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As most of you surely know, the Big Bang Theory explains the origins of the universe. Which is no doubt a good thing to know, but the Big Bang Theory has also been proposed to explain just how baseball games are won and lost.

The Blue Jays rang up five runs in the very first inning last night, and never looked back, even when the other guys started breathing down the back of their necks in the ninth inning. The very first inning was the decisive moment in the game.

They put a big crooked number on the scoreboard.

Earl Weaver talked over and over, for fifteen years as a manager and in his two books, about the importance of big innings. You win with pitching, fundamentals, and three-run homers. Pitching obviously prevents the other fellow from posting big innings, and three-run homers always ensure a big inning for yourself.

Weaver also used to say that "If you play for one run, that's all you're going to get." As he liked getting more than one run, he avoided those strategies which risked the possibility of the big inning in order to increase the chance of scoring one run - the sac bunt, the stolen base.

The Blue Jays have now played 52 games. In 41 of those games, 79 percent of the time, the team that had the biggest inning won the game. In 7 games, neither team had a single inning better than the other team's. And in 4 games, the team that had the biggest inning lost the game. I don't know if any of you will find that even remotely surprising.

Weaver's Boswell, who by happy coincidence just happens to be named Boswell, Tom Boswell of the Washington Post, was the one who did much to popularize these Weaverian concepts, in particular the Big Bang Theory. The classical Big Bang occurs in a baseball game whenever the winning team scores more runs in a single inning than the losing team does in the entire game. This happens rather often.

Last night wasn't one of those occasions - the Jays 5 run first inning wasn't enough by itself to outscore the Mariners. But in their 52 games this year, the Big Bang Theory held true 28 times. In 28 games, the winning team scored more runs in one inning than the losers did in nine.

The Big Bang Theory is true! Isn't science wonderful?

Now it's 4:00 AM, and I've spent three hours pouring all this data into a spreadsheet, and I really need to take a few days and look at it and see if there's anything cool to be learned from it. Your suggestions are invited!

But I hate to leave you with a skimpy little Game Report. So here's a sample of what we can do. In their 52 games, the Blue Jays have come to bat 456 times (12 times they did not need to bat in the ninth inning.) This table tells you how many times the Jays have scored in those innings and in what quantities. We can do this for the other team, because preventing big innings is a large part of winning - we can look at how often they win when they have a six-run inning (surprise! all the time) and so on and so forth...

Runs Scored1st 2nd 3rd 4th 5th 6th 7th 8th 9th How Often
6 1 0 0 0 0 1 0 1 0 3
5 1 0 0 1 0 2 0 1 0 5
4 0 0 1 2 0 1 0 0 1 5
3 2 2 1 2 2 3 1 1 1 15
2 3 6 3 5 6 3 6 5 4 41
1 5 8 9 5 4 6 12 5 9 63
0 40 36 38 37 40 36 33 39 25 324

Isn't it a little startling just how many innings are scoreless?

Jays 9, Mariners 7: Crooked Numbers | 22 comments | Create New Account
The following comments are owned by whomever posted them. This site is not responsible for what they say.
baagcur - Wednesday, June 01 2005 @ 07:31 AM EDT (#118293) #
Nice Analysis, Magpie
"Isn't it a little startling just how many innings are scoreless?"
It's a long time since I did this but does the spread of runs scored fit in with the poisson distribution? If so, it shouldn't be startling

One other way looking at big innings v small innings might be to look at the jays 52 games and provide their win-loss record when they have scored in more/the same/less innings irrespective of the total scored in each of those innings
Pistol - Wednesday, June 01 2005 @ 08:44 AM EDT (#118295) #
That chart got me wondering how many runs the Jays scored in each inning.
1st	2nd	3rd	4th	5th	6th	7th	8th	9th	Total
28	26	22	34	22	41	27	29	24	253
Dave Till - Wednesday, June 01 2005 @ 09:04 AM EDT (#118298) #
Nice article.

I'm a believer in the Modified Earl Weaver Theory of run scoring: I like big innings, and dislike sacrifice bunts, but I also believe that fast baserunners, and the threat of the stolen base, make opposition pitchers and fielders jittery.
The Bone - Wednesday, June 01 2005 @ 11:06 AM EDT (#118307) #
What I find cool about this chart is close these numbers come to multiples of 52 (number of games played) - Basically what it says it says the Jays can be expected to have 2 innings where 1 or 2 runs are scored per game and have a 50/50 shot at one inning where 3 or more runs are scored

Magpie - Wednesday, June 01 2005 @ 11:19 AM EDT (#118310) #
OK, someone's going to have to explain "poisson distribution" because I think it's got something to do with fish...

