After posting my summary of The Book's strategies for optimizing a batting order, some readers suggested I apply the theory to an actual lineup.  I think that's a great idea.  So -- in the spirit of all great infomercials -- you're not just going to get one lineup, but three!

Minnesota Twins

Jesse over at Twinkie Town has a very nice article on the Twins lineup, quoting my article from Tuesday and listing the players who could fit in each spot, so I suggest you read it.  It's a nice format.  What follows below is how my thought process would work, without all the explanation of why (which is really the important part if you want to convince someone to use different lineup.)

First, find a set of hitting projections for the players who should be starters (based on both offensive and defensive abilities.)  CHONE's among the best, so I'll go with that one.  Against righties, Denard Span's defense and platoon advantage should be enough to start him ahead of Delmon Young, leaving these nine players, sorted from best to worst according to offensive runs created above average per 150 games:

Take the top three hitters (Mauer, Morneau, and Kubel) and put them in the #1, #2, and #4 spots, with the player least reliant on homeruns first (Mauer), the player with the highest relative OBP second (Mauer, although Kubel's the next best choice), and the player with the best power fourth (Morneau).  That gives us Mauer -- Kubel -- XXX -- Morneau so far.

Now slot the next two best hitters (Cuddyer and either Span or Crede) into the #5 and #3 spots.  From The Book:

The outs for the #5 hitter are much more costly than those in the #3 slot.  Result?  The #5 hitter should be better than the hitter in the #3 slot.

That sounds weird, right?  The reason is that the #3 hitter gets a lot more plate appearances with two outs than the #5 batter.  So, he has less chance to do damage, unless that damage is done with the homerun.

Cuddyer is the best hitter of the three, by far.  He goes fifth, leaving Crede (the homerun-heavy guy) third.  So far we've got Mauer -- Kubel -- Crede -- Morneau -- Cuddyer.

Place the remaining four players in descending order of hitting ability (Span, Casilla, Punto, Gomez). Since Span is clearly the best hitter of the four, he goes sixth, and we fill out the rest as so, given that Casilla, Punto, and Gomez all have the same (lack of) skill-set, just to varying degrees of badness:

1. Mauer
2. Kubel
3. Crede
4. Morneau
5. Cuddyer
6. Span
7. Casilla
8. Punto
9. Gomez

By the way, this is the lineup people are picking to win the AL Central?  A weighted total of runs per 150 yields +20 runs, which, well, is a bit above average, actually.  Pitching and defense...

New York Mets

There's a lot of talk about hitting Jose Reyes in the third spot this year, so we might as well figure out if that's a good move.  CHONE says:

The three best hitters are Wright, Beltran, and either Delgado or Reyes.  All but Reyes have too much homerun power to lead off, so that leaves Wright for the #2 hole (a higher percentage of his value is tied to OBP than with Beltran) and Beltran for cleanup.  Reyes would actually make for a solid #5 or #6 hitter, but there's nobody else you want leading off.  Castillo, who's getting a lot of press in New York, just isn't that good at the plate.  Because the lead-off hitter will come to bat a lot with runners on base after the first inning, he actally needs to be able to drive someone in.  So Reyes leads off, leaving an order of Reyes -- Wright -- XXX -- Beltran so far.

The next two best hitters are Delgado and Church.  Delgado's the better hitter, but derives much more of his value from homeruns.  Church is more of a walker.  Without a simulator, there's no obviously answer for which one should bat fifth and which one should bat third.  I'm guessing Church is the better baserunner, so we'll put him fifth, leaving us with Reyes -- Wright -- Delgado -- Beltran -- Church so far.

Murphy, Castillo, and Schneider will round out the order, with the pitcher hitting eighth.  There's a lot of talk about hitting Castillo ninth, and that's viable, but I'm not sure it's the obvious move, given he's a better hitter than Schneider.  However, Schneider has more power and a lower OBP, which makes sense hitting ahead of the pitcher.  Again, we'd need a simulator.  The final lineup looks something like:

1. Reyes
2. Wright
3. Delgado
4. Beltran
5. Church
6. Murphy
7. Schneider
8. Pitcher
9. Castillo

Weighting by lineup position, that looks like a lineup producing 45 runs above average, compared to others without a DH.  Of course, there might be something different against lefties.

New York Yankees

Let's assume ARod's in the lineup.  Their hitters project to rank like this:

The best three hitters are ARod, Teixeira, and then, well, a lot of possibilities.  Tex's OBP makes up a bit higher percentage of his value than ARod, so he goes second with ARod fourth.  Nick Swisher hits a lot of homeruns, so we'll pass him over in favor of Derek Jeter for the leadoff spot.  While Jeter's a few runs worse than Matsui and Posada, his baserunning likely makes him just as valuable overall, and a better option for the lead-off position.  If the hitting gap were larger, leading off with Matsui wouldn't be all that crazy.  For now we have Jeter -- Tex -- XXX -- ARod.

The next two best hitters are among Swisher, Matsui, and Posada, all similarly productive.  Matsui and Posada are quite similar, and the best use of Swisher would be in the #3 hole, as he's a low-AVG, high-HR guy.  Matsui will go fifth and Posada sixth, in order to avoid two lefties back-to-back based on Cano and Damon coming up, leaving Jeter -- Tex -- Swisher -- ARod -- Matsui -- Posada right now.

Now we've got Cano and Damon.  Cano projects as a slightly better hitter, although Damon's the better baserunner.  It's a crapshoot whether you want the slightly better hitter first or the good baserunner ahead of a singles hitter.  Gardner rounds out the order, based on spring rumors, although CHONE actually projects Melky to post the better line in 2009:

1. Jeter
2. Teixeira
3. Swisher
4. ARod
5. Matsui
6. Posada
7. Damon
8. Cano
9. Gardner
   

In addition to starting against lefties, Nady should see plenty of pinch hit appearances when the opposing team brings in their LOOGY to face the three lefties at the bottom of the order.  A simple weighted average of runs per 150 puts the Yankee lineup at 120 runs better than average, thanks in part to eight out of nine spots projecting as above-average hitters.

Summary

Remember, batting orders are a bit overrated.  But in order to squeak out that one extra win (which costs $4.5M on the free agent market and is worth perhaps 10% in playoff probability for a team in contention), filling out lineup cards based on the above thought process is a smart move.  To really make the tough decisions, heuristics aren't enough -- a simulation is the way to go.  And when you're talking about a tenth of a win, keeping hitters happy is probably the more important consideration.

To optimize the lineup, put your three best hitters in spots #1, #2, and #4, with #1 favoring low-HR, high-OBP players, #2 favoring high-OBP players, and #4 favoring high-SLG players.  Then put your next two best hitters in spots #5 and #3, with the better hitter going #3 only if he derives significantly more of his value from HRs and isn't that much better than the other option.  Then fill your #6 through #9 spots in decreasing order of talent, with consideration given to handedness, baserunning, and contact vs. power hitters when players are close in hitting ability.  Put good baserunners ahead of contact hitters and power hitters behind players who can't avance themselves.