I've seen some data on BBF on how Negro League players performed against major leaguers. Is there any data on how the Bambino performed in all of his barnstorming games against Negro League players? I found his stats from his trip to Cuba, and 3 games in the 20s against the Royal Giants and Bacharach Giants. From all of those games I have him at 15 for 40 with 5 homers, 3 triples, and 3 doubles. If nobody has researched this I would be willing to take a shot at it.
These games are used to describe how good some of the NLers were relative to major leaguers so I think it makes sense to use them to show how well stars of the majors would have performed if the leagues were integrated.
"Batting slumps? I never had one. When a guy hits .358, he doesn't have slumps."
Rogers Hornsby, 1961