Aaron Judge is going to break the all-time American League home run record while sometimes playing center field for a struggling yet playoff-bound Yankees team that he¡¯s keeping afloat nearly by himself. Imagine not voting him as the Most Valuable Player.

Shohei Ohtani is going to hit 35-plus homers while also throwing 150 innings or so of 2.50 ERA ball as a pitcher. He is not worse than he was when he won the MVP unanimously last year, and he¡¯s having another season without precedent, aside, of course, from himself. Imagine not voting him as the Most Valuable Player.

You can see why this conversation is going to get so impassioned. While we believe that Judge is likely to win the balloting, there¡¯s not really a wrong answer here. Both players are having all-time great seasons. To find a flaw in either is nitpicking. The award will matter, but it also won¡¯t. We¡¯ll be talking about these seasons for decades no matter who finishes first.

We won¡¯t and can¡¯t answer the question of ¡°which player deserves it more¡± today. But we do want to touch on an important part of the conversation, a topic that seems to come up a lot: Does Wins Above Replacement fail to capture Ohtani¡¯s full value? It¡¯s a metric that carries a lot of weight in the MVP discussion, and one that was never really built for a two-way player like Ohtani.

If, the thinking goes, he¡¯s not getting credit for being two players in one, perhaps his MVP candidacy should be boosted. So: Is that what¡¯s happening?

The short answer is: Maybe a little, but probably not by very much. The long answer is ¡­ complicated.

It¡¯s a question that might matter a lot. While MVP conversations are rarely -- and shouldn¡¯t be -- a simple ¡°rank the WAR¡± ballot, there¡¯s a pretty strong correlation between piling up the WAR and winning major awards. At FanGraphs, Ohtani is listed as having 8.2 WAR, combining his pitching and hitting, entering Wednesday. Judge is at 9.7 WAR. It¡¯s even closer, just a half-win gap, at Baseball Reference. If you think that much of that gap is ¡°missing credit¡± for Ohtani, then it¡¯s basically a rounding error between them, a tie -- which could affect some voting opinions.

This topic has been coming up for years, at least since 2018, when MLB.com¡¯s Tom Tango thought about it, and probably longer. Last year, as Ohtani¡¯s first truly great season ramped up, the Ringer, Baseball Prospectus and The Athletic all looked into how we could value Ohtani, and if current metrics were up to the task.

Much of those discussions were in the context of Ohtani¡¯s 2021 season and MVP race against Vladimir Guerrero Jr., and since the numbers, opponent, and rules have changed, it¡¯s worth another look. Let¡¯s set a date to be back here again next year, talking about the same thing when it¡¯s, let's say, ¡°Ohtani vs. Julio Rodr¨ªguez.¡±

So where are these numbers coming from? Let¡¯s get into what WAR is measuring, before we get into what it¡¯s not -- and run some hypotheticals on what it could or should be doing.

Where WAR is giving credit (position players)

Ohtani is getting credit for being two different and unrelated players, Ohtani the hitter (3.5 WAR) and Ohtani the pitcher (4.6 WAR). Put together: 8.1 WAR. Let¡¯s talk about the position player part of that.

As a hitter, 3.5 WAR sounds pretty good. It is pretty good. Yet it absolutely pales in comparison to Judge¡¯s 9.3 WAR. There are two pretty good ways to explain that.

A) Judge has been a better hitter.

This is the easy part. Though Judge has taken more plate appearances (611), Ohtani (585) isn¡¯t really far behind. But Judge¡¯s times up have been of a much higher quality, because even though Ohtani¡¯s .265/.356/.534 (146 wRC+) is excellent ¡­ Judge¡¯s .310/.414/.692 (206 wRC+) is better. By a lot. It¡¯s one of the 25 greatest hitting seasons in history, and it's top 10 if you just look at the integrated era. It¡¯s not just about the home runs. In WAR terms, he¡¯s been more than twice as valuable, in some part because -- and this will surprise people -- Angel Stadium is a friendlier hitting park than Yankee Stadium.

New stats or old ones, Judge has been the superior bat. He's even been a slightly better baserunner. This all isn¡¯t really up for discussion. Big advantage to Judge.