If I was a sober and sensible fellow, with a game that started at 10:00 my time, I might plan my Game Report in advance (and maybe have half of it already written.) But NOOO! I get some weird idea around the eighth inning, and end up staying up for hours entering numbers into a spreadsheet.

All this after first being distracted by Willy spotting the second best typo I have ever posted at this place...

And now I feel bad because I didn't do make the same table for the opposition, because... well, it so obviously ought to have been done.

C'est la guerre. But now... it's much easier to keep the spreadsheet updated than it is to set the thing up, so I think I can have some more fun with it.

Rob - Wednesday, June 01 2005 @ 11:22 AM EDT (#118313) #
The Bone, that is very cool. Someone should take a look at the 2004 statistics, see if the numbers combine for 161 games in any way.

In other news, the uncoachable lefty is the subject of today's story by Jeff Blair, Coaches take hands-off approach with Lilly.

Arnsberg on Lilly: [We] are turning it all over to Ted right now. I've tried to get in his house and it hasn't worked. His manager...Ernie Whitt...they've all tried it, too, and it hasn't worked.

I guess the best way for me to put it is: I'll take a kid who is chomping at the bit every third day over a guy who is content with mediocrity and is happy to pitch every fifth day, whether that guy is a 10-year veteran or whatever.

Nothing new, now that I think about it. We knew this already, didn't we? Gitz probably predicted way back when the trade was made that this story would appear on page S3 of the Globe and Mail in the first week of June 2005. Still, I never expected the pitching coach to say Lilly is "content with mediocrity." It looks like Ted will not be long for Rogers Centre.

Sister - Wednesday, June 01 2005 @ 11:38 AM EDT (#118318) #
For a poisson distribution to be fit the assumption is that events are independent and random (I think?). Are the number of runs scored in consecutive innings against the same team an independent and random event?
BCMike - Wednesday, June 01 2005 @ 11:46 AM EDT (#118319) #
Maybe it's just me, or it could have been his socks, but does it look like Vernon Wells has widened his stance a bit?
Ryan C - Wednesday, June 01 2005 @ 12:16 PM EDT (#118321) #
Wow that seems like a pretty scathing quote from Arnsberg. I'm guessing this makes it a whole lot more likely that he gets moved by the deadline or in the off-season.
Craig B - Wednesday, June 01 2005 @ 12:24 PM EDT (#118323) #
For a poisson distribution to be fit the assumption is that events are independent and random (I think?). Are the number of runs scored in consecutive innings against the same team an independent and random event?

No, but kind of close, because of two important factors - first factor, the large variations in the quality of pitchers within a team means that run-scoring innings tend to bunch, and scoreless innings tend to bunch. Second factor, the cyclical nature of most lineups works (to a slight degree) to countervail that because poorer hitters are usually bundled at the bottom of the lineup, making it likely that after a run-scoring inning put together by the good hitters, the poor hitters will come up and put together a scoreless one.

So for example, the first inning sees the largest number of runs scored of any inning, while the second inning sees the fewest. (Bill James found this in 1988.) This is mostly, in my opinion, due to the lineup effect.

Still, it means that run-scoring isn't truly a Poisson process, since the number of runs for non-overlapping intervals of innings isn't independent for all innings.

