The White Sox rank 11th in the American League with four runs scored per game. Their .309 OBP ranks 12th; their .390 SLG places 9th. Like most teams, the Sox have several players hitting above their ability (Paul Konerko, Andruw Jones), and several players below (Juan Pierre, Gordon Beckham, Alexei Ramirez, Carlos Quentin, A.J. Pierzynski). The Sox projected to have a below-average offense from the start, but if they just wait it out they'll improve on the current output.
Pierre has been particularly disappointing, as has the team's production from their DH rotation. Joe Cowley of the Chicago Sun-Times believes free agent Jermaine Dye could help, and Dye agrees. He wants to do more than just DH, potentially helping at outfield and first base. Dye also clarified recent rumors, saying the Cubs' $3MM offer wasn't formal and he spoke last to the Brewers. He added, "I'm not going to a bad team, and I'm not playing for $1.5 million."
It doesn't make sense for the Sox to bid much more than that, so money would be one issue. Manager Ozzie Guillen isn't sure where he'd put Dye, and thinks the player might need a month to be ready (Dye says two weeks). Whether or not there's a fit with the White Sox, Guillen wants to see Dye come back and play for a big league team.