Greenberg hit 331 career HRs and 1/7 of those would be 47.29. He had 53 against the Yankees. So a bit more than you would expect. The Yankees allowed a HR% of 1.52% over the years 1933-46 (he was in the military from 42-44 and good chunks of 41 & 45 so this is not quite right, but I hope it is close). The league average was 1.56%. So the Yankees were about average in terms of allowing HRs. Also, the Yankees and Tigers were just about tied for the lowest SLG allowed in the AL over these years, .351 (Tigers were 0.00064 lower-what teams allowed is in a table at the end of the post). They Yankees allowed the lowest average of .254. So against what might have been the best pitching staff of these years in the AL, Greenberg upped his game. Of course, the Yankee fielders might have helped.
He had a career HR% of 6.37% but against the Yankees it was 7.26%. So he did especially well against them. Here are his AVG-OBP-SLG against them: .333-.409-.667. His whole career was .313-.412-.605 (if we take out 1947, his year in the NL, they were .319-.412-.616). So he really hit alot better against them than other teams (probably walked less frequently)
In Yankee Stadium he had .319-.375-.608. Pretty good for a righty with that death valley they had, over 400 to left center. His HR% there was 5.45%. He probably had an SLG of over .700 against them at Tiger Stadium.
Why did he hit so well against them? Was it because he was from New York? Who knows.
Here are the top 25 guys in SLG vs. the Yankees since 1913 with 250+ PAs (from the Baseball Reference Play Index). SLGtot is their career SLG. Then the difference between their career SLG and what they did against the Yankees. Then how many PAs vs. the Yankees along with their BA and OBP.
It was not until the 1990s and 2000s that anyone came close to what Greenberg did (Rodriguez and Cabrerra). Tiger's pitcher Frank Lary (from the 1950s and 60s) was called "The Yankee Killer." But maybe Greenberg should have had that nickname.
Here are the top 10 in terms of how much better they did against the Yankees
Now those leaders with 400+ PAs
Here are all the right-handed batters with a .500+ SLG and 200+ career PAs in Yankee Stadium (I think this includes only the original park but both before and after the renovations of the 1970s when LF center was brought in from like 450 to 400 or so). Again, Greenberg is up there and no one passed him until Jim Rice in the 1970s and 80s, after the wall got closer.
Here is what each AL team allowed opposing hitters from the years 1933-46. The league averages were BA .270, OBP .342, SLG .368