If nothing else, the White Sox absorbed that valuable piece of information once more in a 9-5 defeat against the Angels in the series finale at U.S. Cellular Field on Thursday afternoon in front of 27,487 fans.
Over the past week, the South Siders had opportunities to sweep both the Yankees in a four-game set as well as the Angels, each first-place teams in their respective divisions, in the finale of a home series, only to have their brooms brushed aside. But Chicago clearly is getting closer to joining the ranks of the American League's upper class, particularly following a 5-2 stretch against New York and Los Angeles.
The White Sox took three of four games from the Yankees and two of three from the Angels.
"Everybody's up there working hard," White Sox first baseman and team captain Paul Konerko said. "It's just tough for guys like that to go three days without a lot of success. That's why I say it's tough to sweep a team. ... They're a good team. We'll take two out of three."
Perhaps content with the knowledge that they already had won the series, however, the White Sox did not come out especially strong during Thursday's series finale.
"It was like a Little League game out there, walking people, giving up home runs, a lot of stolen bases," White Sox manager Ozzie Guillen said. "The first couple innings weren't pretty."
White Sox starter John Danks struggled to keep his team in the ballgame in the early going. The Angels scored five runs off Danks in the first two innings, and the White Sox never were quite able to recover.
In the first inning, Juan Rivera grounded a pitch off Danks' leg toward third baseman Gordon Beckham with two runners on. Beckham barehanded the ball, but threw wide of first, allowing both Erick Aybar and Bobby Abreu to score, putting the Angels ahead, 2-0.
In the second, Danks surrendered a 404-foot homer to catcher and No. 9 hitter Jeff Mathis, a two-run shot that gave the Angels a 4-0 advantage.
Los Angeles added one more in the frame when White Sox right fielder Jermaine Dye caught a ball for the inning's second out with a runner on third, put his head down and began running toward the dugout as if it were the third out. Dye's mental lapse allowed Chone Figgins to tag up and score easily from third, as Dye realized too late that his catch marked only the second out of the inning.
"I mean, Jermaine, I'm sure, would say there's no excuse for forgetting the outs," Konerko said. "At the same time, when you're going to have a pace of game like that, and those walks and balls and everybody standing on their heels -- like I say, there's no excuse to ever forget the outs -- but almost every time it happens, it looks just like that as far as the way the game is going."
Danks (9-8) actually did well to make it into the seventh inning after surrendering six runs in his first three innings of work on Thursday. He battled back, lasting 6 1/3 innings and allowing seven runs (six earned) on nine hits with five strikeouts.
Still, Danks was less than thrilled with his performance.
"I didn't help myself out much," Danks said, "and I wasn't ahead in the count enough to really make them hit my pitch. So I've got to get better."
The highlight offensively for the White Sox came in the bottom of the second when Jayson Nix sent a first-pitch offering from Angels pitcher Ervin Santana into the left-field bullpen. The home run scored Konerko and Mark Kotsay, who had walked and doubled, respectively. Nix's eighth long ball of the season trimmed the White Sox deficit to 5-3, but they would get no closer than two runs the rest of the way, as the Angels added single runs in the third, fifth, seventh and ninth innings.
"It's not easy when you go on the field and you're one hit away from tying the game and all of the sudden you're down by five," Guillen said. "That takes everything out you."
Chicago's only other runs came on a bases-loaded walk to Kotsay in the third and a solo home run by pinch-hitter Dewayne Wise in the ninth inning. It was the team's first pinch-hit RBI this season.
The White Sox (56-53) tallied nine baserunners in the game's first three innings, but just four over the final six innings.
The Angels (64-42), meanwhile, kept up the offensive pressure all game, belting four home runs.
"We've been swinging the bats really well for a couple months now," Angels manager Mike Scioscia said. "The first couple games, they shut us down. We broke out with a good offensive day. We drove the ball out of the park."
The loss, coupled with Detroit's 7-3 win over Baltimore, dropped the White Sox two games back of the Tigers for first place in the AL Central.
Now, the White Sox must turn their attention to a sub-.500 team for the first time in nearly three weeks, when the Indians come to town for the final three games of a 10-game homestand.
While a sweep would be nice -- elite opponent or not -- Konerko said he would be content with simply capturing another series before the team embarks on six-game road trip at Seattle and Oakland.
"I thought we did a nice job of not letting down after the Yankees series," Konerko said. "We've just got to keep it going here. It would be really nice to get on that plane Sunday to go to the West coast with at least two out of three."
Jesse Temple is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.