As you might remember, we recently pored over a Data Table that used Bill James' Pythagorean Method to determine the Expected Win-Loss record of every major league team.

I regarded the results as very good news for the 2006 Blue Jays. If the Jays score 775 runs and allow 705 next year, they're much more likely to go 89-73 than to put up another 80-82 record. I may not have been Named for Hank, but I know when the glass is half-full.

Ah, if only things were so simple!

As we are all very much aware of by now, the Blue Jays were an 80-82 team in 2005 - a losing record despite scoring 70 runs more than they allowed. However, these aberrations tend not to persist from year to year.

It turns out, in fact, that the Jays under-performance - 9 wins fewer than expected - was on a semi-historic scale. In the last 10 seasons, only one AL team was that far below the expectation created by their runs scored and allowed. That would be the never-to-be-forgotten 1999 Kansas City Royals. The Royals improved by 13 games the following season, without any significant change in their runs scored and allowed. It was a blip. It was just One of Those Things.

R Billie, however, worried that the glass might be half-empty:

Looking at raw runs scored and allowed for the Jays is deceptive because a great deal of the games they played featured them scoring very few runs. They were shutout the most often in the league I believe. Their Pythagorean results are propped up by a number of blowout wins...

If this is in fact true... well, the glass is still half full! Because beating the other guys senseless is a characteristic of good teams. And losing lots of close, low-scoring games is a characteristic of unlucky teams.

There are two empirical realities in play here: the Jays win-loss record on the one hand, and the number of runs they scored and allowed on the other. These two realities normally have a close and logical relationship. In the case of the 2005 Blue Jays, they don't.

Essentially, I am suggesting that it's the W-L record that is deceiving; that it's been thrown out of kilter by Toronto's ghastly (16-31) record in games decided by a single run.

R Billie, if I understand him correctly, is suggesting that the runs scored and allowed is misleading, that the team padded their run differential in a handful of lopsided games.

There is indeed something very odd about the Toronto offense, although I couldn't say if R Billie's specific observation is sufficient to account for it.

Last week, in Toronto Versus The AL East: Some Statistics, Lucas pointed out that:

For whatever reason, the Jays managed to score more runs than their peripherals would predict.

He noted that one obvious reason was the relatively high number of home runs the Blue Jays hit with people on base (better than half) as opposed to the rest of the AL. This accounts for 15-20 extra runs. Toronto hit 72 of their 134 homers with runners on base, and a normal figure would have been 58 of 134.

So there really are two mysteries at work. Just how did the Blue Jays manage to score 775 runs, anyway? The Runs Created formula, which I still persist in using, suggests that they should have scored about 715 runs.

The other mystery remains - given that they actually did score 775 runs, how did they only win 80 games?

What all this suggests is that the Toronto offense was incredibly efficient at creating runs, over and above what their offensive components suggest; yet incredibly inefficient at arranging runs into groups conducive to actually winning ball games.

So who the hell knows? I doubt that we can actually settle anything, but hey! We got lots of time until Opening Day, right?

By the way, I think R Billie's argument may be a very good fit for the 2005 Oakland A's. Oakland under-performed their Pythagorean expectation by six games; they won five games by margins of greater than 10 runs; and unlike Toronto, Oakland had a normal record in one-run games. In the case of the A's, it makes a certain amount of sense to regard those five blowouts as seriously skewing their expected W-L record.

Of course, Oakland exceeded their expected Runs Scored total by an even greater amount than the Blue Jays did...

Well, let's have some Data Tables! Maybe we'll learn something interesting. One of the things I think worth examining is W-L record by runs scored and runs allowed - i.e., when the Jays scored four runs, how did they do. And we'll also have a look at margin of victory - W-L record in games decided by one run, two runs, fifteen runs.

A tip of the cap to Bauxite John Northey, who posted some of this same information in another thread, but I want to provide a little more detail.

I also want to compare the Jays to some other AL teams. Not all of them, or we'll end up being drowned by the numbers. (Like we won't be anyway. If you do want to see this information for every ML team, it's all available on this page over at Baseball Prospectus.

