I think player B wore the number 23- and just give me a yes on that if I'm right. A lot of fans my age who rooted for player B have a lot of sour grapes thinking player B has not gotten his due. First, his number was retired, although that team retires every number under the sun. Second, for what player B was, he was not all that great. On top of that, his numbers fell off very sharply after six or seven very good seasons. There are plenty of players on player B's team in the HOF, so stop whining.
Player A was one of the premier hitters of his era. He put up high averages for most of his career- yes, most on the archrival of B's team. Also, player A won several batting titles and hit over.340 several times. I am not a big fan of player A, and he may be the weakest HOF with 3,000 hits, but the campaign for player B will have to wait for the Vet committee, who have their hands full with at least ten players with better stats than player B.
I did not look that up by the way, and I'm sorry I figured it out and ruined your hypothetical experiment.