Since the year of the Black Sox scandal, the White Sox have only been shut out in three consecutive games four times.
If the White Sox can't manage to score a run against A.J. Burnett & Co. tonight at Yankee Stadium, it'd mark the first time since 1968 that the team has been shut out in three consecutive games. That '68 team has a dubious mark of offensive futility, though, as they were shut out for three consecutive games twice that season. The other two Sox teams to reach that tri-shutout mark were the 1967 and 1958 squads.
Being shut out in three consecutive games isn't a death knell for a season, though. The Phillies were shut out in three consecutive games in May of 2010—by the Mets, no less—and still made the NLCS. The same holds true for two consecutive shutouts, as both the 1993 and 1983 White Sox suffered back-to-back shutouts and made the playoffs.
The Sox will probably score at least one run tonight. Burnett is averaging nearly four walks per nine innings and has been the victim of some bad fly ball luck with three of his four starts coming at Yankee Stadium. For his career, Burnett has a 5.58 ERA against the Sox in seven starts with 16 walks in 40.1 innings. This is the same guy who once issued a bases-loaded walk to Jayson Nix. While the Sox offense is struggling mightily, facing Burnett at Yankee Stadium should be a good antidote to the recent shutout streak.