But the defending World Series champions remain faithful to Chicago and simply use the field at Angel Stadium to their own advantage.
To open the three-game series on Monday, the White Sox did what the White Sox do, and that's beat the Angels on their own turf, extending a winning streak in the OC to seven games with a 3-2 victory as the two teams fight to gain entrance into the postseason tournament.
Counting last year's ALCS, the White Sox have won nine of the past 10 games in Angel Stadium, including a three-game sweep earlier this season.
The loss for the Angels wasn't just a statistical curiosity, either.
With the A's losing in Minnesota, the Angels saw their number to elimination in the American League West trimmed to 14 games, while their number for elimination in the AL Wild Card was reduced to 12 behind the Twins.
It was also the second time in the past three days the Angels failed to gain ground on the A's to remain 5 1/2 games back. Both times the Angels lost by one run.
"It is frustrating, especially with the circumstances," said Adam Kennedy, who went 0-for-3 but keyed two excellent defensive plays. "We have to take advantage of the opportunities when they're given to you, but we haven't done that."
For their efforts, the White Sox remained 1 1/2 games back of Minnesota in the Wild Card and pulled within three games of the idle Tigers in the AL Central race.
"When you're behind I don't know if time is ever an ally but if there is a sense of urgency I think that has been there since May when we were 11 games down and needed to get into our game," manager Mike Scioscia said. "It is frustrating that we had opportunities (tonight) and didn't get into our game."
Playing runner-up to the White Sox is familiar territory for the Angels, at least in those games covering recent history. The overall series is dead-even at 320-320, but it's the latest stretch that has colored the proceedings black and not red.
Last October, the Angels left Chicago with a 1-1 split in the ALCS only to watch the White Sox reel off three straight wins to capture the pennant.
It was also no great upset. The Sox then charged into the World Series, where they swept the Astros for their first title since 1917.
Beyond the team performing an encore Monday was the White Sox starting pitcher, as Jose Contreras continued his mastery over the Angels. The right-hander was the lone Chicago pitcher to lose in the postseason last year when he allowed three runs over 8 1/3 innings as the Angels took Game 1 of the ALCS.
But Contreras was on the hill five days later, tossing the team's fourth straight complete game as the Sox clinched.
On Monday night, Contreras (13-7) was every bit as effective, as he limited the Angels to a single run when Chone Figgins led off the sixth with a triple and scored on a single up the middle by Maicer Izturis. Contreras allowed six hits and walked one.
John Lackey was equal to Contreras on Monday except for one inning, when the White Sox put a 3 on the board in the fifth. That was the difference.
That inning provided sharp contrast, too, as Lackey was nearly unhittable in seven otherwise sharp innings. The right-hander retired the first 10 batters before issuing a walk to Tad Iguchi with one out in the fourth. Kennedy then gloved a hot smash by Jermaine Dye that Lackey deflected but the Angels second baseman caught the ball on the fly and threw to first for an inning-ending double play.
Lackey opened the fifth by walking Jim Thome. Paul Konerko then singled, A.J. Pierzynski doubled home a run, Joe Crede knocked in one with a base hit and Rob Mackowiak lifted a sac fly as the White Sox built a 3-0 lead.
"Lackey was really good tonight. He had three bad batters, that was it," Pierzynski said. "Jose matched him pitch for pitch and we found a way to score three runs."
Lackey (11-10) induced a double-play ball out of Juan Uribe and then retired the next eight batters in succession, including a string of five straight strikeouts. He gave up four hits with two walks to take his fourth loss in his past eight starts.
"I had pretty good stuff, that's about as good of stuff as I've had all year," Lackey said. "I felt really good, I pretty much gave up the 0-2 hit to Pierzynski. Get that down about two inches and I'm all right. Left a fastball up to Konerko and that's about it."
The Angels managed eight hits and pushed across a run in the ninth when Vladimir Guerrero and Garret Anderson led off the inning with two singles. But Juan Rivera bounced into a double play to score Guerrero and Howie Kendrick struck out to end the game as Bobby Jenks recorded his 40th save.
Contreras also benefited from some solid defense. After Izturis' RBI single in the fifth, Orlando Cabrera lined into a double play. Then in the seventh with Rivera on first and one out, Kennedy lined out to first for a double play that ended the inning.
"John pitched a good game. In that one inning he tried to put some guys away but give them credit. Konerko got the hit and Crede found the hole," Scioscia said. "Offensively, we couldn't pressure them. We have to get better and that is the bottom line."
Mike Scarr is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.