There’s a dark side to batting a great hitter third

Let’s get this out of the way before we get into anything else: the batting order is not a huge deal. Yes, this post is about the batting order (in particular, the third spot), but it’s not made with the pretense that this is a particularly make-or-break issue. Rather, the reason why I think this warrants a post is because despite the relative non-salience of batting order considerations, some of the arguments about these considerations are lacking. In particular, and to avoid mincing words: if you focus solely on opportunities to hit with men on base (or, even worse, men in scoring position) as a way of justifying your batting order choices, you’re not looking at the whole picture, and thus using suboptimal reason.

Barreling right along into the meat of it, thinking about the batting order means thinking about the situations in which each batter (and lineup spot) will experience over the course of the season. To help us assess these situations, we generally talk about run expectancy: for a given base-out state (e.g., none on+none out, or runners on the corners+two out, etc.) how many runs score, on average, for the rest of the inning? There are a lot of run expectancy summaries out there — Tom Tango has had this page on his website for years. While we don’t know exactly what the 2021 season will look like in this regard (deadened ball, no DH in the National League, etc.), 2019 seems like a decent proxy, Here’s what the 2019 looked like in terms of run expectancy:

With runners on second and third and none out, an average of right around two runs scored in the rest of the inning in 2019. By comparison, only a run scored, on average, after both first and second, one out and man on third, one out. And, of course, as you move towards the bottom left (more outs, fewer baserunners), the run expectancy really plummets, all the way down to two outs, none on resulting in just 0.11 runs on average.

Of course, the table above is missing the context of how often each situation comes up. For that, see below.

League OBP is not particularly high these days, and as a result, close to six out of every 10 PAs take place with the bases empty. Of course, a quarter of all PAs are none out, none on — after all, every inning starts with one, and if every inning was three up, three down, this proportion would be even higher.

Why present both of these? Primarily, they serve as a useful baseline for any kind of lineup analysis, even without further math. But, importantly, we can combine them to calculate a weighted average run expectancy, which in this case, happens to be 0.51. In other words, in 2019, in any inning, the average number of runs expected to score was 0.51. (Runs per game per team in 2019 were 4.83, which is inherently consistent with the very basic idea that each half-inning scores a bit more than half a run.) So, scroll back up to the first table above. The color-coding is based around this 0.51 figure, such that below it is red (and gets redder) and above it is green (and gets greener). Someone who somehow always bats with none out, none on, is really just getting some pretty generic situations to make runs happen (0.53 versus 0.51). Batting with the bases loaded is of course conductive to making runs happen; hitting with two out, none on is awful. This is all basic stuff, all we’re doing above is putting numbers to it.

So, let’s talk about how hitters actually contribute to these numbers. Both are pretty obvious, but it seems like most of the focus is on the whole “come up with men on base” thing. Look at Freddie Freeman’s quotes in Mark Bowman’s recent article (emphasis mine):

“The two-hole with the pitcher hitting, the opportunities for RBI situations aren’t as great,” Freeman said. “But I do realize hitting in the two-hole over 162 games, you’re going to get way more plate appearances than you would in the three-hole.”

Those are the contrasting sides of the argument. Would it be better for Freeman to compile more plate appearances while batting second? Or would it be better for him to compile more run-producing opportunities while batting third...

To argue whether he should continue batting second or move back to the third spot, it’s more important to look at the number of plate appearances and run-producing situations he might encounter in either spot.

With the DH in place in 2020, Freeman logged 125 plate appearances over 26 games batting second. That equates to 4.8 per game. He came to the plate with a runner in scoring position in 28 percent (35 of 125) of those PAs.

Conversely, Freeman logged 134 plate appearances over 32 games batting third. That equated to 4.2 per game. He batted with a runner in scoring position in 26.9 percent (36 of 134) of those PAs.

Now, when the DH wasn’t in place during the 2019 season, the second spot in the order (756 PAs) came up just 21 more times than the third spot (735 PAs) for the Braves. But a runner was in scoring position more frequently for the third spot (23.6 percent) than for the second spot (21.8 percent).

So, the likelihood of runners being on base (and on which base, and with how many outs) drives run expectancy. But, notably, neither Bowman’s article nor Freeman as quoted in the article touched on the other part of the equation: a hitter’s ability to reach base also drives run expectancy. It’s not just about who you can knock in, it’s also about whether you can be knocked in if you reach base. And this is where the focus on “opportunities” falls woefully short.

