W L PCT GB TO PLAYBoston is also 6.5 GB in the wild card standings.
Rays 80 50 .615 --- 32
Yankees 80 50 .615 --- 32
Red Sox 74 57 .565 6.5 31
The odds of making the playoffs are slim. Baseball Prospectus gives the Red Sox a 10.9% chance (last night's loss dropped the chances by a full 7%) Cool Standings has Boston at 6.2%.
The Red Sox have three games left against the Rays (September 6-8) and six games against the Yankees, including three at Fenway to end the season (September 24-26, October 1-3). Even if the Sox could go 6-0 or 5-1 against New York, it simply may be too late.
If the Rays and/or Yankees go 16-16, the Red Sox would need to go 22-9 to tie.
The good news is that at various points in (approximately) mid-May to the end of June, the Red Sox were that hot. From May 17 to June 19 and from May 29 to July 3, the team went 23-8. That is their best record over any 31-game stretch this year.
So if both the Rays and Yankees play better than .500 ball, the Red Sox would have to finish the season playing better than they have played at any time this season. Like I said, that is the good news.
The bad news is that the Yankees have not had any 32-game stretch this year in which they have played .500 ball. The worst has been 17-15 (April 20 to May 23, May 9 to June 11, and July 25 to August 27, for example.)
Tampa Bay went 12-20 from May 24 to June 29 -- which was around the time of Boston's hot streak. During Tampa's 12-20 slide, the Red Sox went 23-10 -- a difference of 10.5 games in the standings! If that little slice of history could repeat itself ....
As we all know, just because something has ever happened before does not mean it cannot or will not happen. Baseball is full of examples of improbable comebacks and collapses: the 1914 Braves, the 1964 Phillies, the 1995 Angels*.
* BP says this is the worst collapse in history -- by far. On August 20, the Angels had a 99.988% playoff probability (odds of collapse: 8,332-to-1 against).
Maybe you can get there from here ...