The ancient Romans were a superstitious lot. The Latin adjective for "left" is "sinister," and the word had all of the negative connotations then that it does now. Furthermore, left-handed individuals were barred from serving in the Roman legions, one of the pillars of their society. Indeed, in societies throughout the world, left-handedness and more generally leftness have often been viewed with suspicion, antagonism, and fear.
Why do I bring this up? Well, the problems for the Red Sox defense are, for the most part, on the left. The numbers don't lie:
LF Jason Bay: -14.1 runs in 107 games. -14.5 runs per 150 games
3B Mike Lowell: -9.9 runs in 81 games, -16.1 runs / 150 g
3B Kevin Youkilis: -1.7 runs in 37 games, -8.2 runs /150 g
and the dearly departed
SS Julio Lugo: -8.2 runs in 32 games, -41.9 runs /150 g
The exceptions to this yawning chasm on the left are two of the players at SS (four if you count Chris Woodward and Gil Velasquez, which I won't) - Jed Lowrie and Nick Green. Green has been 4.5 runs above average in his 76 games at SS (8.0 runs / 150 games), while Lowrie has been 2.8 runs above average in 18 games (21.7 runs / 150 games). Aside: I'm somewhat disappointed Green hasn't lost more in his UZR rating the past few weeks; failing to turn two routine double plays in the Tazawa start should have been more costly.
In the up-the-middle positions, we have three catchers who can't throw out anyone; sadly catcher defense isn't rated on UZR. Moreover, Jacoby Ellsbury is having a terrible year: -8.5 runs in 107 innings (-13.2 runs in 150 games). Last year, Ells was above-average in CF (3.0 runs in 66 games), and superb in LF (9.3 runs in 58 g). As an aside, I think the lack of speedy LFs makes it easier for a Crisp or Ellsbury to excel there, because the standard of competition is lower. UZR compares fielders to the average of their peers at that position, and it's better to be compared to slow OFs like Jason Bay and Manny Ramirez than other speedy CFs.
So the good defense, aside from Green, is concentrated on the right. Dustin Pedroia (8.4), JD Drew (8.0) and Kevin Youkilis (4.5, 12.0 /150g) lead the team in UZR.
The acquisition of Casey Kotchman should improve team defense slightly, again on the right side of the field. Kotch has been a great defender over his brief career: in 442 games, his UZR at 1B is 8.9 runs above average (3.2 per 150 games). On the year, he's at 3.8 runs above average, or 6.0 runs per 150 games. Martinez may be a better first baseman than catcher, but he doesn't hold a candle to Youk or Kotch when it comes to defense.