It lacked the fanfare of a division-clinching victory, or the exuberance of Francisco Rodrigurez’s record-setting 58th save, but around the time that the Angels popped the champagne corks last week, they surpassed another record. Roughly two weeks since I pointed out their impending date with history, they inched past the 2004 Yankees‘ all-time mark of 12.7 wins above their third-order Pythagenpat projection—that is, their projected won-loss record after adjusting for run elements, park, league, and quality of competition. Since then, they’ve just kept going; through Wednesday, the Halos held a 92-59 record, the best in the major leagues despite their having outscored their opponents by just 63 runs. After adjusting for everything under the sun to get a truer bead on the quality of their offense, the Adjusted Standings show them as 14.2 games above their third-order projection of 77.8-73.2. While it’s possible they could backslide a bit before the season ends, right now they have a solid claim as the most overachieving club of all time.

Here’s the updated all-time top 10:

Rnk Year Team       W-L    Pct    R     RA  AEQR  AEQRA   D3    Won
 1  2008 Angels    92-59  .612   698   635   689   667   14.2   Division + ???
 2  2004 Yankees  101-61  .623   897   808   911   831   12.7   Division
 3  1970 Reds     102-60  .630   775   681   757   676   12.6   Pennant
 4  2007 D'backs   90-72  .556   712   732   708   739   12.2   Division
 5T 1954 Dodgers   92-62  .597   778   740   782   749   12.1
 5T 2005 ChiSox    99-63  .611   741   645   740   684   12.1   World Series
 7  1905 Tigers    79-74  .516   512   604   524   601   11.9
 8T 1924 Dodgers   92-62  .597   717   679   717   684   11.7
 8T 2002 Twins     94-67  .584   768   712   759   741   11.7   Division
10  1954 Indians  111-43  .721   746   504   717   511   11.4   Pennant

To put the Angels’ performance this year into a bit more context, consider that the team with the second-best record in the majors, the Cubs (91-59, half a game behind the Halos), has a raw differential of 184 runs, just shy of three times the Angels’ mark. Meanwhile, the team with the most similar third-order projection to the Angels is the Indians, with a projected record of 78.7-73.3. Despite outscoring opponents by 36 runs, their actual record stands at 75-77 at this writing. This bears repeating: the Angels have a record better than the Cubs, but considering their run differential and strength of schedule, they’re closer to the Indians in terms of quality.

When I covered the Angels and their fellow overachievers in this space a few weeks ago, I promised to follow up with a look at history’s great underachievers. There’s no team chasing the pot of fool’s gold at the other end of the projected record rainbow this year; the most underachieving team is just 7.3 games below their third-order projection, a total that wouldn’t crack the bottom 100. More on the identity of that team in a moment; for now here is the list of historical underachievers:

Rnk Year Team        W-L     Pct    R     RA  AEQR  AEQRA    D3
 1  1993 Mets       59-103  .364   672   744   672   736   -15.1
 2  1935 Braves     38-115  .248   575   852   593   835   -14.6
 3  1986 Pirates    64-98   .395   663   700   666   697   -13.6
 4  1946 A's        49-105  .318   529   680   529   662   -12.8
 5  1905 Browns     54-99   .353   512   608   521   601   -12.7
 6  1937 Reds       56-98   .364   612   706   620   700   -12.4
 7  1939 Browns     43-111  .279   733  1035   752  1003   -12.2
 8  1962 Mets       40-120  .250   617   948   631   924   -12.1
 9  1917 Pirates    51-103  .331   464   595   468   579   -11.9
10T 1984 Pirates    75-87   .463   615   567   612   564   -11.8
10T 1975 Astros     64-97   .398   664   711   668   711   -11.8
12  2001 Rockies    73-89   .451   923   906   910   870   -11.5
13  1993 Padres     61-101  .377   679   772   681   764   -11.4
14T 1961 Phillies   47-107  .305   584   796   599   782   -11.1
14T 1924 Cardinals  65-89   .422   740   750   745   752   -11.1
16T 1967 Orioles    76-85   .472   654   592   657   602   -11.0
16T 1907 Reds       66-87   .431   526   519   527   522   -11.0
18  1936 Phillies   54-100  .351   726   874   739   869   -10.9
19  2006 Indians    78-84   .481   870   782   882   800   -10.7
20T 1912 Dodgers    58-95   .379   651   744   665   742   -10.4
20T 1952 Tigers     50-104  .325   557   738   563   716   -10.4

