An in-depth look at how Joc Pederson might hit against lefthanded pitching

I was discussing the Joc Pederson signing with a number of other SB Nation writers and editors and Ivan, a writer/editor at our SB Nation Braves site Talking Chop, offered me a detailed statistical analysis of how Joc might do against lefthanders playing for the Cubs in Wrigley Field.

I turn the rest of this post over to Ivan for that analysis, and thank him for this terrific detailed writeup.

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On Friday, news broke that the Chicago Cubs signed outfielder Joc Pederson to a one-year deal worth $7 million. This came across as fairly strange (to me, anyway) for a couple of reasons at the time, and another that manifested itself slightly later.

• The deal was way below any expectation for him, which were in the $18M/2 (MLB Trade Rumors) to $20M/2 (Fangraphs) range. Furthermore, this admittedly weird free agency season has not been one particularly ruinous to players, with many of those who have signed coming in above expectations — undershooting them by both length and average annual value (AAV) makes Pederson somewhat of an outlier so far.
• As reported by Jeff Passan and others, Pederson liked the opportunity in Wrigley because he could play every day and show he’s more than a platoon bat by succeeding against lefties. This is fairly unusual! In my mind, players who want to re-enter free agency quickly want to do so in a way that enhances their appeal to teams, and willingly taking more plate appearances where you lack the platoon advantage seems like a poor way to do so.
• Later that day, Eddie Rosario signed with Cleveland for $8 million on a one-year deal. Given that Rosario is generally expected to be worse than Pederson in 2021, this cemented the question in my mind.

That question, put plainly, is: how much did Pederson’s desire to bat against lefties harm his expected production (and therefore, his 2021 contract)?

To briefly examine this, we need some context. First, Pederson is, well, not good against lefties. Really, really not good. His career wRC+ against lefties is 59, albeit in just 385 PAs. That total is notable: after his rookie season, the Dodgers did not allow him to face more than 77 lefties in a season. As a sophomore, only 16 percent of his PAs came against southpaws (compared to 22 percent as a rookie). That rate fell to below 10 percent in 2019, and in 2020, he was allowed to stand in the box against just 10 lefties across 138 total PAs. This is, suffice to say, really low. For context:

In brief, the Dodgers used him as a standard lefty for a bit, and then BONK! Go to platoon jail, Mr. Pederson. Not that it wasn’t deserved: in 2015, Pederson managed a 90 wRC+ against southpaws, which is actually considerably better than how well the average lefty-lefty matchup goes for the hitter (80 wRC+ in 2015, between 80 and 88 from 2015-2020). Since then, though, it’s full-on yeesh: 35, 64, 38, 34, and then a silly 112 mark in his 10 2020 PAs. Nor is the fact that we’re talking about fewer than 400 PAs here driven by some unfortunate ball-in-play variance:

In aggregate, Pederson has underperformed his xwOBA against lefties by .012 since 2015 — it’s not a tiny gap, but he’s been awful against them either way. The Dodgers were well-justified in keeping him away. Since the start of 2015, only 78 lefty hitters have stood in against southpaws 350 times or more. Of those 78, Pederson has the second-worst wOBA and sixth-worst xwOBA. Since the start of 2016, going down to 200 or more PAs, he’s second-worst and 11th-worst out of 103, respectively. Since he had his lefty-hitting privileges mostly yoinked away in 2018, he’s fourth-worst and ninth-worst out of 117. You get the idea: Joc no hit lefties good.

I will admit that while I have a decent sense of how Steamer and ZiPS, the two holistic (i.e., not offense-only) projection systems hosted on Fangraphs work, I don’t know the specifics. To that end, there’s a bit of a black box when it comes to Pederson’s 2021 projections, which are screenshotted below:

You can see that nether system (nor Depth Charts, a blend of the two that uses Fangraphs staff assignments for playing time) sees Pederson as a full-timer. Yet, I can’t know exactly how many PAs he’s projected to lose due to platoon considerations versus other reasons. To answer my question, then, I’m forced to make two initial assumptions, neither of which true, but both of which are helpful to approximating the answer I want:

1. A “full season” is 600 PAs (this just makes math easier); and
2. Every additional PA Pederson would get would come against a lefty (this is not going to be true, but it might be close).

Note: there’s also an implicit assumption that the current projections assume some rate of facing lefties that approximates his history — I have no way of knowing whether this is true but I’m not sure why it wouldn’t be.

In any case, here’s a basic way to break Pederson’s Steamer projection down into component pieces:

The math here is internally consistent (and this is the same thing as the screenshot above, too, with just a bit more detail). Essentially, an average player is worth 2 WAR per 600 PAs. At a rate of roughly 10 runs to one win, you can very easily back in to the various numbers here using this formula. For example, for the Depth Charts row, 2.0/600 * 518 = 1.64+0.80-0.51 = 1.93, which is the 1.9 number. Due to rounding, a win not being exactly 10 runs, and so forth, you can’t perfectly replicate the WAR column with the other numbers, but you can get very close.

