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Once more, it's time - way past time, in fact - to check in with the ancient sage of the desert.

(I forgot to finish this after the end of the season. Best trot it out now, and be done with it.)

First, let us remember why we bother with the old windbag. It's not entirely because I have a massive Excel database and I like to get some use out of it. There are genuinely good reasons to listen to the old fool.

Every year, there are a few teams whose won-loss records simply do not resemble what you would reasonably expect, from the number of runs they actually scored and allowed. And for those teams, what Pythagoras has to say is at least as relevant - if not more so - than the actual won-lost record.

Consider the Snakes. Pythagoras took a dim view of the 2007 Diamondbacks - 90 wins be damned, he said - this isn't a contender. This is really a .500 quality team. Just because in both 2005 and 2007 the D'Backs were able to win way more games than their runs scored and allowed suggested didn't mean they were sure to keep doing it. And in 2008, they didn't get it away with it again.

And so to business. Who were 2008's biggest overachievers? Who were the biggest underachievers? (I imagine you know the answer to that one already.) And how did it happen?

Here are your Pythagorean results for 2008.
          PYTHAGORAS SAYS                  REAL WORLD
G W L PCT RS RA Diff | G W L PCT W change Pct change
BOS 161 96 65 .597 841 691 150 | 161 94 67 .584 -2 -.013
TOR 162 94 68 .578 714 610 104 | 162 86 76 .531 -8 -.047
TB 162 92 70 .571 774 671 103 | 162 97 65 .599 5 .028
NYY 161 87 74 .542 786 723 63 | 161 89 72 .553 2 .011
BAL 161 72 89 .447 782 869 -87 | 161 68 93 .422 -4 -.025

AL Central
MIN 163 90 73 .553 829 745 84 | 163 88 75 .540 -2 -.013
CHI 163 90 73 .553 811 729 82 | 163 89 74 .546 -1 -.007
CLE 162 86 76 .528 805 761 44 | 162 81 81 .500 -5 -.028
DET 162 78 84 .479 821 857 -36 | 162 74 88 .457 -4 -.022
KC 162 71 91 .439 691 781 -90 | 162 75 87 .463 4 .024

AL West
LAA 162 89 73 .546 765 697 68 | 162 100 62 .617 11 .071
TEX 162 75 87 .465 901 967 -66 | 162 79 83 .488 4 .023
OAK 161 75 86 .467 646 690 -44 | 161 75 86 .466 0 -.001
SEA 162 66 96 .406 671 811 -140 | 162 61 101 .377 -5 -.030

NL East
PHI 162 94 68 .580 799 680 119 | 162 92 70 .568 -2 -.012
NYM 162 90 72 .555 799 715 84 | 162 89 73 .549 -1 -.006
FLA 161 81 80 .502 770 767 3 | 161 84 77 .522 3 .020
ATL 162 78 84 .484 753 778 -25 | 162 72 90 .444 -6 -.039
WSN 161 61 100 .376 641 825 -184 | 161 59 102 .366 -2 -.010

NL Central
CHC 161 100 61 .619 855 671 184 | 161 97 64 .602 -3 -.016
MIL 162 88 74 .542 750 689 61 | 162 90 72 .556 2 .013
STL 162 87 75 .536 779 725 54 | 162 86 76 .531 -1 -.005
HOU 161 77 84 .479 712 743 -31 | 161 86 75 .534 9 .055
CIN 162 71 91 .436 704 800 -96 | 162 74 88 .457 3 .020
PIT 162 66 96 .409 735 884 -149 | 162 67 95 .414 1 .005

NL West
LAD 162 87 75 .539 700 648 52 | 162 84 78 .519 -3 -.020
ARI 162 83 79 .510 720 706 14 | 162 82 80 .506 -1 -.004
COL 162 73 89 .452 747 822 -75 | 162 74 88 .457 1 .004
SF 162 67 95 .416 640 759 -119 | 162 72 90 .444 5 .029
SD 162 66 96 .410 637 764 -127 | 162 63 99 .389 -3 -.021
The Overachievers

1. Los Angeles Angels +11

There are essentially two things that skew the Pythagorean record as opposed to the real world record - unusual performance in one-run games and blowouts. (The Diamondbacks have overperformed their Pythagorean expectation in the past because of their hoprrible record in one-sided games.) No team in baseball won more games by a single run than the Angels.

2. Houston Astros +9

The Astros broke even in the close games. Like the Diamondbacks of yore, they had a disturbing tendency to get their brains beaten in. They won four games by six runs, exactly as many as they lost. But when the margins got bigger than that, the Astros were generally on the wrong side of the scoresheet. They won 3 games decided by more than seven runs, and lost 11. They lost by more than ten runs four times. In those 14 games, they were outscored by 79 runs. In their other 148 games, they outscored their opponents by 48 runs, and went 83-65.

