Hideki Matsui is going to come off the DL today. Phil Hughes and Carl Pavano are not far behind. The Yankees are stronger now than at any point during the season. Can they somehow sneak in to the playoffs?
Baseball Prospectus gives the Yankees just over a 4% shot at making the playoffs. The Yankees basically have to give up on the division, as they are ten games behind the front-running Rays; even if Tampa finishes the season 19-19 (which is unlikely, considering how good a team they are), the Yankees would have to go 29-9 just to force a tie with the Rays. Even if these two things happen (both of which are extremely unlikely), the Red Sox could steal the division if they go 24-13 in that stretch. Obviously, the Yankees hopes of winning the division are nearly non-existent.
The wildcard picture is pretty bleak as well. The Red Sox are probably a better team than the Yankees (as evidenced by their respective run differentials: the Sox have outscored their opponents by 117 runs this year, while the Yanks have outscored their opponents by 47 runs), and Yankees currently trail the Red Sox by five-and-a-half games. If the Sox go 17-18 during the rest of the season (an unlikely proposition), the Yankees would have to go 23-15 to tie them. While it's possible that the Sox will play .500 ball down the stretch, it's far from likely; and even if they did, the Yankees would still have to play well even to tie Boston.
Furthermore, of the Yankees 38 remaining games, 22 are on the road and only 16 are at home - a significant difference for a team that (like most others) has struggled away from home. The Rays have 20 road games and 18 home games remaining; the Red Sox have 18 road games and 21 home games left on their schedule.
Complicating matters further are those pesky Central Division teams. Either the White Sox or Twins will likely take the division, but both teams are currently ahead of the Yankees in the wildcard standings. Therefore, the Yankees must not only significantly outplay the Red Sox over the rest of the season, they must also outplay either the Twins or White Sox. While this is a far less daunting task, the presence of the White Sox and Twins certainly decreases the Yankees' playoff odds.
Last year's Philadelphia Phillies taught us never to count any team out of the playoff race. However, the Yankees are staring at some long odds, and chances are Derek Jeter will have more free time this October than he has ever had in his major league career.