Note that what all of this says, in sum, is that Pederson will give you marginally above average production across his PAs. The combination of a well above-average bat and slightly above-average corner outfield defense (remember that “Total Defense” includes the heavy corner outfield positional adjustment, which is negative 7.5 runs per 600 PAs) gives you basically what he’s expected to be for 2021.

So, what if we add “facing more lefties” to the mix? In particular, what if we go up to 600 PAs, adding only extra lefties? That means +100 PAs for Steamer, +163 PAs for ZiPS, and +82 PAs for Depth Charts. We need to guesstimate how well Pederson will hit lefties. One way to do this is to take his career rate: 59 wRC+. Another is to take his career xwOBA: .263, which translates to roughly a 71 wRC+ (basic derivation without thinking too hard — among Dodgers with 50+ PAs 2015-2020, averaging Juan Uribe and Carl Crawford at .264/67 and .275/75 yields 71; it’s nowhere near perfect but close enough). There’s a third way too that may be more appropriate, but is also very optimistic: the regressed platoon splits method described by Tom Tango and Matt Klaasen. I won’t go into the math, but if I’ve done it right, this yields a .302 wOBA (89 wRC+). The reason this last approach yields a more respectable number is because it regresses platoon splits using a basis of 1,000 PAs against southpaws, and given that Pederson has fewer than 400 of them in his career, there’s a whole lot of regressing his performance against to the mean lefty platoon split that brings it up. So, in sum, we have a nice array of three options of what Pederson might do against lefties in 2021:

• 59 wRC+, based on his career outputs against lefties;
• 71 wRC+, based on his career “inputs” against lefties; and
• 89 wRC+, based on a regression of his platoon splits to league-average lefty splits.

The rest is arithmetic that really just requires converting wRC+ into batting runs. An easy rule of thumb: take the deviation of the wRC+ from 100, multiply by 0.80, and those are your batting runs over 600 PAs. (It mostly works, though the exact factor changes season-to-season. You can see it works reasonably well in the table above. Regardless of what season-to-season factor is used, the error from using 0.80 instead of something in the ballpark is going to be under a run.) For defense and baserunning, we just extrapolate the existing rates over the new PAs, since there’s not much reason for defense to change if Pederson is facing more lefties, and baserunning is so teeny it doesn’t really matter here.

The end results here are… not very inspiring for Pederson and for a decision to play him against lefties.

• In the worst case, where you assume he’ll hit lefties as well as he has in the past, he loses between a quarter and half of a win in his extra PAs, dropping his overall value pretty substantially, from 1.7 to 2.0 (with room for a platoon partner to add extra value) to 1.2 to 1.7 (with less room for said platoon partner).
• If you figure his inputs against lefties are more predictive than his outputs (they are), he loses less than half a win, but it’s still a loss. The new range is 1.4 to 1.9, and we’re really nitpicking fractions of a measure that isn’t meant to be quite this granular, but the point is that there still isn’t any real benefit here.
• If you do buy in to regression, wherein Pederson becomes a non-terrible play against lefties, he actually does accrue very fractional positive WAR in these extra PAs. But, it’s a tiny amount; a useful platoon partner should easily outproduce his marginal production, unless you’re so hard up for position player depth that you have no average bench players (0.5ish WAR per 600 PAs). The net increase here is 0.1 WAR (from 1.7-2.0 to 1.8-2.1), so, a big ol’ meh.

In the end, this was a lot of arithmetic to prove… essentially nothing. To summarize what we learned:

• Joc Pederson is bad against lefties.
• Even in the most optimistic, heavily-regressed scenario, the marginal gain to his numbers for playing games against lefties is teeny-tiny. It’s unlikely to be a net gain to his team, either, unless they have no useful bench players that could bat against lefties for him.
• The value proposition of his contract might actually be worse if the whole don’t-platoon scheme ends up happening. But, his contract is still a sizable bargain in absolute terms, and it’s still weird that Eddie Rosario, who ends up in the same range, out-earned him on the free agent market, if only by $1 million.

Joc Pederson and/or the Cubs’ decision to give him greater exposure to lefties may not fundamentally change his production profile away from its 2 WAR-ish central estimate (though, see the ZiPS rows in the table above!). Even so, it’s not too clear how it benefits him or the team. Even if you (and he) really believes that he will hit lefties at his regressed, 89 wRC+ rate, it wouldn’t prove to teams bidding for his services a year later that he’s a considerably better investment because he’s a full-time 2 WAR outfielder as compared to a platoon-type 2 WAR outfielder. Those teams (and all teams) would prefer the latter, as it frees up more PAs for someone to mash lefties and provide additional value.

I still wish the Braves had signed him; $7 million for average production is pretty spiffy, even if bad decisions give you some avoidable downside risk there.