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How much has Aaron Judge’s injury cost the Yankees?

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A mathematical approach to the superstar’s wrist injury.

MLB: New York Yankees at Miami Marlins Steve Mitchell-USA TODAY Sports

By all accounts, the Yankees are on the precipice of Aaron Judge’s return. He’s taking on-field batting practice, and hitting balls hard. There’s still pain being reported, but you have to think that 80% of Aaron Judge is better than a whole lot of players that could be in instead of him. But what was 0% of Aaron Judge worth?

Judge has been out of action since July 23, and was put on the DL on July 27. At the time of the injury, he was fourth in baseball in fWAR at 5.0, and he still leads the team in that mark. A 155 wRC+ also paced the Yankees. It’s not an exaggeration to say that when Judge went down, he was a very real MVP candidate. The only players ahead of him when he fractured his wrist were Mookie Betts, Mike Trout and Jose Ramirez, pretty good company.

Since he’s gone down, the Yankees have obviously seen a drop in performance. There are no MVP caliber players just waiting for teams to pick them up as replacements. I found myself doing some back of the envelope math to see what the Yankees have actually lost in Judge’s absence, and then thought that I should move from the back of the envelope to the first sheet of an Excel workbook.

To start, we should know what production the Yankees got in lieu of their every day right fielder. The two chief replacements for Judge have been Shane Robinson and Andrew McCutchen. The former posted a 16 wRC+ and exactly 0.0 fWAR, while hitting a single, glorious home run:

Robinson was the definition of replacement level; he could be swapped out for any random Quad-A outfielder and we probably would not have noticed a difference. If Clint Frazier was healthy, that’s almost certainly what would have happened. For this exercise, that replacement-ness is actually very useful, because it provides a pretty neutral base for examining how much losing Judge has hurt the team.

After Robinson came McCutchen, in a trade a few hours before the waiver deadline. He’s only played nine games with the Yankees, so any statistical analysis is mostly noise. A 132 wRC+ and 0.3 fWAR means he’s been a baseball god relative to Robinson, but there’s really not enough data here to say what Cutch has actually contributed to the team. He’s been a sufficient patch in the leaky dyke, but you can’t say he’s been a success or failure at this point.

If we combine Cutch and Robinson, we see that the Yankees’ replacements for Judge have posted 0.3 wins, three home runs and a weighted average 67 wRC+, or WAwRC+, as I always say. I’ll give you a second to recover from the dry heaves. Surely Judge would have been better than that. The fun (?) part is, how much better?

So, at the time of injury; 5.0 fWAR, 155 wRC+, 26 home runs. Let’s start with the easiest to extrapolate, the home run total. Judge’s power is actually a little bit down this year compared to last. The difference between his 2017 and 2018 batting averages is a rounding error, but his slugging has dropped 80 points. He’s still hitting the ball about as hard as a human being physically can – his hard hit rate is actually up, but the chief culprit for the decline in power is a drop in flyball rate, more than seven basis points down from last year.

When he went down with an injury, just 36.1% of Judge’s batted balls were in the air. That’s the lowest mark he’s posted in professional baseball since he was in High-A, so I think it’s very realistic to say that number would have crept up if he had kept playing through 2018. Maybe it wouldn’t have gone all the way to 43.2% like last season, but when the players with the most similar batted ball profile to him in terms of GB/LD/FB rates – Yonder Alonso and Justin Upton – have been able to maintain about a 40% FB% this year, I think it’s safe to assume that Judge would have regressed towards that mean.

Combine that with the fact that he hits the ball harder than anyone not named Giancarlo Stanton, and his HR rate of 37.8/650 Pas would rise proportionately. Getting 3% more balls in the air, with a career HR/FB% of around one-third, means we could expect about four more home runs than the pace Judge was on, or 41-42 for the full season. Now, he’s projected for an average of three in about ten games by ZiPS and Steamer for the rest of the season, so it’s reasonable to conclude that the Yankees lost 12 home runs in the time Judge was out.

So the Yankees lost 12 home runs, but gained three from McCutchen and Robinson. That’s a net loss of nine home runs, and Tom Tango’s linear weights hold that a home run is worth about 1.65 runs, so the Yankees have missed out on 14.85 runs JUST off the loss of home run power. That alone is about a win and a half, which wouldn’t make that much difference in the division, but certainly would ease the anxiety around the wild card standings.

For Judge on a personal level, this power boost would put him at around 6.5 fWAR, which would be good enough for sixth in all of baseball at press time. That’s without incorporating Judge having his best baserunning and defensive season of his career so far. For a right fielder, a great defensive year – think Mookie Betts, always – adds about two wins. Judge was having a good defensive year, probably worth about one win over 150 games. Prorating that to the 40 he’s missed gives you about a quarter of a win, and the baserunning prorated would be another tenth of a win. All of a sudden, Judge would be knocking on the door of a seven-win season, and a good, healthy September stretch run would give him ashot at a second straight eight-win season.

For context sake, here is a list of all the players who have started their careers with two straight eight-win seasons:

Mike Trout, 2012-2013

Benny Kauf, 1913-1914

Joe Jackson, 1911-1912

That’s it. Judge could have joined one of the most exclusive clubs in baseball had he never been hit in July, and we’ll always be left wondering what if.

So to sum up, the Yankees have probably lost somewhere between one and a half and two wins already with no Aaron Judge. Depending on his actual return, and how long it takes him to get back to normal, that could balloon to closer to three wins. It may not end up mattering in the long run, but being up five or six games over the Athletics instead of two or three would make me feel a lot better personally.

There’s also the loss of what could have been a historic start to a career. Judge isn’t going to get to that eight-win threshold this year, but save for an errant inside fastball, he could have. Yankee fans were robbed of a chance at seeing something that’s only been done one time since the dead ball era, and that sucks. All we can hope for now is that Judge’s recovery finishes up, he returns to the lineup, and the Yankees get their MVP back.