Topping this ignominious list is the 1993 Mets, a team best remembered for Bobby Bonilla‘s infamous threat to New York Daily News writer Bob Klapisch: "I’ll show you the Bronx!" Klapisch had just co-authored a book about the 1992 Mets—a team that finished 72-90 despite having the majors’ top payroll—called The Worst Team Money Could Buy, but the irony is that their successors were so much worse. The 1993 Mets were a 74-win team that somehow found a way to lose an extra 15 games, thus claiming primacy not only on this list, but also setting a record for marginal payroll dollars per marginal win according to a lengthy study by the late, great Doug Pappas. At $3.394 million per marginal win, a record that stood until the 1996 Tigers came along, they richly deserved their sobriquet.

The rest of the list tilts towards very bad teams from the pre-expansion era, when there was less competitive balance than today, and at any given time a few teams were simply filling out the schedule and waiting for the next chump to come along and take the franchise off their hands. A pair of baseball’s homeliest teams, the 1935 Braves and 1939 Browns—both weaker siblings in two-team towns—aptly represent this era as already-awful teams made all the worse with a little extra bad luck and/or bad timing. Those Braves, who featured Babe Ruth‘s swan song, still own the lowest winning percentage in National League history since 1901 thanks in part to an eye-popping (or maybe eye-gouging) 7-31 record in one-run games. As for the team with the lowest winning percentage in AL history, the 1916 Philadelphia A’s (.235 on a 36-117 record), they tie for 35th on the third-order underachievement list at -9.4 wins, short of an invitation to this pitiful party.

Representing expansion-era baseball is the team that broke the 1935 Braves’ record for losses in a single season, the 1962 Mets. They may have caused Casey Stengel a few less headaches if they’d played up to their potential, but would they be remembered as fondly? One wonders how much of that 12.1-game shortfall could be accounted for solely by Marvelous Marv Throneberry’s baserunning.

Possibly the best team on the list is the 1967 Orioles. They were the defending World Champions at the time, and they not only outscored their opponents by a handy 62-run margin, they had the league’s second-best offense according to EqA, and the second-best bullpen according to WXRL; their third-order projection called for 87 wins. Yet they had a mediocre rotation relative to the rest of the league, and were an anemic 33-55 in games decided by one or two runs, with a differential distorted by the fact that they went 18-8 in games decided by six or more runs. They wound up on the outside looking in when it came to the pennant race, finishing in sixth place, excluded from the thrilling four-team race won by the "Impossible Dream" Red Sox (a race chronicled by yours truly in It Ain’t Over ‘Til It’s Over, now available in paperback).

The most recent team on this list, and the one that might give the ’67 O’s a run for their money, is the 2006 Indians. That season followed the year they missed the playoffs despite 93 wins, the American League’s best run differential, and the top spot on the year-ending Hit List; the ’06 Indians bellyflopped their way to a 78-84 record despite outscoring opponents by 88 runs. They had losing records in one-, two-, three- and four-run games for a combined 45-64 record in such close affairs, and a 33-20 record in games decided by five or more runs, including 13-3 in games decided by nine or more runs. Their offense was second in the majors to the Yankees in EqA, their rotation was among the best in the league, but their bullpen was about as useful as a free bucket of pus. As I noted in the prequel to this piece, bullpen quality has much to do with third-order over- or underachievement.

As for this year, the "honor" of being the most underachieving team actually belongs to the Red Sox, who through Wednesday are 7.3 games shy of their third-order projected record of 96.3-55.7. Prior to this year, only four teams had ever finished a full season at least four games below their projection and still made the postseason:

Rnk Year  Team      W-L    Pct    R     RA  AEQR  AEQRA    D3   Won
 1  1997  Astros   84-78  .519   777   660   768   664   -7.9   Division
 2  2007  Red Sox  96-66  .593   867   657   906   677   -7.1   World Series
 3  1974  A's      90-72  .556   689   551   680   555   -5.4   World Series
 4  1948  Indians  97-58  .626   840   568   818   582   -4.7   World Series

Historically speaking, that’s a surprising finding, particularly given the number of teams in pre-divisional play who ran away from the pack and made the pennant races an afterthought. Intuitively, one would think that a little third-order slack might not matter much, given a large enough margin over other teams, but it’s apparent that falling shy of one’s third-order projection by more than four games and still making the postseason is a very rare thing.

