Where do you come by the part in bold?
Statistically, there's no case for it. The Yankee offense scored 789 runs with an RC of 832 last year. ARod will be out for the same amount of time, Teixeira (134 RC) replaces Giambi (94 RC), but then Nady needs to replace Abreu's 106 RC (doubtful). Figure things break right for them with Matsui, Posada, and Damon, and what are we talking about, 930 runs?
The Sox RC was 927 last year. This is with them getting a .650 OPS out of their catchers, .718 out of SS, and Ortiz being hurt half the year. Any improvement there will cover any dropoff from Youk or Pedroia not being able to replicate what they did. Bay should easily replicate the 7.6 RC/G Manny put up last year.
I agree that the Sox didn't do much to improve, at least not in terms of upgrades "on paper". No, any improvement will come from progression for Ellsbury and Lowrie, and/or bounce backs from Ortiz or Varitek. The potential for improvement is there, but at worst, you can say the expectation should be that they don't experience a dropoff.
Back to my question, where do you see them having a distinct offensive advantage?