But, to keep things manageable, along with the Blue Jays, we'll run the numbers for Oakland, Chicago, the Angels, the Yankees, and the Red Sox.

Why these teams? Because Oakland looks similar to Toronto at first glance: they won fewer games than their Pythagorean numbers suggest; like Toronto, they scored fewer runs than their offensive numbers say they should have done.

The Angels are the only AL team that exactly matches their Pythagorean projection, and no AL team allowed fewer runs (tied with Cleveland).

The White Sox are in because they over-performed their Pythagorean expectation more than any other AL team, and they give us another pitching and defense team.

Representing the offensive powerhouses will be a pair of AL East divisional rivals. No AL team scored more runs than the Red Sox, so we include them, along with the Yankees, who give us another high-scoring team to look at. Here also are a couple of teams who did markedly better than Pythagoras leads us to expect...

So this gives us the four post-season teams, plus GM Ricciardi's past and present employers. I didn't plan it that way, it's just a happy coincidence.

What are we looking for? I don't know - how about anything that looks strange?

Here are the W-L record of these six teams when they scored x number of runs:

        WhiteSox     Angels	    Yankees	       RedSox	        A's	    Blue Jays		
Runs  W   L   Pct    W   L   Pct     W   L    Pct    W   L   Pct    W   L   Pct    W   L   Pct
 0    0   7   .000   0   6  .000     0   2   .000    0   5  .000    0  12  .000    0  14  .000
 1    3  10   .231   1  14  .067     3  16   .158    1   8  .111    1  15  .063    1   6  .143
 2   12  17   .414   8  10  .444     3   9   .250    2   9  .182    5  18  .217    5  18  .217
 3    7   4   .636  13  14  .481     3  16   .158    6  14  .300    5  11  .313    5  13  .278
 4   15   6   .714  10  11  .476    10   9   .526    7  13  .350    8   8  .500   11  10  .524
 5   20   8   .714  16   5  .762    14   7   .667   12   6  .667   17   4  .810    6  11  .353
 6   14   6   .700   9   3  .750    15   5   .750   17   7  .708   15   4  .789   13   3  .813
 7    7   2   .778  15   2  .882    10   1   .909   15   2  .882    5   1  .833   13   3  .813
 8    8   2   .800   5   1  .833    12   1   .923    9   3  .750    8   1  .889    7   2  .778
 9    5   1   .833   7   1  .875     7   1   .875    7   0 1.000    6   0 1.000    8   0 1.000
10    2   0  1.000   4   0 1.000     2   0  1.000    7   0 1.000    5   0 1.000    3   2  .600
11+   6   0  1.000   7   0 1.000    16   0  1.000   12   0 1.000   13   0 1.000    8   0 1.000											
     99  63   .611  95  67  .586    95  67   .586   95  67  .586   88  74  .543   80  82  .494

There are some things you can count on. Nobody wins when they score 0 runs. Nobody loses when they score 11 runs.

With two exceptions, these teams start winning more often than they lose once they get four runs on the board. One of the exceptions is entirely predictable. The Boston Red Sox have the worst pitching in the bunch. You would therefore expect that they would have to score more runs in order to win. But the Angels? The Angels gave up 163 fewer runs than the Red Sox - how does that happen?

The Angels had the fifth best offense in this group - they were a little below the league average, but better than the White Sox. They should have won more often than they lost once they scored four runs, and while they didn't, they were close. However, they should not have won as many games as they did when they scored just two or three runs, even given their excellent pitching and defense. And the White Sox - they're in another galaxy - Chicago had a winning record when they scored only three runs, and an excellent record when they scored two runs. How did they do it?