3. Tampa Bay Rays +5

The Devil Fishies played .617 ball (29-18) in one-run games, the best winning percentage in the American League. Having spent the best years of my middle age exploring the subject, I can breezily assert that who wins and who loses a one run game is as much a matter of luck as anything else. No reason they can't stay lucky, I suppose. But absolutely no reason to count on it, or expect it.

So count your blessings, you guys. The reckoning approaches, unless you've taken counter-measures. And even then...

The Underachievers

1. Toronto Blue Jays (-8)

Yes, this is most tiresome. But if everybody's winning percentage matched what Pythagaros says it should have been, the Blue Jays would have posted the fourth best record in the major leagues. Read 'em and weep. They still would have finished second in their own division, of course - it's a tough neighbourhood.

Sigh.

2. Atlanta Braves (-6)

There are many things that have no rational explanation, and here we are. A team that plays below its Pythagorean expectation - significantly below, at least five games off - one year is extremely unlikely to do so the next year. It happens from time to time, but when it does you can absolutely depend on it not happening a third year in a row.

And then there are the Atlanta Braves. Two years ago, the 2006 Braves won just 78 games. Pythagoras said they should have won 84, so we won't expect that to happen again. You should expect them to do better in 2007. And indeed they did do better - they won 84 games in 2007. But not only did they do better - they were better. Despite finishing third behind the Phillies and Mets, the Braves had the best run differential in the division in 2007. They probably should have won 89-90 games.

Obviously, it seemed extremely unlikely that the Braves would significantly underperform their Pythagorean expectation three years in a row - mainly because it just doesn't happen - and furthermore they entered 2008 having made a couple of obvious upgrades. They could expect a full season of Mark Teixeira, who had been nothing short of tremendous for them in just one-third of a season in 2007.

It also struck me that the addition of Tom Glavine improved the Braves even more than the move made by their division rivals in New York, who were  replacing the very same Glavine with none other than Johan Santana, improved the Mets.  In New York, Santana was replacing a league average pitcher. In Atlanta Glavine was replacing three bozos who went 6-18 with an ERA over 6.00. It made sense to me, anyway.

It didn't work out too well, did it.

It is said, and wisely, that Young Pitchers Will Break Your Heart. This is well known, but you know what else - so will the old ones. The Braves rotation featured two guys over 40, and while the Red Sox won a World Series in 2007 with two such geezers in their rotation, it may not have been a wise strategy to emulate. Both Smoltz and Glavine went down early. Mike Hampton - yes, Mike Hampton - pitched more innings for Atlanta than either Smoltz or Glavine. The Braves had an amazing run of of poor results in close games - at one point, they were 5-21 in one-run games - the season got away from them, and they traded Teixeira to the other league. And yet again, the Braves performed significantly below what the old sage expected. Which is weird.

3. Seattle Mariners (-5)

In 2007, the Mariners went 88-74 and accordingly went into the winter thinking they had a pretty good team, a genuine contender. They fortified themselves with a couple of Proven Starters - Erik Bedard and Carlos Silva - and readied themselves to challenge the Angels in the AL West. But Pythagoras, in his wisdom, suggested that the Mariners did not understand their own situation. The 2007 Mariners were 14 games over .500 despite allowing more runs than they scored - they were a whole lot more like a 79-83 team. Pythagoras marked them as a team Certain to Fall.

The Mariners fell further and harder than anyone could have reasonably expected, of course. Their off-season acquisitions didn't work out at all. Bedard seems to have alienated pretty well everyone in Seattle, and went down for the season with shoulder problems in early July. Silva demonstrated exactly what happens to a team-dependent pitcher when you put that pitcher in front of a really bad defensive team. In fact, all winter I secretly nursed this wild notion that Carlos Silva - the guy who went 4-15 this past season - could give the 2009 Blue Jays exactly what A.J. Burnett gave them in 2008 - some 200 league average innings. Silva is that dependent on his defense, and Toronto's defense is as good as Seattle's is the other thing. Maybe we could send them Lyle Overbay - a local boy, fills a hole at first base, improves their wretched defense. Am I crazy?

(Horrified Bauxites everywhere shriek with one voice: "Yes! Crazy! You may actually need to be locked up!")

Anyway, the Mariners went from exceeding their Pythaforean expectation by 11 games to falling short by 6 - and that accounts for 17 games of the entire 27 game plummet between 2007 and 2008. They were indeed legitimately worse - but the difference between the two squads is nowhere near as large as the two won-loss figures suggests. Things that plummet to the ground sometimes bounce back into the air.

Unless they lie broken and crumpled on the pavement, of course.

Pythagoras Speaks! | 19 comments | Create New Account
The following comments are owned by whomever posted them. This site is not responsible for what they say.
Excalabur - Thursday, January 01 2009 @ 02:50 PM EST (#195352) #
This hasn't hit the front page yet, but it turned up in my RSS feed, so I'll assume it's live for comments.

