The Year in Review I: Pythagoras Speaks
Thursday, October 11 2012 @ 09:30 AM EDT
Contributed by: Magpie
There are certain rituals I conduct once every season is in the books...
And one of them begins with the following explanation.
As everyone knows, the number of games a team wins and loses can generally be predicted by the relationship between the runs they score and give up. Elementary, my dear Watson. We are interested, as always, in the teams that don't match up to their Pythagorean expectation. There are two, and only two, reasons this can happen: a) an unusual level of performance in close games in general, one-run games in particular or b) an unusual record in blowouts. The right combination of unusual performance in both of these areas can produce some very, very strange results indeed.
What makes this especially interesting is that these two explanations say completely different things about the ball club affected. If a team has an exceptionally good or bad record in one-run games, they've just had a run of strange luck, one way or the other. That is all. The results of one-run games really are as random as a roll of the dice. To repeat, for the umpteenth time, my Mantra of the One-Run Game:
In a close game, the impact of random chance is sufficient to overwhelm the impact of overall quality.
You remember that unspeakably awful 2003 Detroit Tigers team, who went 43-119? Those Tigers had a better record in one-run games (19-18) than the 2003 Atlanta Braves, who finished first and won 101 games that year. Bobby Cox's Braves went just 17-25 in one-run games. That sort of thing happens all the time, and represents one of the fundamental truths of the game - that one-run games are one of the mechanisms that enforce the Law of Competitive Balance, dragging everyone towards .500, pulling the bad teams up and dragging the good teams down.
Blowouts, on the other hand, actually tell us something about a team's quality. As a general rule, you just don't lose by six runs because you caught a bad break. Nor do you win by six runs because you got a little bit lucky that day. It takes genuine ability to make a habit of beating the other team senseless.
Something else I like to keep an eye on. Some years back, I introduced a new phrase to the Baseball Lexicon: the Pythagorean Swing. Suppose a team underperformed it's Pythagorean expectation one year by 3 games. Let us then suppose that this very same team then went out and over-performed its Pythagorean expectation the next year by 9 games. That's a 12 game swing to the good, right there without the team doing anything different on the field. I'm glad to have noticed this - it was the strange case of the 2008-2009 Padres that brought it to my attention. Among other things, it explains much of what happened in the NL Central this season. (So in the case of the 2012 Jays, what the final three columns in the table below tell you is that in 2012 the Jays underachieved by 1 game, and that in 2011 they overachieved by 2 games. That's a Swing of 3 games to the bad.)
One final note on The Method. There are a number of ways to calculate a Pythagorean Expectation. All are based on the relationship between Runs Scored and Runs Allowed. Some use the square of those numbers, some methods insert a component (typically 1.8 or 1.83) instead. Strictly speaking, no method is more accurate than the other - all are constructing a fantasy, a projection. As I explained last year, I very much prefer squaring the runs figures rather than using a component. There may be good theoretical reasons for using a component instead - I wouldn't know. I do know that Pythagorean records constructed by squaring the runs scored and allowed figures will much more often match the actual win-loss records of the teams. There won't be nearly as many discrepancies between What Happened and What Could Have Been Expected to Happen.
I conduct this exercise in order to identify the divergences from what is expected. I'd rather not use a formula that multiplies those divergences like rabbits.
Why should we care about this fantasy? And why in particular do I care? My preference is always, always, always strongly in favour of actual counting numbers as opposed to any type of projection whatsoever.
Because what Pythagoras can sometimes provide is a more accurate appraisal of a team's true strength than the W-L figures do, in exactly the same way that ERA can provide a more accurate view of a pitcher's performance than his W-L record. And that's something you want to know as you go forward. One year ago, Pythagoras thought that while Arizona and Milwaukee were
certainly better than the Reds, the three teams were much closer
in quality than their records indicated. But heading into this last season, the Brewers and Diamondbacks were probably feeling pretty good about themselves. The Reds certainly weren't; they had to think they had some work to do.
Anyway, on to the make-believe standings!