They did it with even better pitching than normal. Their pitchers, who were the best in the league anyway, stepped it up when they didn't have a lot to work with. Here's how many runs these teams were giving up in these groups of games:

Runs	Chi	LAA	NYY	Bos	Oak	Tor
						
0	4.00	3.00	7.00	5.00	4.00	3.71
1	4.15	3.73	5.42	5.33	3.44	3.86
2	3.34	2.89	5.67	6.27	4.17	4.13
3	2.64	3.52	5.32	4.65	3.94	4.11
4	4.00	4.62	4.68	5.50	4.38	4.05
5	4.18	4.05	4.00	4.00	3.76	5.47
6	4.45	4.00	3.80	5.54	4.37	4.06
7	4.44	4.82	3.73	4.41	6.33	4.75
8	3.70	5.83	5.23	4.92	4.44	3.56
9	4.17	4.13	5.75	4.14	5.00	4.88
10	7.50	4.25	3.00	5.00	3.40	6.00
11+	5.00	3.57	5.81	4.75	3.00	4.63

	3.98	3.97	4.87	4.97	4.06	4.35

There's a very clear division here - when the offense wasn't getting much done, the pitchers for all four of the teams that actually had quality pitching stepped up and tried to meet the challenge. But the especially outstanding performances were those turned in by the White Sox and Angels pitchers when given just two or three runs to work with. It helped them do not just better than an average AL team - it helped them do better than you could reasonably expect even given their own quality staffs.

At the other extreme, the Boston and New York pitching essentially just gave up the ghost - if the other guys were shutting down the bats, the Yankee and Red Sox pitchers seem to have been gripped by Despair. The teams were able to win 95 games by putting their pitchers in that position as little as possible.

There is one huge blip in these numbers, an utter anomaly.

Logically, one would expect that as a team scores more runs, their chances of winning increases. For the most part, this is exactly what we see. With one glaring exception, the winning percentages increase for each team as the runs scored increase. (There are minor variations, of course, like the Yankees being 3-16 when they score one, and 3-9 when they score two, but I'm not concerned about that.)

That exception involves your Toronto Blue Jays. What the hell happened when they scored five runs? They went a very respectable 11-10 when they scored four runs - how do they go 6-11 when they score five?

Well, as you can see from the next table, their pitching inexplicably failed, allowing 5.47 runs in those 17 games.

It wasn't the starters, by the way - Toronto starters were 6-5, 3.67 in those 17 starts. The bullpen, however, had three blown saves (two by Speier, one by Batista) and took six losses. For the most part, I think this is largely a coincidence - I don't think the Toronto bullpen was a problem in 2005.

Of more relevance is the fact that when Toronto scored five runs, they lost 6 games by a single run without winning any.

OK, on to Runs Allowed:

      WhiteSox     Angels       Yankees      RedSox       A's        BlueJays  
RA   W  L   Pct   W  L   Pct   W  L   Pct   W  L   Pct    W  L   Pct    W  L   Pct
 0  10  0 1.000  11  0 1.000  14  0 1.000   8  0 1.000   12  0 1.000    8  0 1.000
 1  25  1  .962  27  2  .931   8  0 1.000  15  1  .938   14  2  .875   15  3  .833
 2  17  3  .850  13  7  .650  13  5  .722  16  1  .941   19  8  .704   20  1  .952
 3  18  6  .750  13  8  .619  21  2  .913  18  3  .857   14 10  .583   13 11  .542
 4  15 10  .600  10  9  .526  18  4  .818  11  8  .579   14 11  .560    8 11  .421
 5   7  5  .583   7  7  .500   6 10  .375  12  6  .667    5 10  .333    9 18  .333
 6   4  9  .308  11 10  .524   4 10  .286   5  9  .357    4 13  .235    4 13  .235
 7   1 10  .091   1  8  .111   3 11  .214   4 12  .250    3  7  .300    1  8  .111
 8   2  5  .286   2  7  .222   3 10  .231   3  9  .250    2  1  .667    0  2  .000
 9   0  7  .000   0  1  .000   2  4  .333   3  6  .333    0  4  .000    1  6  .143
10   0  5  .000   0  4  .000   2  4  .333   0  0  .000    1  3  .250    1  2  .333
11   0  1  .000   0  0  .000   1  2  .333   0  1  .000    0  1  .000    0  2  .000
12   0  1  .000   0  4  .000   0  5  .000   0 11  .000    0  4  .000    0  5  .000
                  
   99  63  .611  95 67  .586  95 67  .586  95 67  .586   88  74  .543  80 82  .494

There are a few little items in here that strike me as interesting. The Red Sox had the highest scoring team in the league. This doesn't seemed to have helped them particularly in the high-scoring games - Boston's pitchers allowed 10 runs or more a dozen times, and they Red Sox lost all 12 games. (The Yankees actually won 3 games despite this kind of pitching.) What Boston's offense achieved instead was to make the team almost unbeatable when they got good pitching. They were 49-5 when allowing 1,2, or 3 runs. That's pretty impressive.

