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Look now, look again: Charlie Culberson and the mockery of xwOBA

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Charlie Culberson is doing some things that no one has done before.

Miami Marlins v Atlanta Braves Photo by Mike Zarrilli/Getty Images

There are many ways that this article could start. One of these ways could be juxtaposition: showing the Charlie Culberson of yore, compared to the Charlie Culberson of the here and now. For example, did you know that if you added together Charlie Culberson’s 2016 and 2017 wRC+s, you’d get a number (121) lower than his 2018 wRC+ (125)? Or, did you know that if you draw a chart of Culberson’s cumulative career wRC+, that it basically consistently stays within a range of 50 to 70, until around July 7, where it’s steadily climbed above 80 for the first time in his career? Or, even better, the article could have simply pointed out that prior to arriving in Atlanta, Culberson had accumulated negative 2.4 fWAR in 443 plate appearances, and then contrasted that with the fact that he’s provided 1.1 fWAR in 250 plate appearances since.

That would be one way for it to start. Another would be with a “sorry not sorry” version of a mea culpa: after all, I’ve probably been among the most vocal in decrying Culberson’s existence on this roster since he was acquired as an oddball spare part in the deal that sent Matt Kemp back to Hollywood. I had good reason: IWAG projected Culberson for -0.5 WAR in 306 PAs this year, or -0.9 WAR over a full complement of 600 PAs. Needless to say, that projection has been turned on its head. Weirdly enough, Culberson has actually been something akin to the most productive player in that deal, as Matt Kemp has once again faded down the stretch and currently sits at 1.2 fWAR in 431 PAs, while Adrian Gonzalez was released by the Mets (released by the Mets!) in early June after putting up -0.3 fWAR, and Brandon McCarthy suffered injury and adverse variation in his HR/FB rate to grant him just 0.2 fWAR in fewer than 80 innings pitched so far this season. (Scott Kazmir hasn’t thrown a pitch all year, either.)

But, had I not started this article with a discussion of how I otherwise would have started that article, I probably would have said something like the following: Charlie Culberson’s 2018 season is a demonstration of why baseball is, frankly, the best. You see, baseball is this delicious mixture of what should happen and what does happen. We can think about competitive activities as games of chance versus games of skill, but baseball, like most of humanity’s favorite pastimes, is a mixture of both. Pure chance is too chaotic to be consistently fun: games of pure chance lack the depth to hold the interest of both, as the Skinner box nature of them is laid too bare. Meanwhile, pure determinism is tricky to think about -- the best example is probably something like chess, where nothing is really left up to chance. And hey, lots of people love playing chess, and some people probably love watching chess. But I’m not sure chess fandom can clasp its scrabbling fingers across one’s heart the way an activity with both skill and chance can. (This is probably why you see the World Series of Poker televised, but while it has flirted with showing blitz chess occasionally, ESPN’s overall time spent showing chess matches is comparable, or even lower than, the time it spent televising Magic: the Gathering tournaments in the late 90s.)

(Oh God, I’ve gotten so far off track. Sorry.)

Anyway, the point is that baseball is great, because we have all these wonderful stats telling us what will probably happen. Only for us to turn on the games, and see the exact opposite happen. It’s maddening, but if it were any different, it probably wouldn’t be nearly as interesting.

So, the entirety of this article stems from that idea, and the contrast between these two statements:

  1. Charlie Culberson has been the 13th-most productive player on the entire Braves roster so far this year.
  2. If I could, I’d probably still kick him off the roster [provided that it were possible given MLB roster rules to acquire a replacement in time].

The first statement is a fact; the second statement is very much an opinion. I’m not going to try to convince you that the second statement is an opinion you should also hold; that’s almost beside the point at this juncture. Rather, I’m going to talk about how Charlie Culberson got “here,” because it’s a “here” that almost no other player gets to.

What the hell is xwOBA, anyway?

In order to have this conversation about Charlie Culberson, we first need to talk about xwOBA. But before we talk about xwOBA, we need to talk about wOBA. wOBA is basically the generic offensive statistic these days. Batting average is lame, because it excludes walks, but counts homers and singles the same. On-base percentage is not great, because it treats walks, singles, and homers all the same. Slugging excludes walks, and says a double is twice as valuable as a single, which, in practice, it isn’t. On-base plus slugging (OPS) is a crime against math and logic. Setting all these aside, we have wOBA: a statistic that still appears as a rate, but weights each positive offensive outcome differently. Higher numbers are better, and the value of each outcome is proportional to how many runs it contributes to during an “average” situation. If you take wOBA and adjust it for park and league, you basically get your best-in-class hitting statistic: one that gives you the most accurate picture of the value of the offensive results a player generated.