PYTHAGORAS SAYS REAL WORLD THE SWING
Year Team Ex W Ex L GBL Exp RS RA W L GBL Pct 2012 2011 Swing
2012 TB 96 66 0 .593 697 577 | 90 72 5 .556 | -6 -1 -5 |
2012 NYY 96 66 0 .592 804 668 | 95 67 0 .586 | -1 -6 5 |
2012 BAL 82 80 14 .505 712 705 | 93 69 2 .574 | 11 4 8 |
2012 TOR 74 88 22 .455 716 784 | 73 89 22 .451 | -1 2 -3 |
2012 BOS 73 89 23 .453 734 806 | 69 93 26 .426 | -4 -5 0 |
2012 CHI 89 73 0 .550 748 676 | 85 77 3 .525 | -4 4 -8 |
2012 DET 87 75 2 .540 726 670 | 88 74 0 .543 | 1 6 -5 |
2012 KC 73 89 16 .451 676 746 | 72 90 16 .444 | -1 -7 5 |
2012 MIN 67 95 22 .415 701 832 | 66 96 22 .407 | -1 3 -4 |
2012 CLE 62 100 27 .384 667 845 | 68 94 20 .420 | 6 5 1 |
2012 OAK 93 69 0 .574 713 614 | 94 68 0 .580 | 1 -3 4 |
2012 TEX 92 70 1 .566 808 707 | 93 69 1 .574 | 1 -4 5 |
2012 LAA 88 74 5 .546 767 699 | 89 73 5 .549 | 1 1 0 |
2012 SEA 77 85 16 .475 619 651 | 75 87 19 .463 | -2 2 -3 |
2012 WSN 98 64 0 .602 731 594 | 98 64 0 .605 | 0 2 -1 |
2012 ATL 93 69 4 .576 700 600 | 94 68 4 .580 | 1 3 -3 |
2012 PHI 81 81 16 .503 684 680 | 81 81 17 .500 | 0 -2 2 |
2012 NYM 74 88 24 .457 650 709 | 74 88 24 .457 | 0 -1 1 |
2012 MIA 67 95 30 .414 609 724 | 69 93 29 .426 | 2 0 2 |
2012 STL 94 68 0 .582 765 648 | 88 74 9 .543 | -6 1 -8 |
2012 CIN 91 71 3 .564 669 588 | 97 65 0 .599 | 6 -4 9 |
2012 MIL 86 76 9 .528 776 733 | 83 79 14 .512 | -3 5 -8 |
2012 PIT 78 84 16 .483 651 674 | 79 83 18 .488 | 1 3 -3 |
2012 CHC 64 98 30 .395 613 759 | 61 101 36 .377 | -3 2 -5 |
2012 HOU 57 105 38 .350 583 794 | 55 107 42 .340 | -2 -5 3 |
2012 SF 89 73 0 .550 718 649 | 94 68 0 .580 | 5 6 -1 |
2012 LAD 86 76 3 .532 637 597 | 86 76 8 .531 | 0 -3 2 |
2012 ARI 86 76 3 .532 734 688 | 81 81 13 .500 | -5 5 -10 |
2012 SD 74 88 15 .457 651 710 | 76 86 18 .469 | 2 -8 10 |
2012 COL 68 94 21 .420 758 890 | 64 98 30 .395 | -4 -4 0 |
As you can see, while the participants in the NL post-season remained the same, it was the will of Pythagoras that a couple of good AL teams stayed home and watched luckier men than they cavort in the post-season. Tough luck, Tampa Bay and Chicago.
The Overachievers
Baltimore - I assume this comes as news to none of you; I assume you are all aware of how it happened. The 2012 Orioles went a remarkable 29-9 (.763) in one-run games. No team since the expansion era begun has had a better winning percentage in one-run games. (While the Big Honking Database allows me to go back to 1871, this off-season I've decided to base all historical comparisons on the half century since the 1961 expansion and the simultaneous adoption of the 162 game schedule!) Only 9 teams since 1961 have had a better positive spread between winning percentage in one-run games (.763) and in the rest of their games (.516) than the 2012 Orioles - and most of those teams were terrible teams that simply had a run of random good luck in close games: the 1974 Padres, the 2003 Tigers, the 2012 Indians. I would caution against the notion that the 2012 Orioles were entirely a fluke. They were indeed extremely fortunate to play .500 ball (13-13) in June, despite being outscored 97-127. But from August 1 through the end of the season, the Orioles went 38-20, and outscored their opponents 276-218. The final record is quite a bit better than you would reasonably expect, but the Orioles have at last become the quality team some among you (hello Mike!) have been expecting to see for a long time now.
Cleveland - Pythagoras often extends his blessing to a crappy, out of contention team. Because anything can happen in a one-run game it's really not uncommon for a lousy team to have a run of good luck in close games. The 2012 Indians played .667 ball (24-12) in one-run games, and .349 ball (44-82) the rest of the time. Only two teams since 1961 have had a bigger improvement in one-run games than this year's Indians: the 2003 Padres, who lost 102 games, but managed to go 31-16 in games decided by one-run; and the 2003 Tigers. This team stinks, and Terry Francona has a lot of work to do.
Cincinnati - The Reds were a better team than they looked in 2011, when they had a losing record; they're not as good as they looked this year, when they had the second best record in the majors. Roughly half of this year's improvement was Pythagoras swinging 9 games in their favour; in 2011, they had underachieved by 3 games. What's interesting about Cincinnati is that they won with exactly the same regularity in all types of games. They played .596 ball (31-21) in one run games, .600 ball (66-44) in the rest of them. They even played .606 ball (20-13) in blowouts. Anyway, it was Cincinnati, not Baltimore, who won more games by a single run than any team in the majors this year. In addition, the Reds did very well in low scoring games. The two teams in the majors with runs scored and allowed figures closest to Cincinnati's were the Dodgers and the Rays. All three teams had very similar records when scoring five runs or more: Cincinnati 58-7, Los Angeles 59-4, Tampa Bay 55-7. But the Reds went 39-58 in games when they scored four runs or less, which is awfully good. The Dodgers went 27-72 when they scored four or less; Tampa Bay (who were not good in close games) went 35-64
San Francisco - At first glance, the story of the 2012 Giants is quite similar to Cincinnati. The Giants record in one run games (30-20) was almost exactly the same as Cincinnati's. Unlike the Reds, the Giants record was noticeably better in those games than it was the rest of the time, when they played .571 ball. Still, both teams came away with 4 ot 5 more wins in the close games than you would expect them to get.
