This was originally intended as a normal comparison of the three players but more was added to show that, even for great post WWII players, there is data missing.
This link contains their data. The most relevant is repeated below. The splits and career data is simply copied from Baseball Reference. Below that I did the split sum and split difference.
Look at Home Runs. Mantle's splits add up but Mays and Aaron are off by 5 and 8 respectively.
Games are not added because they batted both (vs RHP) and (vs LHP) in many games.
I didn't try to do OBP (On Base Percentage - really average) because it gets a little hairy with no Sacrifice Flies (SF) before 1954. This also negates OPS (On base Plus Slugging).
I'm working on Righty/Lefty splits for batters with at least 250 HR (vs RHP) and at least 100 HR (vs LHP). There will be discrepancies. How should they be handled? For instance, Mantle's HR add up but his AB do not. That impacts his AB/HR rate. Not much but some. Most of the careers of Mantle, Mays and Aaron have full data. But for Babe Ruth, whose entire career has play by play data missing, his HR splits are 488+210=698. Not 714. The Babe has 12 homers missing. See:
https://www.baseball-reference.com/players/split.fcgi?id=ruthba01&year=Career&t=b
Data Coverage: https://www.baseball-reference.com/about/coverage.shtml
The end.