Kimmi, here's something interesting I found looking at Papi's career splits:
Tie Game .963 (OPS)
Score Within 1 Run .960
Within 2 Runs .955
Within 3 Runs .946
Within 4 Runs .937
More than 4 Runs .864
It's interesting how his OPS drops a bit as the game margin increases, and then drops a lot in one-sided games. It doesn't prove anything, but it does at least suggest that his focus is a bit sharper when the game is closer. In a lot of those one-sided games you're facing the dregs of the other team's staff, too, so you'd think that's where you could really fatten up. But if you've watched a lot of Sox games you do get the feeling in those blowout situations that Papi just wants to hack away and get the at-bat over with, to conserve himself, perhaps.