Craig B - Wednesday, June 01 2005 @ 12:28 PM EDT (#118326) #
Incidentally, if lineups were randomly selected, and a team's pitchers were used similarly (i.e. a number of pitchers in strict rotation, one batter at a time) then I would suspect run-scoring within innings would be a Poisson process. The only countervail there would be the use of one-run strategies, but I don't think managers have any actual tendency to bunch these in any notable way.
sweat - Wednesday, June 01 2005 @ 12:43 PM EDT (#118329) #
I have a feeling whether Lilly improves or not that he will be traded. If he improves, and the Jays are out of contention I could see Texas looking for a quality LHP. Personally, I'm hoping that the Jays will be in it, and need to keep Lilly atleast untill the ofseason.
Stellers Jay - Wednesday, June 01 2005 @ 01:13 PM EDT (#118333) #
If they can get a piece of the puzzle for the near future for Lilly himself or in a package with a prospect or two, they should do it in a heartbeat. If he is still with the organization at the end of the year, I think it's quite likely he is non-tendered and they will get nothing in return. He is making 3 million and change this year and will likely get a raise on that in his final year of arbitration, next year.
Flex - Wednesday, June 01 2005 @ 02:04 PM EDT (#118345) #
On the subject of Lilly, I hate to say I thought you so, but ... I thought you so. I remember the day the Jays acquired Lilly, I thought, this guy's never gonna be much more than serviceable, otherwise why would so many teams have traded him off? And when Lilly made the all-star team last year and a bunch of pundits picked him as our second-best starter, headed for big things, I thought... nope.

I didn't actually say any of that, or write it, because I didn't wanna be a party pooper.

But I thought it ... loud and clear.
Petey Baseball - Wednesday, June 01 2005 @ 02:41 PM EDT (#118348) #
Okay people, we've got a Ted Lilly fan ticked here.

So he's been inconsistent. Is it really fair for Jeff Blair and all you Lilly bashers to make this personal and compound the problem by poking at his way of going about things? Give me a break, the guy had a helluva year last year and he gives you 4 bad starts and your ready to release him? And as for the charge that he is content to be a mediocre pitcher and doesn't look like he cares? C'mon we all know that Lilly is very competitive and will stand up for his teammates just as much as Halladay or whoever. To me he has a GREAT deal of competitveness and just needs to be trusted. So all the Lilly bashers bother me because they simply aren't making sense. Teddy has also had some lights out performances this year as well, just the 2 or 3 awful ones have been awful. He's been inconsistent.....nothing more. These personal attacks on his character and lack of competitiveness are false and just plain wrong.
Mike Green - Wednesday, June 01 2005 @ 02:58 PM EDT (#118349) #
I certainly do not question Lilly's competitiveness or his general ability to pitch. His DIPS ERAs over his career place him at between 4 and 5, and even this year, when he has struggled, his pitching has not been as poor as his ERA would suggest. Still, over the long haul, it is entirely unclear whether Lilly will be an above average pitcher.

Jeff Blair was reporting what he saw in terms of the interaction between Arnsberg and Lilly. That is exactly what a reporter should do. It is certainly common for a pitching coach to be unable to help a particular pitcher, and some pitchers have succeed without such help.

The one comment that I was not fond of in the Blair article was the suggestion that Lilly would have been sent to the bullpen, save for his contract status. I do not understand this at all, and I find it difficult to reconcile with the decisions to send Bush down and to place Speier in a less demanding role. If Lilly needed to go to the bullpen in order to make some adjustments under less pressure, then it should have happened. If Lilly didn't need the removal of pressure to make the adjustment, then it need not. But contract status should have had nothing to do with it.

I do remain generally pleased with the performance of the pitching staff under Gibby and Arnsberg. The Lilly and Bush situations are happily the exception rather than the rule.
Magpie - Wednesday, June 01 2005 @ 03:22 PM EDT (#118355) #
So for example, the first inning sees the largest number of runs scored of any inning...

Assuming, of course, that your lineup construction makes sense. And I think most managers have finally figured it out by now.

The odd thing here is the 6th inning explosion (and I must look at see if it's the same for the Jays opposition.) Two obvious explanations come to mind: 1) the starter begins to tire; 2) the wrong guy comes out of the pen. After all, who uses their best reliever, or even the second best, in the 6th inning?

Elijah - Wednesday, June 01 2005 @ 04:17 PM EDT (#118360) #
Uncoachability is the anathema for athletes. No one wants to be labeled that way. Not Allen Iverson. Not Ted Lilly.

The problem I see with Lilly resistant to change (assuming what Arnsberg says is true) is that he can be better. Perhaps what he gave the Jays last year (I mean, he still had an ERA over 4.00) is only scratching the surface of what he could do.

Yes, Lilly is a good big league pitcher. And while I have no clue how competitive Lilly is, Halladay was willing to receive instruction when he needed it. And we've seen over the last several years how competitive Halladay really is. Doc has tremendous natural talent but that by itself does not guarantee greatness (or even goodness) at the major league level.

