josh,

excellent post, and a good sample scenario. you're prob'ly right, in that situation most managers would pitch around larry --- but would they gain in the bargain? according to tangotiger's linear weights studies, walking larry would play into the cards' hands. taking your example: if eckstein, batting leadoff, comes up with a man on 2d base and 1 out, the cards can expect to score 0.725 runs. if, batting 2d behind an intentionally walked larry, he comes up with men at 1st and 2d and 1 out, the cards' run expectation is 0.971. (data is at http://www.tangotiger.net/RE9902.html). in essence, the question is: would you rather have eckstein bat with 1 on and 1 out, or with 2 on and 1 out?

on the other hand, tangotiger also thinks the #2 slot is the most abused in mlb. he profiles the ideal #2 hitter as a guy who has a high obp, draws lots of walks, and hits 25 hr . . . . ie, larry walker.

i am still working on getting a simulation study together --- that should tell us something

Interesting post, guys. I seem to recall that a math professor did a study on ideal lineups a year or so back. His findings were that the best way to maximize your offense was to:

1. Hit your best hitter 2nd (ie Pujols, Bonds, etc.)

2. Hit the pitcher 8th.

Basically, it was the best spot to both maximize the number of at-bats given the teams best hitter, and at the same time put him in an opportunity to bat with runners on more often (with a regular hitting 9th). Basically, your last paragraph scenario.

I personally would have no problem with the "big 4" hitting in the top 4 spots. Traditionalists would scream, of course.

I also always thought that the Giants should use Barry Bonds as a leadoff hitter. That would not only give him a few more plate appearances over th season (30 to 45), but would also guarantee him getting pitched to at least once per game. Who's going to intentionally walk the leadoff guy in the 1st inning just to avoid a home run?

walker / pujols / edmonds / rolen lineup is growing on me . . . . i'll see if i can get that simmed too

I think you guys are all over thinking the batting order.

http://mb7.scout.com/fbaseballfrm8.showMessage?topicID=867.topic]Optimal Batting Orders

There is a really long discussion there and it seems that ALL batters do worse in the leadoff spot because there are gaurenteed to bat with nobody on at least once a game and they normally follow the pitcher.

Here is what Tangotiget posted a while back:
"For now, these are the best profiles for each batting spot, assuming all the above is true:
leadoff - high walks, low homers, high SB
2nd - high walks, high singles, high SB, low CS, low HR
3rd - pretty much average all the way thru
4th - high singles, high doubles, high HR,
5th - low SB
6th - low singles, low doubles, low SB
7th - low singles, low walks, low doubles, low SB
8th - same as 7th
9th - high HR, high SB "

Obviously that was for the AL and NL but it doesn't seem like you should bat the pitcher 8th or have a power guy in the leadoff spot. Even in the 2nd spot, you don't want too many HRs.

Now again we are talking about maybe a swing of 5-15 runs over the course of the season so everything is pretty close together.

On a side note, I remember reading on some Cardinal blog last year that about halfway through the year that LaRussa had been using the IDEAL lineup. (which had Edgar down at 6th). Now obviously if Edgar hit like 2003 then he should have been batting 2nd but he didn't so he was fine at 6th.

stewie ---- maybe we are making a mountain out of 10 runs a year, but i agree with what tangotiger posted over at baseball musings: "Personally, I consider finding 10 runs 'a lot,' since that's 1 win, and teams pay 2 million$ for that."

random chance determines a lot of outcomes in baseball (more than we'd all like to admit), but here is one thing you really can control --- may as well try to get it right

I agree, 10 runs IS significant. I was saying that while it is definitely very interesting and worth discussing the difference between batting Walker, Pujols, Edmonds, Rolen, etc. and Eckstein, Walker, Pujols, Rolen, Edmonds, etc. is probably less than 5 runs over the course of the season so we should always keep that in mind.

I used to words "over thinking" more to describe theories of batting Bonds first and hitting the pitcher 8th than to trivialize 10 runs.

On average, managers don't do THAT bad a job of lineup construction. The 2nd spot is probably the hardest to figure out. After that, most managers seem to do pretty well with the rest.

One thing to keep in mind is that Marquis and Ankiel are excellent hitters for pitchers. And according to the post-dispatch, Mulder still remembers how to bat from his college days playing first base. So you shouldn't assume a sac. bunt in all those situations. I would like to see the big guys all right at the top, but I don't think Tony will do it. Plus putting Eckstien at the top or Grud the Stud second breaks up an inning of: Grudzielanek, Eckstien, Molina, (Pitcher)

Stewie: You're right, but I don't think we're expecting a huge breakthrough. Instead it's along the order of tinkering with your car to squeeze a few extra horsepower out of it.

I honestly don't think of a "Bonds hitting 1st" thought as over-thinking. I think of it as a chance to keep the bat in the guys hands more often than he currently gets. (Intentionally walking a guy 100 times is probably more over-thinking, flaxseed oil or not.)

As far as our pitchers hitting - Marquis was great last year, but don't expect anything out of Ankiel or Mulder. Neither of them have had a decent number of at-bats in years. And even when Ankiel did, it wasn't that great. (Career .207/.258/.310 numbers in the majors.)

I fully expect Eck to hit 1st, with Walker, etc. hitting 2 through 5, and I'm actually fine with it. I just like "what-if" scenarios.

You probably won't find many pitchers with career numbers better than Ankiel's - if .207/.258/.310 are correct.

Bob Gibson was considered an excellent hitter for a pitcher and his career numbers were .206/.243/.301

Those are fine numbers for a pitcher, sure. But the point above was not to expect to see our pitchers bunting a lot because they hit so well. I, personally, won't be expecting a lot out of a career .258 OBP hitter who hasn't had a hit in the majors since 2000.

The first step is to identify your two most obvious best hitters. In this case, you don't have it easy. Pujols is your best, and then you've got Rolen and Edmonds, followed closely by Walker.

So, you start with Pujols, and I have him forecasted at 37HR and 71BB. That's better at #4 than #2, though at extreme levels like Pujols, it's not always so easy to have rules of thumb.

Out of the others, Walker has the least power, so you should bat him leadoff. Between Edmonds and Rolen, there's really not much separating them. Edmonds might get more walks, so I'd go Edmonds as #2 and Rolen as #3.

But I would guess that swapping Edmonds/Rolen would change at most 2 runs, and more likely under 1 run. And Pujols as #2/#4 would be another at most 2 runs. It's a really tough call here, because there's not much differentiation among the players.

Pitchers should bat #8, yes, especially for a lineup like this one.

So, I'd go: Walker, Edmonds, Rolen, Pujols,x,x,x,pitcher,x
Maybe the next best one is:
Walker, Pujols, Rolen, Edmonds,x,x,x,pitcher,x

This is just off the top of my head.