The Underachievers
St. Louis - The 2012 Cardinals were one of the best teams in baseball, a better team than their record suggests, and I think they were probably a better team than the one that finished almost 10 games ahead of them. St. Louis wasn't all that lucky in close games (21-26), and they did make a habit of beating the other guys bloody. I think you have to really respect the 2012 Cardinals. They lost Albert Pujols. They were without Lance Berkman and Chris Carpenter for almost the entire seson. They replaced a legendary Hall of Fame manager with a rookie, who had never managed anywhere before. I'm starting to get pretty tired of them, which is always how I show Respect for the other teams.
Tampa Bay - Maybe Joe Maddon's luck just ran out. As I've said approximately four million times, good teams normally have worse records in close games. Over the last five years, Maddon's Rays had managed to resist that trend fairly successfully. But the dice finally rolled the wrong way on them this year, and it more than made up for some of the good luck they've enjoyed in years past. The Rays were a much better team than the Orioles, but they played 10 more close games than Baltimore and didn't come close to winning as many. Tampa went 21-27 in one-run games, and that's why they're watching the Orioles on TV this October.
Arizona - The 2011 Diamondbacks exceeded their Pythagorean expectation by 5 games almost entirely because they were extremely fortunate in the close games. They played .636 ball (28-16) in one run games, and .559 ball (66-52) the rest of the time. In 2012, their luck in one-run games simply reversed itself. They played .357 ball (15-27) in one-run games, and .550 ball (66-54) the rest of the time. That's how a team went from 94-68 and first place, to 81-81. That's the whole story right there.
And just for fun, I played around with the freshly updated Big Honking Database and I thought I'd share!
Biggest Pythagorean Over-Achievers Since 1961
1. Cincinnati 1981 - This list is based on winning percentage - as some of us can actually remember, 1981 was a strike year. The 1981 Reds scored 464 runs and allowed 440. They should have played .527 ball. Instead they went 66-42 (.611) - that positive spread of .085 is the largest in the last 50 years. Even the 1974 Padres, with their phenomenal run in close games, couldn't raise their overall winning percentage as much. .
2. Arizona 2005
3. NY Mets 1972
4. NY Mets 1984
5. Pittsburgh 1994
6. San Diego 1974
7. NY Yankees 2004
8. Baltimore 1981
9. LA Angels 2008
10. Arizona 2007
You're wondering where the 2012 Orioles are? In the very next spot, 11th place. The Blue Jays have never been noted for exceeding their Pythagorean expectation. In these annual reviews of the subject, I only single out teams who exceeded expectations by at least five wins. Only once in their history have the Blue Jays done that, in Jim Fregosi's second season on the job. In 2000, the Jays went 83-79 despite being outscored by 47 runs.
Biggest Under-Achievers Since 1961
1. NY Mets 1993 - A completely forgotten team, and with good reason. The 1993 Mets scored 672 runs and allowed 744 - very like this year's Kansas City Royals. The Royals 72-90 record is about what one should expect from that kind of performance. The Mets went 59-103.
2. Pittsburgh 1986 - In 1985, the Bucs collapsed completely (57-104). It cost Chuck Tanner his job, and Jim Leyland got his first managing gig. The Pirates were quite a bit better in 1986 (they added Barry Bonds and Bobby Bonilla), but they went a grisly 16-37 in one run games, and finished at 64-98.
3. Baltimore 1967 - They went 21-33 in one-run games, which led to an extremely disappointing result for the defending world champs. When they didn't immediately bounce back to the top of the AL the following year, manager Hank Bauer was fired (with a 43-37 record.) He was replaced by Earl Weaver, which worked out pretty well.
4. Pittsburgh 1984 - They had the best ERA (3.11) in the majors, outscored their opponents by 45 runs... and went 75-87. They were great in blowouts (17-8), not so great in the close ones (20-33.)
5. Baltimore. 1972 - In 1970 and again in 1974, Weaver's Orioles won 40 one-run games. Only two teams since 1961 have won more games by a single run (the 1978 Giants and the Miracle Mets of 1969.) In between, the pendulum snapped back - the 1972 team went 26-32 in one-run games.
6. Cleveland 2006
7. Houston 1975
8. Chicago Cubs 1970
9. Kansas City 1999
10. San Francisco 1972
The Blue Jays, of course, have had some remarkable Pythagorean underachievers in recent years. The 2009 team, who somehow went 75-87 despite outscoring the opponents, sit just outside the Top 20 and the 2005 team, which had a losing record despite outscoring the opposition by 70 runs aren't far behind. But the most painful by far was the 2008 team, which had the second best Pythagorean record (94-68) in the entire American League. But they spun their wheels for half the season, got their manager fired, and ended up winning just 86 games to finish 8 games behind Boston and 11 behind Tampa Bay.
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