Almost one-third of the way through the season, and an interesting question was posed by srdmad in the Gameday Thread today, with regard to what order we would hit people in. A lot of discussion ensued and so I thought it might be fun to do a spot of research into this.

I should point out, studies have shown that the order in which players hit does not make a tremendous difference to production. The difference between the best and worst lineup is little more than half a run per game - and the "worst" in this aspect includes totally nonsensical ones, which have the pitcher batting leadoff. Remove those from the equation and there is even less difference in the final results.

First the traditional approach for an NL team, from Wikipedia:

1. The first or leadoff hitter should be a good baserunner and good at getting on base. He should be willing to watch many pitches so that his teammates get a better chance to see the opposing pitcher's stuff. It is a waste to put a power hitter in the leadoff spot.
2. In the traditional approach, the second hitter should be a good bat handler. He needs to be able to take pitches to give the leadoff man a chance to steal. He should also be able to make a sacrifice bunt or hit and run play. Another theory is that any player with a high on-base percentage should occupy the spot, no matter his other skills, in order to create RBI opportunities for the team's best sluggers who normally hit in the next two spots.
3. The third hitter is supposed to be the best all-around hitter on the team. He should be able to hit for average and power, and ideally should be able to run the bases well.
4. The fourth or cleanup hitter is supposed to be the best power hitter. His job is to drive in the top three hitters when they get on base.
5. The fifth place hitter is usually another power hitter, but one who isn't quite as good as the cleanup hitter.
6. The sixth place hitter is something like a second leadoff hitter. If the team has a second player with leadoff-type skills, he'll often bat 6th.
7. The seventh place batter is normally a spot for a batter who lacks the skills that would put him higher in the order.
8. In leagues in which the pitcher is required to bat, teams will often pitch around the eighth place hitter, so it's desirable to have a patient hitter there. It used to be traditional to bat the catcher eighth because the catcher was often changed along with the pitcher.
9. The ninth spot is reserved for the pitcher in non-DH leagues. In DH leagues, it is often seen as a second leadoff spot, so teams will pick a batter with leadoff-type skills.

Now, from my SB Nation brothers over at Beyond the Box Score, comes this analysis of line-up construction, which reached the following conclusions:

1. This is the most OBP-centric spot in the lineup. Your hitter here might very well be your best hitter, IF his best attribute is his OBP. A hitter with a .425 OBP and a .500 SLG would fit in here well, provided that there's not a better OBP threat elsewhere on the roster. When I looked at it, I decided that Derek Jeter is really the optimal leadoff hitter. He has a good OBP and acceptable power, and he's generally a solid hitter.
2. The 2-hitter should be the lineup's most balanced hitter, a good combination of OBP and SLG. David Wright fits the bill here, as does the player I chose, Chase Utley. The first guy I thought of was Mike Lowell in his prime, when I looked at the results and coefficients.
3. This was the biggest surprise: the 3 hitter should be the player that doesn't fit into any of the other spots. Every other spot has some significance, but if I were building a lineup, I would just put the leftover player in the 3 hole. This seemed very counterintuitive to me when I first heard it, but David Pinto noted, "Part of what it's telling us is that you need to spread out your easy outs." I still struggled to get this, but I'm starting to, now. Marc said something to the effect of "the worst players have to go somewhere." I guess this is really it; the other spots just have greater needs. If you can get a good hitter here, it means that your lineup is very deep.
4. This is the bopper. This guy's best attribute should be his power, with OBP being of secondary importance. He should be the foil to the leadoff hitter, in a way; both players could be similar if they're both very complete. Andruw Jones, though, is an ideal #4 hitter: slightly above average OBP, and "phenomenal cosmic power," to quote Aladdin.
5. Picking the 5 hitter is simple: it's the second choice for the two slot. Paul Konerko, who I picked for this spot, had a very similar line to our #2 hitter, Chase Utley.
6. The 6 hitter shows the biggest difference between SLG and OBP on the roster. This is because you're going to want to have guys driving in the leftovers. The 6 hitter is the most exclusively power-dependent hitter of the bunch. His OBP is VERY unimportant. Alfonso Soriano and Jay Gibbons are good picks for this slot.
7. The 7 hitter is the less extreme version of the 6 hitter, with less of a need for power and more usage for OBP. I picked Vernon Wells here.
8. This is the worst hitter in the lineup. If it's the pitcher, he goes here, unless it's Dontrelle Willis or Jason Marquis or someone similar. This is because you'd rather not put the pitcher close to two of the best hitters in the lineup: the 1 and 2.
9. The 9 hitter should be a "punchless wonder," of sorts. Scott Podsednik, Gregg Zaun, and Brad Ausmus fit into this role nicely: guys with acceptable OBPs and absolutely no power. This is the "stereotypical leadoff hitter" to the extreme. He's not actually leading off because you don't necessarily want these guys to imbibe plate appearances, I think.

Using the players' current stats (before today), I plugged them into this Lineup Analyzer, using a composite figure for pitchers. Here's what it suggested would be the most efficient lineup for the Arizona Diamondbacks:

1. Justin Upton
   
2. Conor Jackson
   
3. Orlando Hudson
   
4. Stephen Drew
   
5. Chris Snyder
   
6. Eric Byrnes
   
7. Chris Young
   
8. Pitcher
   
9. Mark Reynolds

There are a couple of real surprises there: Drew batting clean-up? Young down in the seventh spot? The pitcher at #8, ahead of Reynolds? This is just purely based on numbers; it doesn't take into account things like the wisdom of splitting up our two potential left-handed starters, in Hudson and Drew. But there's much here that I could live with. I definitely like the idea of Young batting down the order, so that we can take advantage of his team-leading eleven homers.

Statistically, this lineup is predicted to produce 5.22 runs/game on average, based entirely off the raw statistics of OBP and SLG. That is very interesting, because the team, and the lineups actually used by Melvin, have actually produced an almost identical amount: 5.24 runs/game through the first fifty. This probably illustrates how little difference the order of your hitters really makes.

There is a whole chapter in The Book on this topic, but it'll take me a while to wade through its analysis, and see what conclusions they reach. In the meantime, please discuss away...