Three of those four teams became World Champions despite those their shortfalls, including last year’s Red Sox, but while that’s a comforting precedent for Sox fans to look to, there are a couple of big differences between the two Boston squads. Last year’s Red Sox had the league’s second-best rotation, the top bullpen, the third-best offense, and the majors’ best park-adjusted defense. Relative to the league, this year’s bunch is more or less equivalent in terms of the rotation, the offense (though they no longer have Manny Ramirez or a fully healthy David Ortiz in the middle of it) and the defense, but their bullpen is just ninth in WXRL. Consider the principals of these two units (all stats for relief appearances only, ranked among AL pitchers):

Rank  2007                 IP     WXRL   LEV    FRA
  3   Jonathan Papelbon   58.1   5.143   1.62   1.59
  6   Hideki Okajima      69.0   4.429   1.33   2.14
 33   Manny Delcarmen     44.0   1.652   0.99   2.30
 35   Mike Timlin         55.1   1.572   0.79   3.54
 62   Javier Lopez        40.2   0.497   0.87   4.26
 68   Kyle Snyder         54.1   0.392   0.66   4.61
  1   Total              447.0  13.850   0.99   4.13

Rank  2008                 IP     WXRL   LEV    FRA
 17   Jonathan Papelbon   64.0   2.656   1.52   2.82
 28   Javier Lopez        57.1   1.644   1.02   3.08
 46   Justin Masterson    28.0   0.967   0.94   2.28
 47   Hideki Okajima      57.1   0.945   1.53   4.24
 51   Manny Delcarmen     69.2   0.871   1.07   3.73
103   David Aardsma       45.1   0.148   0.68   4.91
317   Mike Timlin         45.1  -1.045   0.82   6.77
  9   Total              444.1   5.834   1.05   4.32

With the exception of Lopez, none of the principal Sox relievers has had a better season in 2008 than in 2007. Neither Papelbon nor Okajima has been as dominant as last year. Delcarmen’s tidy work in late 2007 is more or less equaled by Masterson’s work late this year, but in the past two months, Delcarmen himself has pitched his way to lower-leverage duty. Aardsma has been a less than useful addition, while Timlin has fallen and he can’t get up.

With the dawn of the postseason on the horizon, it remains to be seen whether the Red Sox and Angels can overcome the various flaws which their projected records highlight. For all of the caveats at both ends of the third-order spectrum, it’s worth noting that the two teams hold the top spots in the Secret Sauce rankings, which in the category of relief pitching consider only the work of the team’s closer. What may be even more intriguing—particularly given a peek at the fine print of this morning’s Postseason Odds Report—is the likelihood of the two teams squaring off in the first round, two teams currently separated by three games in their actual records, but a whopping 18.5 in terms of their third-order marks. What a fascinating Pythagorean petri dish experiment that might create.

Thank you for reading

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The under performing teams won 37.02% of their games. The over performing teams won 60.44% of their games. So far so good.

The under performing teams \"should\" have won 44.62% of their games. The over performing teams \"should\" have won 52.66% of their games. Um, anyone else see a problem with this?

There is no reason for their to be covariance between being \"lucky\" and being good. A team that \"should\" go 162-0 cannot get lucky and a team that should go 0-162 cannot get unlucky. I am not sure if the effect in baseball is large enough to matter so I would think that the 20 luckiest and 20 unluckiest teams each \"should\" have won 50% of their games. Maybe the luckiest teams should have won 49.9% of their games and the unluckiest \"should\" have won 50.1% of their games due to the amount of opportunity for luck.

The covariance suggests that the win 3 rate in not quite what it is cracked up to be. I can think of a variety of reasons why this might be the case but I simply don\'t have the data to test these theories.
In a chat a looong time ago, I suggested improving these pythag-win-prediction-type-stats by capping the winning/losing margin of a game at a certain number (say 7), thus minimizing the outsized importance of blowouts (really, what\'s the difference losing 16-1 or 12-1, also choice of mop-up pitcher, etc.).

