White Sox General Manager Kenny Williams knew he had to shore up the team’s bullpen over the off-season after it imploded last summer, but I’m not exactly enamored of his first move along those lines. Williams signed National League middle reliever Scott Linebrink this week to a four-year deal worth $19 million. Yet one of the reasons no one was willing to bid more is that he’s a 31-year-old who looked washed up with two different teams last season.

Linebrink can pitch, no doubt about it. He came into his own with the San Diego Padres in 2004 with a 2.14 earned-run average, and he improved the following year to a sparkling 1.83. He went on in 2006 to lead the NL in holds — the stat created to reward middle relievers for holding a lead — but his ERA almost doubled to 3.57. It rose again last year to 3.71, as he lost his job as setup man for closer Trevor Hoffman to Heath Bell in San Diego and was dealt to the Milwaukee Brewers, who at that point outbid Williams and the Sox for his services by offering up three minor-league pitchers. He went on to lose three more games in Milwaukee, which is why perhaps the Brewers didn’t outbid Williams for him as a free agent.

While Linebrink’s ERA went down slightly in Milwaukee, Bill James’s component ERA stat suggests he benefited from some luck and actually pitched worse. His strikeouts also diminished, a sign of a pitcher on the decline. The most troubling stat is that while Linebrink allowed only four homers in 74 innings in 2005, since then he’s given up 21 homers in 138 innings, for the most part in pitcher-friendly San Diego. Now he’s moving to a tougher league and to Sox Park, a relative launching pad for homers. The Bill James Handbook forecasts a slight improvement next year to a 3.60 ERA, but that’s projecting him pitching in Milwaukee. So this signing has all the earmarks of someone paying too much for a recognized name whose good reputation is out of date.

I hope I’m wrong and Linebrink rebounds to his 2005 level, and he suggests the trade briefly caused him to lose focus last summer, but in the meantime I wouldn’t give up on even Mike MacDougal just yet. Williams wisely rejected getting in a bidding war for Torii Hunter, who while an excellent player will probably not be worth the $18 million a year he’ll be getting at the end of his new five-year contract with the Anaheim Angels. Yet just because the price was lower for Linebrink doesn’t mean the Sox won’t wind up regretting it even more at the end of the deal.