Jeff Zimmerman has released some data on major infield shifts (three infielders on one side of second) for 2013. (UPDATE: And now he says there's an error in the source data, so hold on.) Interesting bits for us:
By a crude metric of BABIP without the shift minus overall BABIP, the Rays and Angels made the shift count the most; each had an overall BABIP five points lower than their BABIP without the shift. This was particularly striking for the Angels, who only had 216 shifts, exactly middle of the pack; they had a high .311 BABIP without the shift and only a .236 BABIP with the shift.
The A's really caught the ball when the shift was on; batters had only a .222 BABIP when the A's shifted. (But I believe their home stadium suppresses BABIP, in part due to the big foul territory.)
The Phillies only shifted 48 times, and when they did they gave up a .354 BABIP. So maybe they were onto something. (The Nats shifted the least, 41 times.)
Among batters, Pedro Alvarez was shifted against the ninth most, 142 times... and he had a .317 BABIP against it (.264 without the shift). The next most shifted against Pirate, Garrett Jones, also beat the shift. The third most shifted against Pirate was Andrew McCutchen and he BABIPed only .233 against the shift and .360 without it. (But it only cost him three total points of BABIP.)