The AL East is even stronger than these numbers would suggest: remember that the AL spends a lot of its time beating up on other members of the division, too.

The AL west should be fun to watch next year: the teams are all pretty mediocre, but they're close in talent, leading, one might hope, to a good pennant race. I have a feeling that LAAA doesn't understand pythag, but we shall see---the new regime in Seattle certainly seems to.
greenfrog - Friday, April 03 2009 @ 10:29 PM EDT (#197823) #
Here's an idea for a poll question: where will Travis Snider be hitting in the order on July 1st (home game against the Rays)? 9th? 8th? 5th? 4th?

Somehow I don't see him languishing at the bottom of the order if he continues to come into his own. Especially if the Jays are hurting for offense as they approach midseason.
Mylegacy - Friday, April 03 2009 @ 10:54 PM EDT (#197826) #
Here's why we "underperform." In 2008 we had pitching - BUT - while Boston and NY were slaughtering Seattle we were playing them to 2 - 1 games ... our offense was SO bad we couldn't KILL teh weaklings. This year we kill the bas*ards!
Mick Doherty - Friday, April 03 2009 @ 11:40 PM EDT (#197827) #
I was never any good at math, so I may be way off here, but it seems logical to me that the Pythagrean W-L differential  should equal (in sum) zero, or to pardon 30 tiny rounding errors, maybe +1 or -1. But if I've done my math right, the total performance across the majors was -9. Not only that, but 17 teams underperformed while 11 overperformed or were even.

That just seemed weird to me.

Magpie - Friday, April 03 2009 @ 11:45 PM EDT (#197828) #
but 17 teams underperformed while 11 overperformed or were even.

You can thank the Angels and Astros for that, I would think. Collectively they were 20 games over.

As for the rounding...dunno.  I multiply games played by the Pythag to get the number of wins. It doubtless has many decimal points, which then gets rounded off. Losses are just Games minus wins.
Chuck - Saturday, April 04 2009 @ 05:58 AM EDT (#197835) #
but 17 teams underperformed while 11 overperformed or were even.

Further, in Bill James' refined version of the formula (I don't know which version was used here), he suggests using an exponent of 1.83 rather than 2. Perhaps that would shave off some of the difference.
TamRa - Saturday, April 04 2009 @ 02:36 PM EDT (#197855) #
some of you math wizs explain this to me.

I understand that an exponent of 2 is essentially X times itself.

What is an exponent of 1.83?

The only guess i can come up with is that it's X(X(.83)) (I hope I'm expressing that correctly)...i.e. x times .83 of X

True? If not then what?


Mike Green - Saturday, April 04 2009 @ 02:54 PM EDT (#197858) #
It's easier to understand if you think of it in fractional notation.  X to the power of 3/4 (i.e. .75) is the 4th root of x cubed.  So, X to the power of 1.83 would be the 100th root of X to the 183th power.  Obviously, no one is doing calculations by hand of these things!
Richard S.S. - Saturday, April 04 2009 @ 03:15 PM EDT (#197861) #
Barajas and Barrett make the catching position at least average if not better.  First Base platoon will be better than average.  Aaron Hill will be better than average.  3B: avg. or better.  SS: at least avg.  Left: much better than avg.  Center: avg or better.  Right: avg. or better.  D.H.: at least avg.  Bench; at least avg.  The question is: how many more runs?
TamRa - Saturday, April 04 2009 @ 03:41 PM EDT (#197864) #
It's easier to understand if you think of it in fractional notation.  X to the power of 3/4 (i.e. .75) is the 4th root of x cubed.  So, X to the power of 1.83 would be the 100th root of X to the 183th power.  Obviously, no one is doing calculations by hand of these things!

It's conversations like this that make me realize just how VERY little i know about higher math.

Because I have no f'n clue what you just said!

I think I'll just stick with squaring them and let you guys have the 1.83 stuff.


Mike Green - Saturday, April 04 2009 @ 04:07 PM EDT (#197866) #
I'll try to help WillRain.  Take the simple case.  Say, 16 to the power of .75 (i.e 16 to the power of 3/4).  The 4th root of 16 is 2 (2 to the power of 4 is 16).  Two cubed is 8.  Ergo, 16 to the power of .75 is 8. 
vw_fan17 - Saturday, April 04 2009 @ 10:10 PM EDT (#197873) #
Ok, WillRain.. I just can't help myself and NOT post. Being a former lecturer and all..
Think of it this way:

x ^ 1 = x
x * x  = x ^ 2
x * x * x = x ^ 3

square root of x = x ^ 0.5 = x ^ (1/2)
cube root of x = x ^ 0.333 = x ^ (1/3)
4th root of x = x ^ 0.25 = x ^ (.25)
etc..


x^2 = x * x = x ^ 1 * x ^ 1 = x^(1 + 1)
x/x = x^1 / x^1 = x(1 - 1) = x ^ 0 = 1

So, you can add/subtract exponents.

