Right now, Tuesday, Sep 10, the 3d wild card slot, currently held by the Twins, is a dogfight among the Twins, who have the 3d slot, and the Tigers, Sox, and Mariners. The latter 3 are all 73-70 and 3 games behind the Twins.
All 4 teams have 18 games to play. The Twins are in the catbird seat, but have just lost 4 straight. Up ahead are 2 more against the Angels, 3 vs the Reds, 4 @ Cleveland, 3 @ Boston, 3 vs Miami, and 3 vs Baltimore.
If the Twins finish 9-9, the Sox (or Tigers or Mariners) have to go 12-6 to tie them, so a big edge to the Twins.
If the Twins go 7-11, which right now looks very possible, the Sox/Tigers/Mariners only have to go 10-8 to tie the Twins, which is doable.
While I think it's possible for the Twins to be caught, I have difficulty seeing the Sox doing the catching. Bullpen is a disaster, and the hitting is inconsistent.