51 years ago, a couple of Sox rookies took the team to within one game of its first ring in many years.
Both Lynn & Rice had over 600 PAs and finished 1-2 in ROY voting, as well as 1-3 in MVP voting.
Fred Lynn: .331 21 105 (.401/.566/.967) Led the league in SLG & OPS.
Jim Rice: .309 22 102 (.350/.491/.841)
I'm not trying to put Anthony and Mayer in the same class as those two, but it does seem like many teams that go far are given major boosts by a rookie or two. (I know, Anthony is not technically a "rookie," but he's close enough for me.)