Batter's Box Interactive Magazine Batter's Box Interactive Magazine Batter's Box Interactive Magazine
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.
The Year in Review I: Pythagoras Speaks | 17 comments | Create New Account
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dan gordon - Thursday, October 11 2012 @ 10:04 AM EDT (#264438) #
The Orioles beat Pythagoras mainly on the strength of their amazing streak of winning their last 16 extra inning games, finishing the year 16-2 in extras.  If the odds of winning an extra inning game are roughly 50%, the chance of winning 16 of them in a row is roughly 0.00001525, or about 1 in 65,500.  Naturally, they get into an extra inning game yesterday and lose.  They had been 76-0 in games they led after 7 innings this year, another streak that was burned yesterday.  What was the Blue Jays record when leading after 7 this year??
Oceanbound - Thursday, October 11 2012 @ 10:18 AM EDT (#264439) #
What was the Blue Jays record when leading after 7 this year??

Mike Green - Thursday, October 11 2012 @ 10:28 AM EDT (#264440) #
Thanks for this, Magpie.  It would be fun to dig deeper into the success of the A's and Cardinals this year, using the style that Bill James used in the Original Historical Abstract to describe DeWit's transformation of the Reds into the pennant winners of 1961.

Going into the off-season after Pujols left, the Cardinals had an offensive core of Molina, Holliday, Freese, Jay and Craig.  They added Beltran, and that was enough.  It was in the pitching staff that the miracle really took place- with Carpenter out, they were left with Wainwright, Garcia, Westbrook and Lohse.  Not exactly four aces.  They moved Lynn to the rotation (he had spent half a season in the bullpen last year after being a starter in the minors), and he delivered.  There are useful lessons to be found there in utilizing the talents of players like Jay, Craig and Lynn (do all the surprising Cardinals have last names that are also first names?)

As for the A's, there are the stories of the under-appreciated talent and the f'n A trade redux (Reddick), the well-thought out and already analyzed use of platoons, and the success of the young pitchers.  On the latter point, it should be noted that no A's starter threw 200 innings and only two threw 180.  A.J. Griffin did throw 180 innings including his minor league work.  However, the club did throw him right into the rotation. 

In both cases, I am not surprised that the clubs played .500 ball or better, but 90+ wins seems to have been at the top end of what one could have hoped for. 


Chuck - Thursday, October 11 2012 @ 11:14 AM EDT (#264441) #

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 believe James opted for an exponent of 1.83 rather than 2 because it made the model work better, i.e., reduced the mean squared error. Not everyone had a fancy Texas Instruments calculator back in the early 80's, so squaring had to serve as a proxy for the preferred exponent. Yes, I suddenly feel very old.

Mike Green - Thursday, October 11 2012 @ 11:42 AM EDT (#264443) #
1.83? It'll have to be re-named the Jamesian record then.  Which seems appropriate, don't you think?
Chuck - Thursday, October 11 2012 @ 12:39 PM EDT (#264445) #

Going into the off-season after Pujols left, the Cardinals had an offensive core of Molina, Holliday, Freese, Jay and Craig. 

Not only did they lose Pujols (37 HR, 906 OPS), they also ended up effectively losing Berkman (31 HR, 959 OPS) who was healthy enough to only play sparingly. Beltran effectively replaced Berkman, giving up some offense for defense, but proving a wash overall.

Speaking of Beltran, his post-season career: 98 AB, 13 HR, 367/483/816.

Mike Green - Thursday, October 11 2012 @ 01:51 PM EDT (#264447) #
I wondered if Beltran's career performance was in the best in post-season history.  I depends on where you draw the lines, but I was surprised to find out that Babe Ruth actually hit a little better in the post-season than he did in the regular season.  It probably goes Ruth, Beltran and Gehrig so far if you use a 100 PA minimum and give Beltran 2 outs, and allow for the fact that Ruth and Gehrig had the extra PAs.
hypobole - Thursday, October 11 2012 @ 02:13 PM EDT (#264448) #
Magpie, I'm glad you pointed out the O's record from Aug 1 on.
Machado certainly looks like he will be a fixture and with Dylan Bundy possibly breaking camp with the big club, the O's look to be a team to be reckoned with for the next few years at least.

Quite a few of Duquette's moves this year turned to gold. Some of it was assuredly luck , but at least in my estimation, he's a lot better GM than most people give him credit for.
vw_fan17 - Thursday, October 11 2012 @ 03:17 PM EDT (#264449) #
Am I missing something in how you calculate the swing? Roughly half of them make sense, but the other half seems off-by-one.