So, to get x ^ 1.75, you could take: x ^ 2 /  x ^ 0.25 (x squared divided by 4th root of x), etc..

1.83 is actually very close to:
x ^ (1 + 0.5 + 0.333) = x^1*x^0.5*x^0.333 =  x * square root of x * cube root of x

Hope that makes at least a little sense.
TA - Saturday, April 04 2009 @ 11:06 PM EDT (#197874) #
1.83 is actually very close to:
x ^ (1 + 0.5 + 0.333) = x^1*x^0.5*x^0.333 =  x * square root of x * cube root of x

=
You know the season's about to start when...

Seriously, how great is this site? While writing Humanities Phd exams I can flick over here and learn about subtracting exponents and find out New Hamphire's roster.

"I live for this!"




TamRa - Saturday, April 04 2009 @ 11:20 PM EDT (#197876) #
I actually CAN follow that. Thank you.

That said, unless I'm getting paid there is no way in HELL I'd go to that much trouble to distinguish the fine distinction between basic pythag and James' refined version.

:D


robertdudek - Sunday, April 05 2009 @ 04:00 AM EDT (#197884) #
That said, unless I'm getting paid there is no way in HELL I'd go to that much trouble to distinguish the fine distinction between basic pythag and James' refined version.

It's even more complicated than that. The pythagorean exponent is not a constant (such as 1.83 or 2 or whatever). It is actually a function of run environment (this has been shown by numerous empirical results).
robertdudek - Sunday, April 05 2009 @ 04:44 AM EDT (#197885) #
I was never any good at math, so I may be way off here, but it seems logical to me that the Pythagrean W-L differential  should equal (in sum) zero, or to pardon 30 tiny rounding errors, maybe +1 or -1. But if I've done my math right, the total performance across the majors was -9. Not only that, but 17 teams underperformed while 11 overperformed or were even.

That just seemed weird to me.


It is not  just a rounding error. It is a flaw in the basic structure of the formula itself (WPCT=A^x/(A^x+B^x). It has to do with the fact that different teams within a league have different run environments and also have different run differentials (runs scored minus runs allowed). To illustrate:

Imagine a 4 team league, which we will call SYMMETRICAL LEAGUE, where each team's total of runs scored and allowed is 1300...

team A: 700 scored, 600 allowed
team b: 680 scored, 620 allowed
team c: 620 scored, 680 allowed
team d: 600 scored, 700 allowed

All of these teams have a run environment of 1300, and the winning and losing teams are mirror images of each other - the run differentials balance out. You can use any constant for the exponent you wish and the pythag calculations will balance out to precicely .500 (i.e. calculate each team's pythag wpct and average them).

Now lets change the distribution, but keep the total number of runs scored and allowed at 1300:

team A: 750 scored, 550 allowed
team b: 640 scored, 660 allowed
team c: 620 scored, 680 allowed
team d: 590 scored, 710 allowed

This distribution is slightly asymetrical, but causes the sum of the individual pythags to average to .4993 instead of .5. In a 30-team league the difference between .4993 and .5000 WPCT is about -3.25 wins.

Now lets vary the run environment and put an extreme team in here:

team A: 850 scored, 540 allowed
team b: 800 scored, 870 allowed
team c: 520 scored, 550 allowed
team d: 750 scored, 960 allowed

This league features one super team and 3 mediocre to bad teams of varying run environments. The pythag calculations (using exponent 2) work out to an average WPCT per team of .5054. Extended to  30 teams it would be just over 26 wins over .500. Obviously such an extreme distribution is not likely to happen in modern major league baseball - nevertheless, the more asymetrical the league is the greater the calculated pythag winning percentage deviates from .500.


christaylor - Monday, April 06 2009 @ 08:17 PM EDT (#197949) #
... and that explanation is an excellent argument for going to a schedule with 0 inter-league games and a balanced schedule with a square number of teams in each league.
Chuck - Monday, April 06 2009 @ 09:18 PM EDT (#197951) #
... and that explanation is an excellent argument for going to a schedule with 0 inter-league games and a balanced schedule with a square number of teams in each league.

And if major league baseball weren't a commercial enterprise, someone might listen to that argument.
christaylor - Monday, April 06 2009 @ 10:04 PM EDT (#197952) #
Would more teams hurt the economics of baseball? Would getting rid of inter-league significantly hurt baseball's ability to generate revenue? If talent were more evenly distributed in the league be a bad thing?

That's the thing about commerce and economics -- humans create it, t'ain't the weather.
Pythagoras Speaks! | 19 comments | Create New Account
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