The “problem” with wOBA, though, is that same thing discussed before: baseball isn’t purely deterministic, or even close. wOBA is based on results, but in baseball, outcomes aren’t deterministically determined by their inputs. In other words -- an obliterated line drive can be hit right at a fielder. The wOBA value of that is .000. Life isn’t fair. This is a lesson that Mike Trout learned on May 11, when he hit a ball at 118 mph… which was caught for an out. To be clear, that was the 14th-hardest ball hit this year… and all Trout got for it was an end to the game.

So, there’s your problem: usually when you hit a ball at 118 mph, you get a hit. The league’s wOBA on balls hit that hard this year is .883. But, Mike Trout got a .000. If Mike Trout hit a ton of balls at 118 mph or faster, his wOBA probably wouldn’t stay at .000. Crediting a player for what should happen based on how hard he hit the ball, rather than what did happen is the principle behind xwOBA. (The “x” stands for “expected.”)

Said simply, xwOBA is the same as wOBA, but it ignores results. Instead, it cares only about two things, to the exclusion of everything else: 1) how hard the ball was hit; and 2) the angle at which the ball came off the bat. It doesn’t care where the fielders were. It doesn’t care about park dimensions. It doesn’t care about wind (even though I think there are non-public variants that do incorporate at least some measure of wind). It doesn’t even care about where on the field the ball is hit, so long as it’s in fair territory.

For all of the above reasons, xwOBA ends up being kind of weird. Remember that monster shot that Ronald Acuña Jr. hit at Marlins Park (“Which one?” you’re probably saying). Well, that one didn’t have an xwOBA of 2.033 (the actual wOBA for a homer), because some balls hit that hard (105 exit velocity) and that “high” (28.7 degree launch angle) still go for outs, or perhaps don’t go for homers. (The xwOBA of that Acuña monster shot was still a pretty egregious 1.842, but he’s hit homers with higher xwOBAs, like the one off Jason Vargas that gave him a 1.996.)

Why is xwOBA great?

Hopefully, the above already gives you a sense of what xwOBA does and doesn’t do, and why it’s more useful, for certain things, than wOBA. A lot has been written about the utility of xwOBA, which I’ll quickly list a few below for those interested in doing more reading:

  • Craig Edwards on Fangraphs opined on the uses of xwOBA here.
  • Jonathan Judge did a detailed study on xwOBA (for pitchers) here, which includes some interesting response and discussion from MLB Advanced Media honcho Tom Tango.
  • Various team-level reviews of xwOBA versus wOBA at points in time: White Sox, Giants, Cubs, Pirates, and so on.

In baseball, it’s hard to take anything for granted. A lot of times, we want to say “this guy is a solid/consistent producer, so he will once again produce solidly and consistently,” but baseball always has a way of mocking us. (See the 2018 seasons of both Nick Markakis and Ender Inciarte, for opposite reasons.) If we set that mockery aside for a minute, however, xwOBA gives us a measure for a hitter to regress to, regardless of what his results have actually been. I think of xwOBA basically as a way of supporting the statement of, “If Player X continues to make the same contact he already has, we should expect his wOBA going forward to be equal to his current xwOBA.” That’s a pretty useful stat, don’t you think?

The basic thing about xwOBA is that you can use it in comparison with a player’s wOBA. If the xwOBA is higher, the player has gotten “unlucky.” If the xwOBA is lower, the player has gotten “lucky.” If you don’t like the word “luck” because you feel it’s too charged with inappropriate meaning, you can use “has been hurt by random variation” and “has benefited from random variation” instead. (Some people get weird about the idea of luck; Robert H. Frank’s Success and Luck: Good Fortune and the Myth of Meritocracy and the reactions to it are good examples of this weirdness.)

xwOBA-wOBA gaps in the population of players

This might seem obvious, but I think it’s important to demonstrate: xwOBA-wOBA gaps are (mostly) normally-distributed. (That’s a fancy way of saying they follow a bell curve.) Because wOBA will regress towards xwOBA, the gap trends to zero over time. That means that in any decently-sized sample, there will tend to be more players with a very small gap than a larger one, and the greater the gap (in either direction), the smaller the array of players with that gap.

2015

2016

(Okay, this one isn’t quite normal and that’s a little strange. I’m not exactly sure what the deal is with some of smaller gaps not following the normal distribution pattern, but the point is that as you actually get into bigger gaps, you see the expected pattern.)

2017

(Again, this is mostly normal but there’s also some weirdness here, with more players having a very slight underperformance of xwOBA. Either way, it still demonstrates the idea that severely underperforming or overperforming xwOBA is unusual.)

