Here's a relatively simple exercise. Check out the left-right splits Junichi Tazawa has put together so far in the major leagues:
Lefthanded batters: .286/.344/.357 (.308 BABIP)
Righthanded batters: .488/.543/.927 (.516 BABIP)
Too small of a sample size? Check out his year in the minor leagues (on-base and slugging numbers are approximated):
Lefthanded batters: .221/.283/.317 (.287 BABIP)
Righthanded batters: .226/.256/.329 (.264 BABIP)
No, Tazawa isn't going to see righties hit almost .500 against him the rest of the way. But the fact that he has something of a reverse split -- he gets hit harder by righties than by lefties -- doesn't appear to be a fluke.
His numbers in the minor leagues were even, if not slightly better, against lefties than against righties -- and he even got a little less BABIP luck against lefties than he did against righties.
It then makes complete sense that Tazawa would repeatedly wiggle out of danger against the Yankees, a lineup full of lefties and switch-hitters, and get rocked by the White Sox, a lineup with quite a bit more balance to it.
If that's not the key difference, good luck finding it: His pitch charts from the two games look almost identical. Against the Yankees, he got hit when he left the ball in the middle of the plate...
... and against the White Sox, he got hit when he left the ball in the middle of the plate.
(The blue dots, as you probably can figure out, are balls in play.)
The best pitchers generally work all four edges of the strike zone but keep the ball out of the middle. Tazawa actually appears to have been squeezed a little bit at the knees on Thursday -- check out the green dots inside the strike zone -- but gave away another entire edge all by himself. He threw about six pitches all night that could be classified as on the inside corner to lefties and on the outside corner to righties. When he tried to throw to that side of the plate, he left the ball in the hitting zone.
His location stayed pretty consistent throughout: Middle-in to righties and middle-away to lefties. Here's how his third inning broke down:
A.J. Pierzynski (L): Single to left on a changeup down and away
Paul Konerko (R): Single to left on a fastball away
Jim Thome (L): Sacrifice fly to right on a fastball away
Carlos Quentin (R): Home run to left on a curveball in the middle
Mark Kotsay (L): Hard-hit groundout on a curveball in the middle
Alexei Ramirez (R): Double to left on a fastball in
Jayson Nix (R): Single to left on a fastball in the middle
Both Tazawa and catcher Victor Martinez blamed the pitcher's lack of control early in the count for putting him in tough spots where he had to throw the ball over the plate.
But in that third inning, an inning in which the White Sox scored four runs, Tazawa got ahead of six of the eight hitters he faced. He went to a 3-1 count to Ramirez, but the White Sox otherwise were swinging early in the count because they were getting pitches to hit.
The White Sox happened to be looking for certain pitches -- and Tazawa couldn't make the adjustment when they started to hit those pitches.