CHICAGO—This time, the Chicago White Sox couldn’t avoid the knockout.

They won four straight elimination games only to bow out with a 6-2 loss to the Tampa Bay Rays in Game 4 of their division series on Monday night. Just like that, what looked like a promising October for the city ended with a whimper.

No parades. Just disappointment.

It was a rough day for Gavin Floyd, whose breakout season ended with a fourth-inning exit, and a difficult postseason for veteran sluggers Ken Griffey Jr. and Jim Thome. Both were 0-for-4 and Griffey ended the game with his th...

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