2018

And then we come to 2018, where the distribution is skewed to the right, because of either: A) xwOBA now includes sprint speed, making it harder to outperform xwOBA and/or B) the ball’s relative de-juicing since xwOBA was calibrated in 2015 has made the league underperform an xwOBA based on a juiced ball as a whole. I’m actually not sure that A) is true, so it might be just B). Anyway, the point is that once again, it’s unusual to deviate from your xwOBA, and in 2018, it’s even more unusual to overperform it by a lot, relative to underperforming it by a lot.

Back to Charlie

So, that brings us back to Charlie Culberson. Baseball Savant has a very handy leaderboard of xwOBA outperformers, which you can access here: https://baseballsavant.mlb.com/expected_statistics?type=batter&year=2018&position=&team=&min=100

If you click that link, you’ll see this glorious mug at the top of the leaderboard once you sort by “overperforming xwOBA” using the “Diff” column:

There he is, all alone in first. If you spend some time on that page, you’ll see that the xwOBA column is colored. The deeper the red, the better the player’s “inputs” at the plate. All of these five players have had blue/”cold”/relatively bad “inputs.” Yet, their “outputs” (results) have been average or better (league-average wOBA is .315 this season). In other words, we’re not talking about either guys who crush the ball and have had good results, just not as good as they’re owed. Nor are we talking about guys who make piddly contact and get lucky, but are still having bad results. This is basically the exact subset of guys who you might derisively refer to as “just getting lucky” -- their inputs are bad, and their outputs are okay-to-good.

The thing is, someone always wins the lottery. And, while being the guy who overperforms his xwOBA the most isn’t quite like winning the lottery (there are fewer hitters than folks who buy lottery tickets, for one), it’s still something where someone has got to do it. In this case, that someone is Charlie Culberson. (At various points this season, it’s also been current runner-up Alen Hanson, but the idea still stands.)

In 2018, through Friday’s games, Charlie Culberson’s wOBA exceeds his xwOBA by .077. Since Statcast began tracking and calculating xwOBA in 2015, no player-season with 100 or more PAs has ever had an overperformance of xwOBA greater than Culberson’s .077 mark. Not only that, but it gets even more wild: the maximum number of PAs for any player-season from 2015 onward that outperformed xwOBA more than Culberson’s .077 is… 63, done by Franklin Barreto so far this year. Basically, Charlie Culberson is doing in 250 PAs what most players can only “achieve” in about 50, before the random variation evens out and their wOBAs trend toward their xwOBAs. Basically, Charlie Culberson is making a mockery of xwOBA, is what I’m saying.

A Brief History of Culbersons extreme xwOBA outperformers

Let’s set some parameters, and say that we’re interested in players who:

  1. Like Culberson in 2018, exceed their xwOBA by more than 0.059. If you look at the histograms above, that’s around the cutoff for the rightmost bin.
  2. Had 100 or more PAs in a season. Normally, I would use 200 PAs, which was the same cutoff used to make the histograms, but I want to be expansive because having more names is more interesting than having fewer names.
  3. Had a below-average xwOBA to go with their xwOBA outperformance. The point is to identify “poor hitters” who mocked xwOBA, not good hitters who got even better fortune than they were entitled to.

With those parameters, here’s what we get, from 2015 onward. Nte that the third parameter was irrelevant to the actual pull of data: no hitter that outperformed xwOBA with 100+ PAs as described in the first two parameters was actually an above-average batter. That’s a separate topic, but suggests that extreme xwOBA outperformance is limited to weaker hitters for whatever reason.

The short version: blue shading means that after his xwOBA outperformance year, the player performed more closely to what his xwOBA said he would do than his wOBA; yellow shading means the opposite.

The first thing that jumps out at me is that so many of these guys were fringe guys. Of the 13 guys on this list whose outperformance was before this year, only five really got even part-time exposure afterwards. The second is that, well, there’s a lot of blue, but perhaps not as much blue as you might expect. Dee Gordon never really became a good hitter, but he did manage to substantially outperform his xwOBA for three straight years (thanks, footspeed). Curt Casali’s 2017 and 2018 are small samples, but he actually took the route of improving his xwOBA, which is also not something you see a lot with this group of players. Jackie Bradley Jr. made some serious offensive strides after his 2015, but still regressed in 2017, and suffered the cruel twist of fate this year that he’s actually severely underperforming xwOBA. Cosmic justice for his 2015, I guess. Drew Stubbs continuing to outperform his xwOBA while improving it in 2016 didn’t really save his career. David Dahl outperformed his xwOBA in 2016, missed a year with injury, and has looked overall better this year, though his line isn’t actually all that impressive given that he plays his home games at Coors.

