Baseball-reference.com has a great feature called similarity scores, where it finds 'similar players' in baseball history to a chosen player. So let's propose a 'hypothetical' similarity lineup with the Sox player and a similarity 'shadow.
C Victor Martinez Joe Mauer (really)
1B Kevin Youkilis Adrian Gonzalez (yeah)
2B Dustin Pedroia Aaron Hill
SS Marco Scutaro Pokey Reese
3B Adrian Beltre Mike Lowell (meet the new boss, same as the old boss)
LF Jacoby Ellsbury Denard Span (and the Twins wanted Ells)
CF Mike Cameron Tom Brunansky (end of the season catch fame)
RF J.D. Drew Carl Everett (not in temperament)
DH David Ortiz Mo Vaughn (who woulda thought)
P Josh Beckett John Lackey (number 1 on sim score!)
P Jon Lester Daisuke Matsuzaka (doesn't look Japanese)
P Jon Lackey A.J. Burnett (is what it is)
P Jonathan Papelbon Takashi Saito (why can't we get players like that)
The point? Sometimes our "endowment bias" sees players differently than they 'are'. For example, most everyone would agree that Albert Pujols is one of the top players in the game. Who is on his similarity score list?