Can Andujar hit enough to overcome his glove?

Third-base prospect Miguel Andújar is the talk of Yankees camp, for obvious reasons. In his first five spring games, he crushed four home runs, plus a double. It's important to point out that Spring Training stats rarely matter, and that's especially true when it's a sample of merely five games. It's reasonable, too, to point out that not a single one of the pitchers he took deep have established themselves as quality Major League arms.
We're making those caveats because we have to, Spring Training hype being what it is. But all that aside, there's no argument that Andujar can mash. He hit .315/.352/.498 across two Minor League levels last year, and even in just eight Major League plate appearances, he made an impact. One of his five hits was a single with an exit velocity of 112.1 mph; only 15 percent of the 614 non-pitchers with five plate appearances managed to do that even once. You don't hit a ball that hard by accident. It's a skill. Andujar has it.
What he might not have, however, are the defensive chops to stay at third, as the reports on his fielding have been mixed, at best. "He still needs to polish some rough edges on defense," reports MLB Pipeline, which also notes his "lapses with his footwork and throwing accuracy."

This raises an interesting question for the Yankees, as they attempt to sort out a second-base/third-base logjam that includes Andujar, Brandon Drury, Tyler Wade, Ronald Torreyes, Gleyber Torres, and non-roster veterans Danny Espinosa and Jace Peterson: How much offense would Andujar need to provide to overcome poor defense?
It's a difficult question, because we don't have reliable defensive metrics on a player who has yet to make a Major League start in the field. (He entered in reserve in three games, compiling nine innings.) Instead, what we can do is to look back at previous slugging third basemen with poor defensive metrics, and try to eyeball what it took for them to still be league-average players (which we'll define as two Wins Above Replacement, FanGraphs style). For the purposes of this view, we'll exclude baserunning value, which has a minor but non-zero impact on WAR.
If he's unplayable at third…
Over the last 10 seasons, there have been 344 player seasons of at least 500 innings at third base, or approximately one per team per year. Single-season defensive metrics have their obvious limitations, but the bottom of the list more than passes the smell test. Ryan Braun in 2007 (-27 defensive runs) and Mark Reynolds (-21 in 2011) never again played the position regularly. The third-lowest score belongs to 2014 Nick Castellanos (-16 defensive runs), and while it took a few more years, he's now a right fielder.
That year, Castellanos was a below-average hitter (.259/.306/.394, a 95 wRC+), a combination which made him a below-replacement player (-0.5 WAR). Reynolds hit 37 homers in 2011, but that's about all he did, as a line of .221/.323/.483 (116 wRC+) was more good than great, and the combination became a 0.1 WAR, or only slightly better than Castellanos.
Braun, however, mashed in 2007, hitting .324/.370/.634 (155 wRC+) on his way to winning NL Rookie of the Year. But the defense was so bad -- remember, he's played literally zero innings at third base since -- that it added up to 2.5 WAR, or slightly above average.
For context, Giancarlo Stanton put up a similar line last year (.281/.376/.631, 156 wRC+). So, if Andujar's defense grades as poorly as Braun's did, he merely has to hit like the reigning National League Most Valuable Player. No pressure, rook.

If he's merely below average at third…
The better his fielding gets, the less his bat has to carry the weight, and no one really thinks he'll have as tough a time as Braun did. Let's say that instead of being a -20 fielder, he's just a -5 fielder. That's Castellanos in the last two years, ending his hot-corner tenure, or Yunel Escobar in 2015.
As it turns out, these are some fortunate comparables. Escobar was league average in 2015 (2.1 WAR), hitting .314/.375/.415 (120 wRC+). Castellanos hit slightly worse (.272/.320/.490, 111 wRC+), and was worth slightly less (1.7 WAR). You can immediately see what kind of bat you'd need to go with below-average fielding.
This seems the most likely outcome, where Andujar is a poor-but-not-atrocious fielder, while being a good-but-not-elite hitter. If he combines this glove with, say, the .282/.325/.490 (115 wRC+) that Corey Dickerson put up last year, he'll be a league-average player. That's a lot more valuable than it sounds.

If he's average at third…
We're not going to pretend Andujar is going to be a plus defender at third, at least not right away. He only just turned 23 on Friday, so there's still plenty of time for improvement, but for 2018, the best-case scenario is that he's league average defensively. What then?
Now we're talking about 2014 David Freese (+1 run), or 2014 Aramis Ramirez (+1 run), or 2016 Todd Frazier (-2 runs). Each ended up more or less around league average, roughly 2 WAR. Each had similar hitting lines to get there:
2014 Freese: .260/.321/.383 (105 wRC+)
2014 Ramirez: .285/.330/.427 (109 wRC+)
2016 Frazier: .225/.302/.464 (104 wRC+)
Though they got there in different ways, all three had slightly above-average bats, average gloves, and average seasons. The 2017 batting equivalent of this would be if Andujar hit like Kyle Seager (.249/.323/.450, 106 wRC+) or Adam Jones (.285/.322/.466, 107 wRC+), solid players who had decent-but-not-strong years.
Andujar can hit, we're reasonably sure of that. But he'll have to field at least a little to make it worthwhile for the Yankees. After all, they do have other options -- and expecting a Stanton-like offensive season to carry his glove is probably just a little bit unreasonable.