Honestly, it's been awhile since I adopted the strategy, and I don;t remember the original source I saw it at, but here's a source that believes wholeheartedly in the sabermetric approach, and has a clear conclusion:
http://www.beyondtheboxscore.com/2011/4/14/2110082/why-dont-sabermetric-gms-have-sabermetric-managers-and-shouldnt-theyI can go fishing for better sources at some other time, but that article outlines the gist of the sabermetric approach on lineup optimization. I'm of mixed opinion about sabermetrics in general; some of it I accept completely and some of it I find repulsive to the old-school fan in me. On the subject of lineup optimization, here's the general theory and my opinion of it:
Leadoff-Sabermetrics says your best OBP guy, who hopefully can run. I agree with this and never will lead someone off who's not one of my 3 or 4 best OBP guys.
2nd-Saber says this is your best well-rounded hitter, kind of like the old-school number 3. I generally follow this.
3rd-Saber says this really isn't an especially important spot. The logic is very interesting, and I agree with much but not all of it. The rationale is that first of all, the 3 hole comes up about 40% of the time with no one on and 2 outs in the 1st inning--the lowest leverage spot possible--, and that lineups are primarily constructed for when the top of the order leads off. Second, according to some of the research, the 3 spot leads off more innings than most other positions, therefore not being ideal for an rbi guy. I like the logic here, but I'm a bit wary, because with no ability to do controlled experiments, I think the lack of bunching of the top hitters would allow for an easier time for opposing pitchers. In the end, what I do with the 3 spot is put the worst hitter of my top end hitters; I won't put a mediocre hitter here no matter what my team is like, but I would never bat someone like Miguel Cabrera 3rd. I think that costs the Tigers runs.
4th--Saber says best hitter with power, and I agree, although I'd rather a guy who gets hits and hits for some power than a Mark Reynolds type, which I would hit 5th
Saber then says to hit guys in descending order of talent down to 7th, and I generally do this (although I weight 5-6 with power most of the time), except that I usually also leave a little power (12 HRs maybe if I have the personnel) before the pitcher if I have it, as this tends to promote intentional walks and add to my team's baserunners.
Then comes the pitcher part. Sabermetrics says hit the pitcher (or any hitter way weaker than the others) 8th so that they do not get in the way of the lineup turning over. My take on this is in between. My criteria are: I will hit the pitcher 8th if I have a shallow lineup (in this case turning over the lineup is important), if I have a really weak position player at SS or C who I can't really pinch hit for later in the game, or if I have a leadoff hitter who hits a lot of home runs. I will not hit the pitcher 8th if I have a really good SP who I am likely to not pinch hit for much or at all.
As for 7th, I have only done that a few times when my pitcher is an 8N and was actually better than my bottom hitters.
I hope this wasn't boring, but you said you were intrigued, so here it all is.