I just started comparing Ted Williams and Joe DiMaggio year by year from 1939 through 1951. The main thing I want to look at is their numbers on the road against the six other teams. The data is from baseball-reference.com. It's just a bit tedious to extract it and figure the results in a spreadsheet.
Basically, I'm taking their road data and subtracting their data against each other's team on the road. That leaves road stats against the other six teams. For instance for DiMaggio, it's his road data minus his data in Fenway Park. For Williams, it's his road data minus his data in Yankees Stadium.
This seemed like the most objective way to compare their batting: against the same teams in the same parks. I thought DiMaggio would generally have an advantage batting against Boston because I thought that Yankee pitching would usually be better than Boston's since the Yankees won more often. So I eliminated how they batted against each other's pitching and I eliminated their home parks where Williams would have an advantage.
I just learned some startling things about their famous 1941 seasons.
Williams highest batting average (BA) was against the Yankees: .471 (.485 in Yankee Stadium, .457 in Fenway Park). Without his success against the Yankees, Williams might not have batted .406.
DiMaggio had his lowest BA against Boston: .268 (.364 in Fenway Park, .184 in Yankee Stadium).
As a result, in 1941 against the other six teams on the road their BA were: DiMaggio .370, Williams .361.
Williams still led in in 1941 in:
OBP .510 .456
SLG .722 .681
OPS 1.233 1.1366
I happened to notice that in 1939 when DiMaggio batted .381, DiMaggio had only one at bat in May and batted only .303 in September. His next lowest month was July: .398. DiMaggio entered September at .405. On September 3 DiMaggio was batting .410 and .401 as late as September 10.
In 1941 when Williams batted .406, Williams entered September at .407 and batted .397 in September. Williams peaked at .413 September 10 and dropped to a shade under .400 September 27. July 24 was the latest date Williams BA with rounding was below .400: .397.