I was told that someone at BP (forgive my lack of memory) said tat they had run the numbers with this adjustment and it did not affect the results. I wonder if any BPer can confirm this?
Dunno who that was, ScottyB. But here\'s the thing: the Pythagorean model even in its simplest form (exponent of 2, rather than 1.83 or a Pythagenpat-produced exponent based on scoring levels) produces correlations of .95 across more than a century of play (2166 teams since 1901). I\'m not saying it\'s not possible to build a better mousetrap, but the granularity of analyzing over 330,000 scores to try to find some sweet spot where the correlation is pushed up to .96 or .97 or something doesn\'t seem worth the time. To me, the beauty of the tool is in its simplicity -- take any team, its runs scored and allowed, adjusted or not, and you can estimate its quality -- and if you compromise that, you lose something.

untracked, you lost me at the part where you were trying to generalize based on 41 of the most extreme outliers out of a sample of 2166 teams.
Hi Jay- Thanks. Certainly a method with r=.95 needs little tinkering.
Hey Jay, that\'s the data I was offered. I suppose I could add the data for this season but unless I am mistaken, I cannot examine the win3 rates back to 1901. Am I incorrect?

In the modern era teams play unbalanced schedules. A team in a strong division would have a bias towards being \"unlucky.\" Similarly, a team in a weak division (or league) would have a bias towards being \"lucky.\" It appears that every team in the AL East is stronger than their record indicates (although in the case of Tampa Bay the difference is less than a game), whereas the NL as a whole is some 14 games worse than its collective record would indicate. I knew the NL was bad, but I didn\'t know it was that bad.

And yeah, 41 teams is a small data set (and in this case, 31 is even smaller), by over the course of around 3100 games the 21 \"unluckiest\" teams managed to only deserve a little under 45% of their wins. If being bad and being lucky are completely uncorrelated than this simply should not happen. The standard deviation over 3100 games is 28 or so, so to be under 1400 wins... well, we\'re looking at around 6 standard deviations. Perhaps a small sample size, but a pretty large effect. Being exceedingly unlucky is clearly correlated with being bad, and I\'m trying to figure out why that is so.
I\'ve been clamoring to get such data as the historical adjusted standings available online for ages, and I will renew my call to see if I can make that so.

You\'ll notice that I\'ve tried to minimize the use of the word \"luck\" in discussing the phenomena of over- and under-performance. While I don\'t doubt such luck - from the random bounces of the ball to the irregular distributions of scoring - plays a part in those discrepancies, I believe it\'s clearly a mistake to attribute all of those disparities to luck.
The covariance shows that good teams are likelier to outperform their Pyth than bad ones. Which would mean that part of Pyth differential is real and not random.

In fact, the correlation of Pyth differential to the previous year\'s differential has been statistically significant since 1959 (r = .06, p = .04). The historical timing of this effect is consistent with the thought that closer or bullpen quality affects Pyth differential in a real way, and this is confirmed by the data: if you exclude the worst underperformers (who could be expected to change their closer), the correlation strengthens, and the teams in the excluded group that did in fact change their closer did significantly better the next year than those who didn\'t. (Sorry I don\'t have the specific numbers on the last two assertions; they\'re buried in an Excel file from last December with 52 worksheets.)

The fascinating thing is that there was a marked *inverse* correlation from 1997-2002 that seems very unlikely to be random. (Without those six years, the correlation is much stronger, and in the last five years it\'s been r = .14, p = .08.) The reason I haven\'t published this stuff is that I\'ve been wanting to figure that anomaly out. But the notion that all Pyth differential is \"luck\" is clearly wrong.

Thank you for posting this. If the rise of the modern bullpen has led good teams to consistently outperform their pythags then quite simply the math has changed. Teams weren\'t nuts when they built their teams for the postseason by surviving 7 innings with the lead and then turning the game over to a pair of relief aces.

As a Mets fan I weep for their postseason chances.

Excellent stuff, Eric, thanks for sharing your findings.
And re the Secret Sauce, a huge part of the Sox underachievement comes from a change in Papelbon\'s luck, which is reflected in the huge drop in WXRL and big drop in FRA, while his component RA has only gone from 2.20 to 2.46. It would be interesting to rejigger the Secret Sauce with a component RA substituted for WXRL, which can contain a significant component of \"clutchiness\" which is probably not predictive.