a bit of a deal last week out of the A's finally passing the Angels after opening up a 7.5 game lead in the standings. But then, as now, the Angels still led in BP's Adjusted Standings, the raw stuff of the Hit List where a team's actual, first-, second- and third-order winning percentages (using various iterations of the Pythagorean formula) are calculated. With that 7.5 game lead back down to 5.5 through Sunday, the Angels climbed back ahead.

Even before last week's list ran, I got an email from a disgruntled A's fan pre-emptively complaining about the rankings. I wrote up a response that while sent as a reply, didn't see the light of day anywhere else. Here it is, with stats through last Tuesday -- a bit outdated, but the point still stands.

• • •

It's always amusing how worked up someone can get when the stats don't conform to their version of reality; last year it was Angels fans cranky about the A's rating higher Hit List ranking and assuming some kind of sabermetric "bias," to the point that I took the time to write a whole article about the Hit List process. This year, the shoe is on the other foot, and at least one A's fan is up in arms. Reader B.O., who has written before to complain about the ranking of the A's before, writes:
I'm going to complain about next week's hit list now because I know I'm going to get all riled up when I see it. How is it possible that the A's have scored 34 more runs than the Angels and are still behind them in 2nd and 3rd order winning percentage (and I therefore assume the hit list)? Have the A's been playing KC all year? How much more difficult could the Angels schedule have been? And shouldn't it even out by the end of the year when they've played all the same opponents? Is it actually taking into account the players on opposing lineups as individuals each day and if so, did all other teams have a rash of DL stints while playing the A's but not Angels?

Assuming you stand by the methodology and rankings, do you really feel confident that the Angels and Rangers have both been better than the A's this year and that their luck is really this horrible? If not, then I would ask what the hit list is really meant to be a measure of.
BJO can hopefully sleep more soundly knowing that the A's have passed the Angels and Rangers on this week's Hit List. But looking into the Adjusted Standings data, it appears that a good portion of that 5.5 game bulge (through Tuesday) is illusory, less the result of adjusting for caliber of competition than a massive gap between the two teams' expected runs allowed and their actual runs allowed:
                      OAK       LAA
Actual RS 640 660
Projected RS (EQR) 641 663
dif -1 -3

Actual RA 595 645
Projected RA (EQRA) 636 612
dif +41 -33
Common underlying reasons for such shortfalls include either luck or differential performance in key situations (whether by starters or bullpen). Sure enough, when we check the two teams' performance in situational hitting against, we see a massive difference in the A's favor (dOPS is the difference between the OPS allowed in a given situation and the team's overall OPS allowed):
Vs. LAA       AVG    OBP    SLG    OPS    dOPS
Overall .257 .319 .410 .729
Runners On .265 .328 .429 .759 +.030
RISP .267 .337 .449 .786 +.057
RISP, 2 Out .235 .328 .372 .700 -.029
Loaded .340 .377 .557 .934 +.205

Overall .266 .334 .413 .757
Runners On .267 .339 .400 .739 -.018
RISP .255 .335 .396 .731 -.026
RISP, 2 Out .243 .335 .361 .694 -.063
Loaded .320 .366 .515 .881 +.134
All in all, it looks like we're talking about a swing of about 75 runs, or 7.5 games in the standings. I'm skipping any park adjustments in this quick and dirty exercise; I think it's safe enough to say that the two teams play in pitcher's parks, and given that we're using OPS, we're hardly dealing with precision anyway. Still, it's apparent that despite an overall performance edge to the Angels, the A's pitchers have fared better in every situational breakdown listed, both in actual terms and relative to the team's overall pitching performance. But just because that's so doesn't mean it would be expected to hold up given larger sample sizes. Yes, the A's have one of the league's best bullpens (2nd in AL in WXRL at 12.9, LAA is no slouch, 4th at 10.3) but reliever performance is notoriously prone to regress over time; what we're measuring is based on individual sample sizes of 50 or 60 innings, which really don't tell us a whole lot that we can take to the bank year after year.

Anyway, unlike the Adjusted Standings, where the Angels still run ahead of the A's based on second- and third-order win percentage, the Hit List does factor in the two teams' actual records, thereby granting some amount of credit for that "lucky" performance and helping the A's inch ahead of the Angels for the first time since July 3. Here's hoping B.O. can finally rest easy.

• • •

A few more points to add to that. First off, I'm frequently asked how the Adjusted Standings and Hit Lists account for the caliber of competition. It comes in via the third-order winning percentage. Specifically, a team's projected runs scored and allowed (Equivalent Runs and Equivalent Runs Allowed) are adjusted up or down based on the composite Equivalent Average of its opponents. In other words, team Y's runs scored are adjusted based on the Equivalent Average Allowed by their opponents, and team Y's runs allowed are adjusted based on the EqA of their opponents.

Second, things don't always even out within a division. Not only do variable interleague and intradivisional schedules factor in (such as teams playing two series at home and one on the road against certain opponents), but there's also the simple fact that, Team Y's pitching doesn't face Team Y's hitting. If you're the Yankee pitchers, backed by the best offense in the league, the rest of the offenses you're facing are more likely to be slightly below average.

Third, neither the Hit List nor the Adjusted Standings account for individual lineups on a given day. I'd love to find a system that does, but for now, we'll have to make do with the kind of general team strength calculations this system offers or look elsewhere for an answer. I'm still pretty confident that run differentials, particularly with adjustment, are vitally important in determining true team strength and predicting future performance.

Anyway, following my response, B.O. emailed me back. First he apologized for his premature griping, then he tried to lay the blame on me for the A's dropping a pair to the Rangers on Monday and Tuesday: "thanks for putting on your curse as things are suddenly not going as well this week." Sheesh. "A little regression to the mean, perhaps?" I suggested, reminding him that "Pythagoras always gets paid." Teams that are eight games above their third-order win projections aren't great bets to stay there.

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