Andrew Benintendi is probably the sole unequivocal success story on this list: e got very lucky when first called up, but as his luck evaporated, his talent picked up the slack. In Benintendi’s case, his xwOBAs (and wOBAs) caught up to his outperformance; in most other cases, the xwOBA served as the magnet that pulled future wOBAs to itself. Some of these cases almost look tailor-made to serve as words of warning: Eduardo Nunez had a .280 xwOBA and a .342 wOBA last year. He parlayed that into a one-year deal with a player option, and then ended up with a .282 xwOBA and .283 wOBA. It happens. A lot, apparently.

Given the above, you can think what you want about Charlie Culberson. But with his xwOBA looking much closer to his prior xwOBAs which resulted in fairly dreadful batting lines, there’s little reason, in my view, to expect that he’s changed for the better. While I guess there’s always the off-chance that he actually improves next year, he has the same chance of doing so as any other hitter -- there’s nothing about his profile that actually suggests that his xwOBA is going to grow later to catch up to his wOBA, rather than the opposite happening and his wOBA slamming back to his xwOBA.

Look now, look again: mockery squared

The section above this one was about an xwOBA outperformer having success after the season in which he outperformed his quality of contact. That’s one way to think about the after-effects of outperformance, but not the only one. If xwOBA is as harsh and unyielding a mistress as we like to think, then it shouldn’t wait for something like an offseason to reassert its authority, right?

To that end, I looked at xwOBA outperformers in the first half of a season’s games, and what happened to them in the second half. I used the same parameters as last time, including 100 PAs in the season’s first half (defined as through June 30), to develop the list of players below. Note that this table includes players with above-average xwOBAs, too, though the results don’t really change if they’re removed.

At this point, you shouldn’t be surprised by the fact that there’s more blue than yellow. But here are some things you should know:

  • First, yes, I cheated. Charlie Culberson doesn’t technically make the cutoff to be included in this table; his first half 2018 xwOBA-wOBA gap isn’t large enough. But that actually illustrates an interesting point, and the purpose of this section. In short: no player with a substantial xwOBA/wOBA gap in a season’s first half saw that gap increase in the second half… except 2018 Charlie Culberson. I also went back to examined every player with a first-half gap of .051 or more. None of them increased their gap in the second half; only one (Eddie Rosario, 2015) matched his gap. The rest saw declines, usually massive ones. Charlie Culberson is the only player in the Statcast era to increase his substantially large first-half xwOBA-wOBA gap in the season’s second half. Of course, the season isn’t over yet. But he’s also more than doubled it! Even if it regresses somewhat, unless he gets horribly unlucky from here on out, it’s going to stay doubled-ish. That’s a true mockery of xwOBA right there.
  • Among these 24 players, second-half wOBA does tend to exceed first-half xwOBA by about 0.020. There are many explanations for this, the most obvious of which is regression to the mean broadly interpreted, but the point is that outperforming your xwOBA in the first half doesn’t mean you’re going to crash and burn in your second half. It just means your true performance level isn’t going to be quite as high as your actual wOBA suggests it is.
  • But, by comparison, second-half wOBA for these 24 players, on average, falls short of first-half wOBA by over 0.055. So, yes, there’s going to be a decline in production. Only one of the 24 players, Cheslor Cuthbert, managed a second-half wOBA higher than his first half wOBA. Hand-in-hand with this, the preponderance of blue on the table suggests that if you had to pick one value (either the player’s first-half wOBA or his first-half xwOBA) to predict his second-half wOBA, you should choose the xwOBA. That seems obvious, perhaps, but this table reaffirms it.

And that just makes what Charlie Culberson has done far more insane: yes, he raised his xwOBA by about 0.015 in the second half. But his wOBA has gone up by more than 0.075. Mind-blowing, really.

So, there you have it. Charlie Culberson has been phenomenal so far this year. That much is true. But, his xwOBA is tied for the lowest among position players on the active roster (with Dansby Swanson), and is barely above that of Julio Teheran (.281 to .278). Maybe you believe in him anyway. But, given all of the above, I don’t think I do.

As a final shot, there’s actually something really amusing about Charlie Culberson’s xwOBA. Right now, he is tied with his veritable twin, Dansby Swanson: they’re both at .281 in that metric. Swanson has had some good fortune himself, as his wOBA sits at .293. But can you imagine had he gotten his doppelganger’s xwOBA outperformance gift instead? He’d have about 1.8 more fWAR (assuming the outperformance held over his 430+ PAs) and be en route to a four-win season instead of barely clawing towards 2.0 WAR. Of course, the outperformance probably wouldn’t hold over 430 PAs... but it shouldn’t be holding over Culberson’s 250 PAs either.

[All data sourced from Baseball Savant. Data through August 24-26, 2018.]