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This is a legitimate question, but one that Red Sox fans shouldn't be overly concerned with, especially after 2011.
The Red Sox currently have five everyday players who bat left-handed: Carl Crawford, Adrian Gonzalez, J.D. Drew, David Ortiz and Jacoby Ellsbury.
However, a number of these situations can be solved when you closely examine the roster that the Red Sox now boast.
The Sox still have another $8 million invested in outfielder Mike Cameron, and despite the fact that he's coming off season-ending abdominal surgery in 2010, he could see a fair amount of playing time in center field and right field, especially when a left-hander is on the mound.
Right fielder J.D. Drew is still an above average hitter against right-handed pitchers, yet is putrid against lefties. Just look at his 2010 splits:
VS. RHP: 329 AB, 18 HR, 49 RBI, .277/.358/.517
VS. LHP: 149 AB, 4 HR, 19 RBI, .208/.302/.309
It would be foolish for the Red Sox to continue the charade of sending Drew up to the plate against lefties, especially when they have a suitable backup in Cameron. Drew and Cameron are both free agents after this year, and neither will be back, so the Sox don't have to worry about playing time issues that could be created.
Also, the Red Sox should be able to get David Ortiz' bat out of the lineup if they feel inclined to sit him against any particular left-handed pitcher.
The Sox have both SS Marco Scutaro and INF Jed Lowrie under contract for next season. There's some speculation that Lowrie's blistering end to the 2010 season could win him the starting job next year, but either way, he and Scutaro could be used in tandem when the Sox sit Papi.
There are two situations that seem appropriate. First, and more likely, is that the Red Sox DH Kevin Youkilis, play Lowrie at third and put Marco Scutaro at SS.
Or if they wish to give Adrian Gonzalez a day off without losing his bat, they could DH Gonzalez and play Youkilis at first, while maintaining Lowrie and Scutaro on the left side of the infield.
It's also possible that Ortiz will not be back next season, which would remove another lefty from the lineup.
Thus, long-term, the "left-handed issue" shouldn't be anything to worry about from a Boston fan's perspective.