According to Baseball Prospectus's playoff odds report, the Boston Red Sox have a 99.7 percent chance of making the playoffs. One quarter of that comes from winning the division, and the rest is from the Wild Card, which they currently lead by 6.5 games over the Tampa Bay Rays, and seven games over the Los Angeles Angels. While Boston doesn't play the Angels again the rest of the year -- there is a reason why the entirety of the Halos' playoff chances are wrapped up in the division, and not the Wild Card -- they do face the Rays six more times in their remaining 19 games. This gives Tampa Bay a very slight -- but existing -- chance to catch Boston and take the Wild Card from them.
You can already see how slight it is, just by looking at Boston's expected chances. The Rays have a 0.3 percent chance of making it to the postseason, and their only way through will be by significantly outplaying Boston the rest of the way, to the point where they will likely need to sweep the remaining season series if they were to make this happen. Crazier things have happened in baseball, of course, and Boston wouldn't be the first team to blow a lead like this with around 20 games to go in the season, but all it may take to eliminate the Rays from a probability standpoint (but not a mathematical one) is a victory or two this weekend.
If the Rays are 7.5 games out following this weekend -- two Sox' wins and one Tampa Bay victory would leave the standings like so -- then they now have to make up 7.5 games in 16 games' time. Boston would need to lose half of their remaining games to miss out on October at that point, assuming that Tampa Bay, at the same time Boston is losing, was winning.
To give you a sense of how hard that is to do, and how difficult it would be for Tampa Bay to catch up in the short time remaining, we can look at how much Tampa Bay's playoff odds have been helped by the Red Sox' recent stretch over the last week, in which they have gone 2-5 thanks to poor series against both the Rangers and the Blue Jays. The Rays, who went 4-3 over the same stretch, increased their playoff odds by 0.2 percent.
Boston certainly isn't helping themselves out by using Andrew Miller and Tim Wakefield, as the two pitchers are just not pitching well at all this season, but with the lead they have, they can take the risk to get their core starting pitchers healthy for October. It's starting to help make things look closer than they are, but remember: Tampa Bay is a serious long shot right now. They have a chance, of course, as they haven't been mathematically eliminated, and baseball has shown that basically anything is possible, regardless of the chances, but the odds are in Boston's favor, and could be even more so should they pull out a few Ws this weekend against their lone remaining threat.