Again, go back to the first table. None on, none out has a slightly above average run expectancy. Add just an out, and you’re down to around 60 percent of average. With two outs, none on, you have the worst situation possible — only about 20 percent of average. Why is two outs, none on so bad? Partly because reaching base doesn’t really help your teammates that much. A single or a walk with none out moves the needle from 0.5 runs to 0.9 runs; with one out it goes from 0.3 to 0.6. But with two out, reaching base does comparatively little: 0.1ish to 0.2ish. A double is similarly far less useful with two outs. Why am I belaboring this point? Because the discussion seems to ignore it. The value a batter brings isn’t only in driving in runs — it’s also in getting on base to be driven in. So if you have a hitter that is good at getting on base, you should probably try to bat him in situations where getting on base is, well, more helpful than two out, none on.

Alright, let’s wheel over to the whole Freeman “dilemma.” (Note: it’s not a dilemma, it’s like a minor kerfuffle at worst.) In 2019, Freeman spent the whole season hitting third. Ahead of him were mostly Ronald Acuña Jr. at leadoff, and a combination of Dansby Swanson and Ozzie Albies hitting second. Here’s what his distribution of base-out states looked like:

Relative to the first one of these posted above, Freeman came up way more with two out, none on, and fewer with the bases empty and fewer than two outs. His overall proportion of batting with a man on base was just about the same as league average, though this isn’t as grim as it sounds because the first table of this sort also included players in the AL. Further, relative to this same “an average player anywhere,” he actually had a lower rate of PAs with runners in scoring position. In short, this chart makes it fairly clear that batting Freeman third was really kind of lame: the Braves were giving their 138 wRC+ bat some pretty mediocre opportunities, run expectancy-wise. The big kicker, of course, is that 24.1 percent in the bottom left: nearly one in four Freeman PAs in 2019 came in the worst possible situation out of all of them. That’s brutal. Overall, if you derive a weighted average of run expectancy with these percentages, you get 0.47 — not much worse than league average, but still pretty underwhelming given that it’s Freddie friggin’ Freeman we’re talking about here.

(A small note here that this is not unfairly driven by Acuña and Albies/Swanson hitting in front of him. The 1-2 hitters for the Braves combined for a .345 OBP ahead of Freeman, way better than league average, and middle-of-the-pack among 1-2 hitter combinations in MLB that year. Freeman was in no way hurt by the guys ahead of him in terms of the opportunities he faced, though you could say he wasn’t particularly helped either.)

Given that Freeman and Bowman discussed hitting second, it’s only fair to do the same analysis for the two-hole in 2019, batting primarily behind Acuña (and the pitcher’s spot immediately before that). Here’s what that breakdown looks like:

I’ll save you having to do the arithmetic by showing you the differences below, though you should be able to tell that it’s pretty blatant when that unfortunate 24 percent drops to just 10 percent, with corresponding increases in the other two base-empty states.

Overall, the changes include:

• 1.5 percent fewer PAs with a man on;
• Fairly minor changes in terms of batting with runners in scoring position, which rotate based on how you consider advanced during a PA;
• And the kicker: a weighted average run expectancy of 0.49 in the two-spot in lieu of 0.47 in the three hole.

Again, these aren’t big differences. They’re small. They don’t really matter. The usual player variation season-to-season is going to drown them out. But when you discuss just the first two bullets above, you totally ignore that a big part of batting is reaching base for the next guy, and that’s way less useful when you hit third because of how often you reach base alone with two outs. When you combine that with the fact that the third spot also gets fewer PAs than the second spot, albeit to a really small degree, I’m not sure it looks like much of a contest. But it’s also a rout in a mostly-inconsequential talking point.

The reality is that none of this is new. This article is rightfully referenced all the time: https://www.beyondtheboxscore.com/2009/3/17/795946/optimizing-your-lineup-by. It’s the same stuff up above, already well-known by 2009. In particular:

The Book says the #3 hitter comes to the plate with, on average, fewer runners on base than the #4 or #5 hitters. So why focus on putting a guy who can knock in runs in the #3 spot, when the two spots after him can benefit from it more? Surprisingly, because he comes to bat so often with two outs and no runners on base, the #3 hitter isn’t nearly as important as we think. This is a spot to fill after more important spots are taken care of.

I’m sure the Braves are aware of this. I’m also sure that Freeman is aware of this. It’s just that this discussion rarely seems to mention “hey, coming up with two out, none on every fourth PA really sucks,” even though that’s the real sticking point about hitting third. Giving your better hitters more chances to hit with men on base is important, sure, but it’s only a piece of the puzzle. Hopefully future discussion of this topic brings the other piece, the one about reaching base to be driven in, into the fold as well.