If you look at the chart below this one, you can see how this happened. The Red Sox offense stepped it up when the pitchers were on their game. This may seem like a waste of resources, offensive overkill - but perhaps it was more efficient, after all. There are many more games when your pitchers allow 3 runs or fewer than 10 runs or more - even if you are the 2005 Red Sox.

The White Sox and Angels both won significantly more games than Boston when their pitchers came up with this quality of performance - however, the White Sox and Angels got many, many more such performances from their pitching staff. (The White Sox were 60-10, the Angels were 53-17.)

Here, by the way, is what the offenses were doing at the same time:

RA	Chi	LAA	 NYY	Bos	Oak	Tor
0	4.40	4.55	 4.57	6.13	6.42	6.25
1	3.73	4.52	 5.13	6.38	5.44	3.72
2	4.75	3.45	 4.44	6.12	4.22	5.90
3	4.29	4.29	 6.74	5.48	4.63	4.04
4	4.32	5.05	 6.41	4.89	4.64	4.16
5	5.33	5.21	 4.38	6.33	4.73	4.52
6	5.38	5.33	 5.21	5.36	3.59	5.00
7	4.36	5.44	 4.64	5.19	4.80	3.22
8	5.71	5.56	 6.15	5.33	6.00	4.50
9	5.29	3.00	 6.50	5.33	4.25	6.14
10	5.20	4.00	 5.00		6.50	8.67
11	5.00		10.67	8.00	2.00	6.00
12	4.00	5.50	 3.20	5.00	6.00	6.40

        4.57	4.70	 5.47	5.62	4.77	4.78

The Yankees are the other offensive powerhouse in this group, and the offense allowed them to pick up a few wins despite allowing a ridiculous number of runs. The Yankees won five games despite allowing 9 or more runs - the Angels and White Sox didn't win any.

The Angels and White Sox won with their pitching, and one of the ways they did that was the sheer quantity of outstanding pitching performances. The Angels had 40 games - almost one in four - when they gave up one run or none, and the White Sox had 36. It is very hard to lose when you get this kind of pitching - the Angels were 38-2, the White Sox were 36-1. This does kind of give you a jump start on the way to winning 90 plus games.

The White Sox offense was able to pick up the pace a little bit when the pitching struggled - the ChiSox and Boston are the only teams in this bunch who won more often than they lost when the pitchers allowed 5 runs. You expect the Boston offense to bail out the arms, but it wasn't really a characteristic of the 2005 White Sox.

Outslugging the opposition wasn't typical of the 2005 Angels, either - but they were the only team in this group to win more often than they lost when allowing six runs. This is surely just one of those weird and random flukes. That you might share my belief that this was a fluke - in those 21 games, the Angels scored 112 runs and gave up 126.

The most striking fact about the Oakland numbers is how often they lost despite exceptional pitching. They were just 33-10 when allowing 1 or 2 runs, 47-20 when allowing 1,2, or 3 - by far the least impressive performance in this group of teams. And we know that Oakland's offense scored almost the same number of runs as Toronto's, which makes them marginally better than league average. It doesn't look like they hit particularly badly in the low-scoring games - they are a little below their overall average, but it's not like they're way below. I know Oakland fans at Athletics Nation were saying the that the team's offense stunk for the first month and a half, and stunk again for the last month of the season - but for a long and glorious stretch in mid-season their hitters were humming away on many cylinders. Put it all together and they look like an average offensive team, when they were actually either quite good or quite bad. Maybe this would explain it...

Despite losing three 1-0 games (poor Josh Towers lost twice), the Blue Jays did just fine when the pitching was very, very good (43-4 allowing two runs or less). The blot on the copybook comes in your basic well-pitched game, when they gave up 3 or 4 runs. The Jays actually lost more often than they won (21-22), and as you can see, one of the problems was that the hitters chose those games to take a little break.