B) Judge adds value on defense.

Judge has rated as an average fielder, splitting time between center and right field.

Without getting too deep into the history of positional adjustments, WAR attempts to adjust for position -- being an average shortstop is a lot more valuable than being an average left fielder, for example -- and Judge has split his time between a hard position (center) and an easier one (right), so he¡¯s receiving a WAR credit of -0.6 runs, or about average.

Ohtani essentially does not play defense. One hundred and nine times, he¡¯s been the DH. Twenty-four more times, he spent part of the game as the pitcher before finishing it as the DH. (He¡¯s had all of eight fielding chances as a pitcher.) When the lineup turns over, when Judge fields, Ohtani sits (90% of the time) or pitches (10% of the time).

It¡¯s actually a lot easier for us to do this in 2022 than it was in 2021, because last year, when Ohtani hit, he was mostly a DH (88% of the time), sometimes a pitcher (10%), and sometimes a pinch-hitter or a corner outfielder (2%). This year, thanks to what¡¯s unofficially been dubbed ¡°the Ohtani rule¡± -- which provides that a starting pitcher who also serves as the starting DH can stay in the game to hit as DH when he stops pitching -- Ohtani has taken 99.5% of his plate appearances as a DH. He¡¯s just a DH.

So, we can compare him to other designated hitters, not to pitchers hitting. He¡¯s been the second-most valuable one, behind only Houston¡¯s Yordan Alvarez. But in order to get him on the same scale as players who field, he receives a minus-14.2 run adjustment (so far) as a DH. We¡¯ll get back to that.

Why is Judge so much more valuable as a position player than Ohtani? Easy, really. He¡¯s a better hitter adding defensive value at a harder position, compared to a lesser (if still extremely good) hitter adding no defensive value. That¡¯s exactly the kind of thing a metric like WAR should be calculating, and is.

Where WAR is giving credit (pitching)

Well, this one¡¯s easy.

Ohtani: 4.6 WAR
Judge: 0.0 WAR

This is one area where Ohtani has really upped his game from last year. He¡¯s striking out more, and walking fewer. Just in the last few weeks, he¡¯s thrown his hardest pitch and started throwing a new, impressive, sinker. Over his last eight starts, as the Angels¡¯ season has faded further from relevance, he¡¯s allowed 11 earned runs. Go back to the start of last June, when he decided to stop walking people, and Ohtani's got a 2.87 ERA over his last 235 innings. He won¡¯t win the AL Cy Young so long as Justin Verlander¡¯s ERA is below 2.00, but he¡¯ll be in the discussion after that.

Judge gets 0.0 WAR, because Judge is not a pitcher. Ohtani's time on the mound is considerably more valuable than Judge's time in the outfield.

That¡¯s how we got where we are. Judge is the most valuable position player, by a lot. Ohtani is the seventh-most valuable pitcher in the Majors, and the second-most valuable designated hitter -- at the same time, of course.

What are we missing? What if some of those things aren¡¯t favorable to Ohtani? Let¡¯s fiddle with some dials.

1) What if Ohtani was a pitcher hitting, not a DH hitting?

As we said above, Ohtani is considered a designated hitter when he pitches, and thus has a higher comparison bar to clear. What if he wasn¡¯t? What if for the plate appearances he had as a pitcher, we relieve him of that burden, and compare him not to, say, J.D. Martinez, but to Max Scherzer -- the hitting Max Scherzer?

It doesn¡¯t really work that way -- remember that Ohtani isn¡¯t a pitcher who is hitting, he¡¯s a pitcher who is also taking up the DH spot. It¡¯s not like gets to hit as a pitcher and also the Angels get a DH, which would be great value.

It also doesn¡¯t matter. Look at his 24 starts. Half have come at home. Ten came at other American League parks. Only two came in National League parks, which means that even under the old rules, he¡¯d have had all of eight plate appearances as a pitcher this year. It would, if you went through all the math, add something like one-tenth of a point of WAR.

¡°What if he was considered a pitcher hitting in all the other games too,¡± you¡¯re asking, and it would surely be a higher boost. It'd be more than a whole entire win, in WAR terms. But it also wouldn't reflect real life, because it's 2022. Pitchers don't hit. He's taking up the DH spot, same as every other team. The difference is just where he goes when he's not hitting.