For example: Baltimore was +4 in 2011, +11 in 2012, yet you have a swing of +8? I would have thought +7? For others, -6 to -1 results in a swing of 5 - as expected. Most of the NL Central seems off, for example..

greenfrog - Thursday, October 11 2012 @ 03:34 PM EDT (#264450) #
A lot of people mocked Duquette's moves early on, but a lot of them have worked out quite nicely. He also managed to stay in contention without trading Machado or Bundy.
Magpie - Thursday, October 11 2012 @ 08:47 PM EDT (#264452) #
Baltimore was +4 in 2011, +11 in 2012, yet you have a swing of +8? I would have thought +7?

Yeah, I forgot to explain that. The W-L numbers generated by the expected winning pct get rounded off. So The 2011 Orioles actually overachieved by 3.55 in 2011, and 11.19 in 2012 - the final Swing was 7.64. I could have avoided this if I'd used integers...
Mike Green - Friday, October 12 2012 @ 11:16 AM EDT (#264467) #
The O's victory in extra innings last night got me thinking about the 1960 Pirates who famously defeated the Yankees in the World Series despite being outscored 55-27.  I checked and the Pirates did outperform Pythagoras during the regular season that year, but by a measly 3 games.  Machado, there a difference...I can't see a difference!
vw_fan17 - Friday, October 12 2012 @ 01:27 PM EDT (#264471) #
Yeah, I forgot to explain that. The W-L numbers generated by the expected winning pct get rounded off. So The 2011 Orioles actually overachieved by 3.55 in 2011, and 11.19 in 2012 - the final Swing was 7.64. I could have avoided this if I'd used integers..

Ok, makes more sense now. Thanks for clarifying!
John Northey - Sunday, October 14 2012 @ 10:31 PM EDT (#264505) #
Just looking at the Jays current 40 man roster....

Pitchers: 24, 6 of whom are listed as 60 day DL but need to be added to roster officially, FA Frasor, Lyon, Villanueva

Catchers: 3

Infielders: 10 inc FA Vizquel, Johnson

Outfielders: 5

DH: 1 (Encarnacion)

Total: 43 players if you include all DL'ed and free agents. Remove FAs and you have 38. None of the 5 are likely to be resigned, maybe Frasor or Lyon but that's it I think.
Richard S.S. - Monday, October 15 2012 @ 04:27 AM EDT (#264506) #

A.A.'s problems have gotten huge.   Now he must put together a top team for Buffalo.   He must now establish real depth in the system, not totally depending on untried prospects.   Anyone who might be removed from the 40-Man also has good value at AAA, so there`s little gain possible.

I don't know who must go on the 40-Man to protect the player from the Rule 5 Draft, but it`s estimated only 1 or 2 need to be protected.  This will become an ongoing problem as the next few years pass and the numbers become 3,4 and 5.

I would like to re-sign Brandon Lyon, even at his price (formerly 2010-2012, 3 Years, $15.0 MM).   I would, however, let everyone else go.   And a decision has to be made about Adam Lind, he occupies a 40-Man spot he might not deserve.

Left Field, 1B or DH, 2B, 2 Bench (Inf.), 3 Starters and 3 Relievers make a possible 11 new people to find homes on the 40-Man.   I expect 3 and 4 people being traded for each new acquisitions.   I`m just waiting for the first penny to drop.

bpoz - Wednesday, October 17 2012 @ 10:17 AM EDT (#264537) #
I will stick with my mid season opinion that if you win 88-92 games you should be in the playoff hunt. This year 92 wins was not enough.

The Jays won 73 games in 2012. I believe that AA said in 2010 that he does not believe teams can/would improve by 10 games or so in a year. Maybe he feels differently now. Injuries?

The 2012 team scored 716 runs. I am hoping that they can improve by 50 runs to 766 without any real improvements in personnel. So that would mean no major performance increases or decreases from anyone, just better health. The team is still young so I am OK staying with JPA, Rasmus, Lawrie & Escobar. EE & Bautista are veterans. DH, LF & 2B are open areas for me that I do not mind being patient with filling. 766 runs is 4.8 per game so that is my hope. So are my expectations realistic?

I know some/many fans/bauxites will be suggesting players that are better. I am all for acquiring better players whomever they are. When they are signed or traded to the Jays or someone else then I may offer an opinion.
bpoz - Wednesday, October 17 2012 @ 10:21 AM EDT (#264538) #
I was curious about player turnover. Would the rate for position players, regulars be 15%-40%. I think the bench & pen would have a higher turnover rate.
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