Finally, here is how each of these teams look in games decided by different margins of victory:

	 White Sox       Angels	      Yankees       Red Sox      A's           Blue Jays		
Margin	 W  L   Pct    W  L   Pct    W  L   Pct    W  L   Pct    W  L   Pct    W  L  Pct
1	35 19  .648   33 26  .559   27 16  .628   27 15  .643   26 24  .520   16 31  .340
2	26 15  .634   17 11  .607   10 11  .476   10 12  .455    9 13  .409   13 13  .500
3	 9  6  .600   11 14  .440   14 11  .560   20 10  .667   14 11  .560   16 16  .500
4        8  7  .533    8  5  .615   15  9  .625   10  8  .556   10  7  .588   10  8  .556
5        4  6  .400   10  2  .833    9  4  .692    7  4  .636   10  6  .625   10  4  .714
6	 7  4  .636    5  2  .714    2  2  .500    2  3  .400    2  4  .333    2  2  .500
7	 2  3  .400    3  1  .750    6  7  .462    7  9  .438    4  3  .571    5  4  .556
8	 5  2  .714    1  4  .200    2  3  .400    6  2  .750    1  3  .250    3  2  .600
9	 1  1  .500    3  1  .750    7  1  .875    1  2  .333    7  3  .700    3  1  .750
10	 2  0 1.000    4  1  .800    3  3  .500    5  2  .714    5  0 1.000    2  1  .667
				
TOTAL	99 63  .611   95 67  .586   95 67  .586   95 67  .586   88 74  .543   80 82  .494

This is full of interesting tidbits. The White Sox, the lowest-scoring team of the six by a considerable margin, were by far the most effective at winning the close games. The Yankees and Red Sox also have fine records in games decided by a single run, but it's off-set to a considerable degree by their losing record in games decided by two runs. Both the Yankees and Red Sox went 37-27, .578 in games decided by one or two runs, and that's pretty well their overall winning percentage. The Angels are at the same level - 50-37, .574 and very close to their overall winning percentage. Only the White Sox are significantly better in close games than the rest: they were 61-34, .642 in games decided by one or two, and 38-29, .582 in games decided by three or more.

The White Sox, of course, are the team that over-achieved their Pythagorean expectation by the greatest amount.

Boston and New York over-achieved as well. In the case of the Red Sox... remember R Billie's concern about blowouts skewing the Pythagorean expectation? He was concerned about Toronto's hitters piling up runs in blowouts. I think, however, that this applies to the Boston pitchers, who gave up a ton of runs in a very small number of games - 153 runs in just 12 games, to be precise. You could certainly suggest that it skews their Pythagorean expectation downward. Meanwhile, the Red Sox were extremely efficient at winning the games when their pitchers did well. And so were the Yankees, who went 74-11 when allowing 4 runs or less, which is even better than Boston's record (68-13) in those games.

The Pythagorean under-achievers were Oakland and Toronto. And here again, R Billie's concern about blowouts having a large influence on the Pythagorean expectation raises its peculiar head. But not with Toronto - with Oakland. The A's were 12-3 in games decided by 9 runs or more - in those 15 games, they outscored the opposition by 100 runs. That's pretty serious overkill. In their other 147 games, they outscored the opposition by a total of only 14 runs, but were still able to go 79-71 - which actually is pretty darn good. It's a few games better than you would expect.

But this doesn't account for the Blue Jays. The Jays were 5-2 in games decided by 9 runs or more - they outscored the opposition 68-36. Which means that in the other games, they outscored the opposition by 38 runs (707-669) and were still a losing team (75-80). If you like, you can tack on the games decided by 7 or 8 runs, because Toronto won more of those than they lost. It still isn't enough. Toronto went 13-8 in games decided by seven runs or more, and outscored the opposition 150-103. And that means that in the other 141 games, the Blue Jays outscored their opponents by 22 runs total (625-602), but managed a rather crummy 67-74 win loss record.

Nope. We are going to have to come to grips with the Big Ugly Skeleton in the Cupboard - you know it's coming! - Toronto's utterly hideous record in close games. And this subject... well, it merits its own study. So stay tuned!