The first casualty of batting left-handed is innocence

When working on a system for evaluating lineups using custom linear weights, I discovered a little sidebar problem that required solving first. When we’re looking at a player’s performance against a pitcher, we need to look at the platoon advantage. The optimal lineup against a right-handed pitcher is not the optimal lineup against a left-handed pitcher.

So the question we’re interested in answering is how, given a player’s projection or true talent level, how can we expect them to perform against left-handed pitching and right-handed pitching?

This isn’t exactly a new area of study; almost as far back as we have records of the sport people have known about the platoon split in baseball. When it gets down to brass tacks, Dan Fox wrote an article that inspired much of what’s below. The problem is that Fox used the sabermetric triple crown stats of AVG, OBP and SLG, and we’re looking for something to use with linear weights.

What we don’t want to do is look at an individual player’s platoon split, at least not without including a heavy dose of regression to the mean. Why?

Let’s take a look at the splits for Nick Johnson. Johnson clubbed RHP in 2008, putting up an OPS of .938, but struggled against LHP, putting up an OPS of .660. That’s a .278 OPS differential – surely a drastic platoon split, yes?

The problem is that we’re looking at a small sample of only 147 PAs. Well, that doesn’t sound so bad, does it? I mean, it’s not great – we’d love to have 700 or 1,000 or 1,500 PAs for every player, but 147 doesn’t sound that small.

The larger issue is that only 48 of those PAs came against LHP. That means that the sample size for our platoon split is only 48 PAs – because when looking at a split, the smaller sample size is the one that determines how reliable it is!

Now, Johnson is an extreme case used to illustrate a point. But even for players who have been in the league for quite a while (and even looking at several years of data), their platoon differentials can be fraught with sampling issues.

Now, the “correct” way to do it would be to regress each player’s platoon differential to the mean. If you are going to accept a shortcut for this, however, it’s best to use the mean, not the unregressed differential.

And here are some component platoon split factors for you to use. They were created by taking a look at the platoon split of every non-pitcher hitting between 1994 and 2007. I took all player’s production in that split and divided by their production against all pitchers, prorated out to the number of PAs in that split. So, if a player had 6 HRs in 50 PAs against LHP, and 12 HRs in 75 PAs over all, I counted it as 8 HRs in 50 PAs towards the totals.

The equation looks something like this:

(1B_SPLIT) / (1B_TOTAL/PA_TOTAL*PA_SPLIT)

BAT
PITCH
1B
2B
3B
HR
BB
HBP
IBB
K
L
L
0.99
0.87
0.86
0.79
0.93
1.64
0.20
1.20
L
R
1.00
1.03
1.02
1.05
1.01
0.87
1.19
0.96
R
L
1.00
1.06
1.00
1.08
1.12
0.67
1.54
0.93
R
R
1.00
0.97
1.00
0.96
0.94
1.15
0.74
1.03

A few notes. You are far more likely to be hit by a pitch facing a batter of the same handedness as you. You are far more likely to be intentionally walked by a pitcher of the opposite handedness as you. And these aren’t carried out to enough decimal places to show it so I’m not even sure it matters, but there actually is a reverse platoon split for right-handed batters when it comes to triples. That could just be a sampling issue, and as I said, when you round out to a sane number of decimal places it doesn’t matter.

The splits for left-handed hitters are more dramatic than the splits for right-handed hitters. The largest gap seems to be in power production; a player’s on-base percentage is less likely to change than his power production. The largest split for right-handed batters are the various kinds of walks; we talk a lot about “lefty-mashers” but the platoon advantage for right handed batters mostly ends up larding a player’s walk totals. One area of further study would be to see if these splits remain relatively consistent depending on the handedness of the batter in the on-deck circle; one possible explanation is that LHP tend to issue more walks that aren’t intentional but aren’t exactly accidental, either.

These are designed to be used much like park factors: simply multiply the component by its corresponding factor. For example, let’s take Adam Dunn. In 2008 Dunn to struck out 164 times in 651 PAs. If Dunn faced nothing but LHP, we would instead expect him to strike out 197 times
instead. If Dunn faced nothing but RHP, we would expect him to strike out 157 times.

That of course presumes that Dunn faced a typical mixture of LHP and RHP. He didn’t. Your typical left-handed hitter faces a LHP in 16% of his plate appearances. Dunn, a full-time player, faced a 60/40 split of RHP to LHP. So we want to first figure out what Dunn would do against a traditional split ratio, then figure out what he would do against nothing but LHP or RHP.

So we now adjust Dunn’s strikeouts to match the usual ratio of pitchers faced for a left-handed batter. Dunn had 60 Ks versus LHP and 108 strikeouts versus RHP. To isolate a value from a context we divide instead of multiplying:

60/1.2 + 108/.96 = 158

That leaves us with 190 strikeouts against nothing but LHP, and 152 strikeouts against nothing but RHP.

Unfortunately this took up much more of my time that I would’ve hoped for, so the lineup-based linear weights will have to wait for another day.

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5 Responses to The first casualty of batting left-handed is innocence

  1. Brian Cartwright says:

    Colin, what did you use for the denominators? Most of the platoon effects are going to be in walks and strikeouts, and more strikeouts will result in fewer balls in play. I’m curious if there’s any platoon difference in babip.

  2. Colin Wyers says:

    Essentially it’s:
    Singles per PA / Singles per PA
    So depending on what you’re referring to, the denominator is either PAs or singles. (Or whatever the event is.)
    It’s essentially a truism that if a split changes a player’s walk, strikeout and home run rates, it changes their BIP rates – in other words it has to be true, because those are the only four available outcomes! (I guess there’s a very slight chance that the walk, strikeout and home run rates alter in such a way that the balance between the TTO events and BIP is still the same, but I’d consider it very unlikely.) The question is now what to do with that information.
    Ideally we’d do platoon splits (or park factors, projections, or almost anything else relating to a question about true talent as opposed to value) using DIPS components instead of traditional components; I’m treating everything as independent variables where really they’re dependant variables.
    I’m not even certain it’s much more work; it could just a question of mindset. It’s something to mull over.

  3. Mrs. Peterson-Kekich says:

    This chart suggests that batters hit singles at virtually the same rate vs. RHPs and LHPs — is that correct?

  4. Colin Wyers says:

    It’s a very modest differential – it shows up if I carry the splits out to three decimal places. But it’s a very subtle difference. Walks, strikeouts and extra base hits seem to be the big-ticket changes in platoon differential.

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