Sabermetric research tells us that batting order does not matter that much. More precisely, a batting order optimized in accordance with what sabermetric research has found to be best and the typical batting order (as opposed to the worst batting order imaginable) probably only makes about an average of one win’s difference for a team over the course of a full season.

Now, I tend to think that it’s more significant than some others. Fans, the media, teams, and, yes, sabermetric bloggers make a “big deal” out of things that are a little bit (in)significant. That is all a way of saying that I realize how much (or little, depending on your perspective) batting order matters, but still think it is worth thinking and writing about.

While managers may still do things we nerds find baffling with their batting orders (putting a weak hitter in the #2 spot is still a big culprit), one thing that sabermetric and traditional baseball thinking isdom generally share as a tenet of good batting order construction is that left-handed hitters should be split up.

This is done so that late in the game the opposing team cannot easily leverage left-handed relief specialists against multiple hitters in crucial situations. This makes sense, of course, but recently I have been wondering if this principle is sometimes applied too rigidly. So, with the admissions that this post will be a bit inconclusive and that I am aware that it is not a “huge” difference, let’s explore when it might be a good idea to bat two lefties in a row.

The first thing to acknowledge is that sometimes hitting two lefties in a row is unavoidable. For example, if a team is starting five left-handed hitters, two of them are going to have to be next to each other somewhere in the batting order, even if it is in the ninth and first spots. But that is not what we are talking about here.

I should also note that while The Book contains some helpful general principles for optimizing a batting order, the author of the relevant chapter, Tom Tango, acknowledges that those are just summaries, and that one really needs to use a Markov model or simulation in order get the “right” order. In other words, while it is fair to criticize a team or manager for “doing it wrong,” one can subjectively understand the cultural resistance to stuff like this within baseball.

When informally trying to think of my own optimized line-ups, the splitting up of lefties is something that often stands in the way of getting the better hitters all at the top of the lineup. While the batting orders recently have been maddening for other reasons, let me focus on the top of the Royals’ lineup from last week simply for the sake of an example of what I am talking about.

Going into the season, pretty much every projection system had Billy Butler, Alex Gordon, and Eric Hosmer as the Royals’ three best hitters. Whatever his other foibles, manager Ned Yost wisely decided to have Gordon lead off. Hosmer and Butler are hitting third and fourth.

Now, some would argue that maybe Butler should move up to second in order to get all of them in a row, but the second spot typically sees a high number of double play opportunities, and then the fourth spot becomes an issue. Getting into all of this and how it affects the rest of the batting order is relevant, but given the endless variations not practical for the sake of space, so let’s just focus on the top two spots.

Prior to the season, second baseman Johnny Giavotella was supposed to hit second, but he did not make the team out of Spring Training (another long story). Right-handed hitting center fielder Lorenzo Cain got a shot at hitting second, but then he got hurt. So, last week, Alcides Escobar got a shot at hitting second. Escobar has a nice new extension and his a good glove man, but he is a horrible hitter — ZiPS Rest-of-Season projections have him as a .299 wOBA hitter, which is considerably higher than his .282 career mark for those wondering if his relative youth should be taken into account.

Despite those lousy numbers in a key lineup spot, I could see where Yost was coming from. If you are set on having Gordon and Hosmer hit first and third and Butler fourth, who is going to split up lefties Gordon and Hosmer? Yuniesky Betancourt (that actually happened, but it’s the same general issue)? Humberto Quintero? Jeff Francoeur? (Okay… Francoeur actually happened at one point, too, and he may actually have been the best choice, but let’s stick with Escobar for the sake of the general point.)

It may not have been the best order given all the possible variations, but if one is keeping the top half the order constant for the sake of simplicity, the choices just aren’t that great. But which of of these things is not like the other. Here are their current ZiPS RoS wOBA projections:

Gordon .347
Escobar .299
Hosmer .352

But what if we put aside the need to separate lefties? Picking one interesting possibility out of the hat, what if third baseman Mike Moustakas, a lefty hitter, is put into the second spot. As a low-walk, high-power guy without much speed, he is far from the “ideal” (whatever that means) number two hitter, but let’s just compare. His current ZiPS RoS wOBA projection is .323. Over a full season of plate appearances, that is about ten runs better than Escobar. Of course, we are not comparing those amounts, since they would both hit in order. What are we comparing?

There is a season-long difference in number of plate appearances between hitting second and ninth (where Escobar would probably hit) — less than one hundred. But because we are worried about in-game situations, that is not quite as significant. Assuming Gordon and Hosmer are “held constant” from opposing pitcher to opposing pitcher, is Escobar’s platoon advantage against a late-game lefty that significant over Moustakas?

Using the projections above, I estimate Escobar’s true talent wOBA versus left-handed hitters to be .304, and Moustakas’s to be .297. So Escobar gets a very small edge. Per plate appearance versus left-handed pitchers, Escobar would be expected to create .005 runs more than Moustakas. (It bears repeating that this is a very simplistic approach: for proper optimization you not only need a simulation, but one that takes into account probabilities of each event for each batter and how they inter-relate, not just “general” numbers like wOBA, OBP, or SLG.)

However, we are talking about later in the game when a lefty reliever might be brought in to face both, say, the #2 hitter and Hosmer. I would assume that one would only put Moustakas in that slot if the Royals (just an example, remember) were facing a right-handed starter. Against righties, Escobar projects to have a .284 wOBA, and Moustakas a .332 wOBA. That is about a .038 run advantage for Moustakas — relatively speaking, quite a bit more than Esboar’s advantage against lefties.

One may rightly point out that lefties are split up even against righty starters because of the possibility that a left-handed reliever could be leveraged against multiple hitters. Leverage is a complicated and debated issue. However, just looking at the summary wOBA figure, we see that Moustakas advantage versus righties is about five that of Escobar versus lefties. Without looking it up and explaining it in an already overlong post, it is hard to imagine that leverage would get that high that often.

More importantly, there is the issue of the number of plate appearances. Unless the starter gets knocked out very early, how many times is a LOOGY going to face that spot in the order relative to a right-handed starter? The LOOGY is probably only going to face the spot once, while the right-handed starter at least two or three times. Perhaps sometimes the “leverage” of the late-game situation would outweigh the relative number of plate appearances, but it would not be every game. On the other hand, one could have much more confidence of having the lefty in question having the platoon advantage multiple times.

There are other things to consider, of course, In the Royals’ particular situation, Gordon-Moustakas-Hosmer would not be two lefties in a row, but three. So in this particular case, the difference is not between having a late-game LOOGY facing one or two lefties, in a row, but either facing one lefty and being taken out, and getting to face three in a row. That particular situation is more complex.

However, ultimately I’m not writing about the Royals’ specifically, or even the 1-2-3 section of a batting order. It is separating lefties in the batting orders generally in which I’m interested. While there are good reasons why managers should try to split lefties up (and having three in a row might be a stronger case for it), I wonder whether having two lefties like Gordon and Moustakas or Moustakas and Hosmer next to each other in the order might be an overall better choice if the alternative is subbing a hitter as poor as Escobar for Moustakas.

Yes, there might be some late-inning discomfort, but maybe scoring more runs earlier in the game would offset it. I truly do not know, but it is worth thinking about, as least as much as anything else in batting order optimization is worth thinking about. Hopefully those who program simulations and models can taken this sort of thing into account (and then make the simulations available to us! Wishful thinking…)