2) What if he was a better hitter while pitching?

¡­ except there¡¯s a problem there. Have you noticed that Ohtani is a better hitter when he¡¯s not pitching? (For this view, we're more interested in "plate appearances in games he's pitching in," so it's 80 PA so far this year, not just the eight.)

2022 -- .736 OPS as a P, .924 OPS as DH
Career -- .787 OPS as P, .893 OPS as DH

This is not terribly surprising. It seems pretty hard to throw 101-mph fastballs and then go take swings. If pitching while hitting makes him a worse hitter, that's also not an aspect that we're quantifying in the conversation.

3) What about the extra roster spots he¡¯s saving?

This is the tricky part. He's theoretically allowing the Angels to get two players (a DH and a pitcher) out of one roster spot. That probably should have some value. But how much?

Here, it gets complicated too. The larger the roster, the less value this seems like it would have, and rosters have been larger. This year, rosters were 28 players for the first month. Then, in May, they shrunk to 26 players, but teams could still roster 14 pitchers. Only in June did we get back to to 26 players/max 13 pitchers, but for only three months, because in September, rosters went back up to 28 again.

It's almost certainly worth something. It's just not exactly clear how to say how much.

As Russell Carleton wrote, regarding the potential flexibility of Ohtani¡¯s versatility, ¡°we can start to see how that value can be a few tenths of a win. That¡¯s not huge, but it¡¯s real value.¡±

That sounds right. It's not that WAR is fully capturing the value of versatility, because it's likely not. It's that it's hard to see it being a massive amount of uncollected bottom-of-the-roster value when the Angels have, including Ohtani, all of 10 players worth at least 1 WAR. (While WAR is not team specific in this way, the Dodgers have 19. The end of a 28-man roster is an endlessly rotating collection of players.)

Ironically, if we¡¯re talking about Ohtani not getting credit for offering roster flexibility ¡­ we might want to talk about Judge capably stepping in as the largest regular center fielder in baseball history as the Yankees roster collapsed around him, and the value that's worth.

4) What about the extra roster flexibility he¡¯s costing?

We just blew your mind. But consider this:

The Angels cannot use their DH spot for rest. The team has had someone other than Ohtani start as a DH just eight times this year. Not that you¡¯re ever upset about having a bat like his there, of course, but it does prevent the Angels from using the DH spot as a ¡°half-day off¡± like many other clubs do. That might be relevant right now given that Mike Trout is managing a back injury, and can only DH when Ohtani does not.

The Angels have regularly had a six-man rotation since Ohtani¡¯s arrival. It¡¯s not entirely because of his presence. But the costs and benefits are extremely difficult to measure. On one hand, you¡¯re keeping Ohtani more rested, which seems important since his rest days are DH days. (Ohtani has never in his career pitched on four days' rest. Three-quarters of his starts have come on six days of rest or more.) On the other hand, a team that has trouble finding five starters now needs to staff six; studies about the effectiveness of it have been inconclusive at best.

5) What about the fact that the Angels aren¡¯t sniffing the playoffs?

Trick question, because this isn¡¯t something that WAR worries about at all. (Nor, increasingly, do voters; both MVPs last year came from non-playoff teams. If Judge and Ohtani were traded one-for-one, we¡¯re guessing both teams would be in similar positions to where they are now. The Angels have a better record than the Yankees since the All-Star break, anyway.)

Ultimately, you can make the argument that WAR isn¡¯t prepared to measure all the things Ohtani does. But it¡¯s also hard to make the argument that it¡¯s significantly missing out on what he offers, either. What the metric is saying -- two incredible players are having incredible years of similar, if differently shaped, value -- seems about right.

When it comes down to it, this isn't an MVP race that ought to be based on WAR, anyway. WAR is correctly telling you that they¡¯re the two best players in the league, by a lot, and that if Judge has an edge, it's a small one. Voters are going to choose based on what fascinates them more -- the Yankee breaking legendary records, or the two-way player continuing to do things you¡¯ve never seen before. There¡¯s really not a wrong answer.