A Thought on Ohtani, WAR, and Wow

(Yes this is the first time I’ve blogged in ages and it’s about baseball. Deal with it.)

Shohei Ohtani, you may have heard, is doing absurd things. The Angels’ principal designated hitter, he’s leading baseball in home runs, slugging percentage, OPS, OPS+, total bases… oh, and triples for good measure. Also he’s 7–3 on the mound with a 3.02 ERA, leading the American League in most strikeouts nine innings and leading all of baseball in fewest hits per nine innings. (Also most wild pitches and hit batsmen, but hey, who’s counting?) Same dude. It’s kind of wild.

A couple days ago, Dan Szymborski, a leading baseball statistician, tweeted some stuff about how we ought to consider Ohtani’s Wins Above Replacement value. Basically the issue is this: Ohtani’s WAR as a hitter treats him as a DH, even when he pitches, and that seems kind of weird to people! It feels like the positional adjustment for a DH, which is extremely penal at -17.5 runs per 162 games, is designed for guys who are a DH because they can’t play the field because they’re really bad at defense. It’s designed to capture the relative ease of finding a good hitter if you don’t have to worry about their ability to field. But you can’t find someone like Ohtani that way, because there isn’t anyone like Ohtani.

Szymborski, though, says that this is a mistake. WAR is about how much players help their teams win. It’s true that Ohtani, in both hitting and pitching, is incredible. But teams don’t need their pitchers to hit! That’s not actually a thing that helps teams win baseball games these days. Obviously both the hitting and the pitching that Ohtani does contribute, a lot — he’s leading all of baseball in total WAR this year, 5.9 to Ronald Acuna’s 4.4 — and there’s some value in the roster spot efficiency. But the sheer unicorn spectacle of it all isn’t actually especially valuable. And that’s what WAR is trying to capture. “If you want to know what’s special or cool or awesome,” Szymborski says, “you don’t ask a statistic.”

He’s right that WAR should be calculated the way it is. But… I don’t think he’s right about the last part. I think we can use the WAR framework to get a sense of just how insane Ohtani is. Because while this is the right way to compute WAR, we can also just… make different decisions about how to compute it, just to see. And I think that does a pretty good job capturing how utterly nuts Ohtani is as a player.

For his career, FanGraphs thinks that Ohtani-the-hitter has been worth 169.6 Runs Above Replacement, and 17.1 Wins Above Replacement. Of that, -61.8 runs above average owe to the positional adjustment for a DH. That doesn’t include anything to account for his time as a pitcher, partly for the reason Szymborski mentioned and partly because his first few years in the league he didn’t bat when he pitched.

We can start with the moderate version of the thought experiment. It’s true that AL teams, and all teams the last few years, don’t get any value out of having their pitcher bat, since they don’t have to. But what if we just gave Ohtani credit for being the pitcher in those games regardless, as if he were playing in the old National League?

It’s weirdly hard to figure out what the positional adjustment for pitchers is/was. FanGraphs has removed it from their stats library, if it was ever there. Reverse engineering off of Tom Glavine’s page, though, I get an estimate of something like +0.25 runs per game. (Alternately we could calculate it as about +60 runs per 600 plate appearances, but using games is a little cleaner for present purposes, and none of it really matters.) That would be an insane +40 runs per 162 games, but starting pitchers never played more than 35 or so games in a season; Glavine topped out at about +10 runs in a season total.

Ohtani has pitched 10, 0, 2, 23, 28, and 16 games in each of his seasons. Currently his stats include exactly zero runs of positional adjustment for these games, as best I can tell. If we want to credit him as though he were a pitcher for those games, then that’s just +2.5, +0, +0.5, +5.75, +7, and +4 runs in each season. That’s a total of +19.75 runs, which equates to about +2 additional Wins Above Replacement. That would boost him up from 17 to 19 for his career. Not nothing, but not a huge shift in how you’d view his career.

But this is not going far enough, is it? If we want to capture the sheer spectacle… well, even when he’s in the lineup as a designated hitter, we know that he is a very good starting pitcher. And starting pitchers suck at hitting! Since 2000, pitchers as a class never had a batting average above .150 or a slugging percentage above .200! We know why that is: it’s because they have to devote themselves to the craft of pitching, and hitting is hard. True, there’s also the fact that they’re not being chosen for their ability to hit. But some of them are better hitters than others: Glavine for example had a career .244 on-base percentage, which is really good (for a pitcher). Zack Greinke has a career .225/.262/.336 batting line, which would almost be tolerable for a shortstop.

Ohtani, again, is a career .273/.359/.549 hitter! And he pitches! He is simultaneously good at both of these tasks, which literally no one else has ever been able to be.

So what if we gave him a pitcher’s positional adjustment for all his games? Again, even when he’s in the lineup as a designated hitter, he is a person who is skilled at pitching, one of the better pitchers in the Major Leagues. That’s the spectacle we’re responding to.