Lilly has been a decent pitcher but in no way has he earned the respect that Halladay (or other guys like Bonds, Clemens, etc.) have. When those guys are struggling, if they say to their coaches, "Leave me alone - I'll work it out myself," they have earned that right to try repair themselves. In fact, Halladay might have more respect because he was willing to eat his pride and allow the coaches to help him harness that ability.

I don't believe the Blue Jays want to trade him and I'm sure Arnsberg wants to see him do well. Calling a player uncoachable doesn't help a player's trade value. My guess is that Arnsberg is trying to wake Lilly up.

Everyone here wants to see Lilly do well - whether they think he will or he won't. But this seems to be the classic challenege situation of "If you say you can do it yourself, go right ahead. But if you don't turn it around, you're going to listen to whatever we tell you to do."
AWeb - Wednesday, June 01 2005 @ 04:24 PM EDT (#118361) #
Just to finish beating on the Poisson distribution (my stats background demands it of me), the distribution of scoring in innings doesn't follow the Poisson distribution very well. Scoring an average of 0.555 runs an inning (where the Jays are so far this season) should translate into 262 scoreless innings, and 145 one run innings, according to the distribution. It also predicts only one inning with 4 or more runs scored. The model does predict 2 run innings correctly though...

As Craig B noted above, there are lots of reasons why runs scored do not appear to be random along these lines. To my way of thinking, the only way you get a Poisson distribution for runs scored is if all hitters in the lineup are average, all pitchers are average, and all of them perform "averagely" every day. So no good or bad days allowed, especially for the pitchers. Since this clearly doesn't happen (Franklin last night wasn't unlucky, he stunk), you get the bunches of runs.

Anyway, enough stats geekery...does anyone else suspect the Bush demotion and Lilly struggles could very soon become related. i.e., if Bush pitches well in AAA, and Lilly stinks some more, Bush could end up replacing Lilly for a while (while Lilly goes to the bullpen?). Since Lilly and Bush have been touted as friends, this might make it easier on Lilly than if he was replaced by Gaudin directly. Of course, Gaudin might not be staying either. Best case, in my opinion, both Bush and Lilly find their game and Gaudin can go back to AAA.
HollywoodHartman - Wednesday, June 01 2005 @ 07:15 PM EDT (#118372) #
Looking at that chart im wondering if it inclued the scoreless 10th and 11th innings and 4 run 12th on May 2nd?
Rob - Wednesday, June 01 2005 @ 07:47 PM EDT (#118376) #
Here is the 2004 version of Magpie's chart above, but first, let's thank Retrosheet for their game logs:
RS   1st   2nd   3rd   4th   5th   6th   7th   8th   9th   Sum    How Often
6     2     2     1     0     1     0     0     1     1      8     20.1
5     0     2     2     2     0     1     2     0     1     10     16.1
4     3     2     3     2     1     3     3     4     2     23      7.0
3     6     5     4     3     5     3     7     3     3     39      4.1
2    12    11    17    13     9     8    11    12     9    102      1.6
1    24    24    28    25    27    24    22    22     8    204      0.8
0   114   115   106   116   118   122   116   119   103   1029      0.2

"How Often" means how many games it would take the Jays to score X runs. So, it would take them 16 games to have a 5-run inning, 7 games for a 4-run inning, and they would have a 1-run inning every day, just about.

If you're wondering, the Big Bang Theory held true in 31 of Toronto's 67 wins.

This is how many innings it took the team, on average, to score however many runs:

R    INN
6  181.1
5  144.9
4   63.0
3   37.2
2   14.2
1    7.1
0    1.4

As I figure it, a completely average game for Toronto in 2004 would include:
Six scoreless innings
One 1-run inning
One inning with 2 runs
One inning with 1, 3, 5 or 6 runs (almost always one run, though).

The information used here was obtained free of charge from and is copyrighted by Retrosheet. Interested parties may contact Retrosheet at 20 Sunset Rd., Newark, DE 19711.

Rob - Wednesday, June 01 2005 @ 07:56 PM EDT (#118378) #
Oh, and the Jays scored four extra-inning runs in 2004. That explains the difference between those numbers (715 runs) and the real total (719).

Jays 9, Mariners 7: Crooked Numbers | 22 comments | Create New Account
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