Paul Konerko was asked before the game Saturday about how different things would be for the White Sox if they hadn’t signed Jose Abreu last fall. Abreu was courted by many suitors, including the Astros, who were willing to invest tens of millions in a rookie who had never played pro baseball.

But, as Konerko pointed out, as great as Abreu’s impact has been, a team needs more than a high-impact slugger to win games. And the Sox’ 4-3 victory against the Astros proved that.

“There’s definitely been a lot of games he’s single-handedly put us in the driver’s seat or come up with a big home run,” Konerko said. “Having said that, there’s a lot of teams out there that want offense that don’t win. So you look at some of the teams we’ve had here over the years with Frank [Thomas] and Magglio [Ordonez], it’s kind of a known thing that that’s not enough. You need more than that.

“But there’s definitely a lot of games that I can think of with them where they factored in not only with the driving in of runs, but with getting on base and scoring the other ones.”

Abreu went 1-for-5, and his hit gave him at least one in 28 of the last 29 games and 10 in a row, but this wasn’t one of those nights when he carried the Sox. He remained stuck on 29 home runs, and his slugging percentage dipped slightly to .624, both categories he led the majors in entering play.