First we have to remove the DH positional adjustment from his stats, those -61.8 runs currently on his ledger. That’s about +6 wins; now he’s up to 23 for his career. But then we have to give him +0.25 runs for every game he’s ever played. Actually we should probably disambiguate games where he’s in the starting lineup from ones where he’s not, since he has only one at-bat per game when pinch-hitting, compared to an average of 4.35 per game as a starter. Let’s say +0.05 runs per game as pinch-hitter?

He’s been in the starting lineup 592 times, and used as a pinch-hitter 54 times. So that’s uhh… +148 runs for the former, and +2.7 runs for the latter. Call it +150 total? Which brings his career to… 382 Runs Above Average, and something like 38.5 WAR. Well over twice his current figure. And whereas he’s currently 1123rd all-time in career WAR as a hitter, this would have him… something like 370th.

That’s a lot better, obviously, but still not that impressive… except that he’s only been in the league for six seasons, and has under four full seasons’ of games under his belt. Here are his adjusted WAR totals for each of these seasons, again, just evaluating him as a hitter, with the real figures in parentheses:

2018: 5.8 (2.7)
2019: 4.9 (1.7)
2020: 1.4 (0)
2021: 10.0 (5.0)
2022: 9.5 (3.8)
2023: 6.8 (3.9)

Now we’re talking! Those two seasons around +10, those are obviously up there with some of the great seasons of all time. And we haven’t even mentioned the part where he pitches yet! What happens if you add his pitching WAR (using the FanGraphs version based on runs allowed, which I like better for these purposes)?

2018: 7.2
2019: 4.9
2020: 0.9
2021: 13.9
2022: 15.7
2023: 9.6

That’s, uhhh, that’s…

Peak Barry Bonds put up seasons around 12.5. Babe Ruth’s very best season ever was 14.7, in 1923. The best pitching season on record is Pedro Martinez in 1999, 11.6 WAR, or, if you prefer RA9-WAR, Walter Johnson’s 16.2 in 1913 (excluding 19th century stuff when pitchers threw practically every day; the best mark of the live-ball era is Bob Gibson’s 13.5 in 1968). Calculated this way, Ohtani is on pace for something like 19 this year. If you want to take account of the fact that Shohei Ohtani is a very good Major League pitcher even when he’s at the plate, then it looks like these last three seasons from Ohtani have gone where no one has gone before. Oh, and his career mark of 52.3 WAR total would rank about 180th among position players, and something like 120th among pitchers. Fair enough I think to just combine those and say something like 300th all-time, in, again, what amounts to like four full seasons.

There’s another way to make a similar kind of calculation, though. We can convert so-called “weighted on-base average” directly into runs above or below average. Ohtani’s career wOBA is .379, good for +133.8 Runs Above Average from hitting. Roughly speaking every 20 points of wOBA above average corresponds to 10 runs per 600 PA. Ohtani’s had 2632 plate appearances, so he’s been worth about +30 RAA/600 PA for his career, so that indicates that the league-average wOBA is about 60 points lower than Ohtani’s, or about .320. That sounds about right.

The average pitcher’s wOBA, though? Well back in 2000 pitchers put up a .173 wOBA; by the time they put in the universal DH that had sunk to about .140. Let’s call it .150, shall we? Nice round number. Ohtani’s .379 mark is, well, like 230 points above that. That’s not 30 RAA/600 PA, it’s 115 RAA/600 PA! Babe Ruth, if you’re wondering, was about 78 RAA/600 PA.

Multiplying out by Ohtani’s career plate appearances, we get a revised figure of +504 RAA from batting. From +133.8 as currently calculated.

Oh, and I think that we should still be zeroing out his positional adjustment in doing this calculation, so that’s another 62 runs tossed onto the ledger.

The sum total, then? 602 Runs Above Replacement, and something like 61 Wins Above Replacement. Just as a hitter. You add back in his pitching and it’s around 75 WAR, something like 80th all time, counting pitchers and hitters both. In, again, six rather attenuated seasons.

I dunno why this is so much higher. Maybe the positional adjustment for pitchers is understated somehow?

Now I am not saying that we should use these kinds of calculations for things like MVP voting (note that if we did, he would’ve been eminently deserving over Judge last year, like not close to close). I think there’s a better case for using this for something like the Hall of Fame, and I think if you do then it’s pretty clear that he’s already a Hall of Famer, once he literally qualifies for the ballot anyway. But also just… if your sense is that he’s better at baseball right now than anyone’s ever been, you’re right about that. We can in fact quantify that you’re right about that! Last season was, if you want to view it this way, the single greatest season anyone’s ever had in the history of the sport, and this year he’s on pace to do even better, by like a lot.

Crazy stuff.