Going into their last rest day of the season, the Rays finally had a good day. The Rays won, the Red Sox lost, the Orioles lost, and the Indians lost. That leaves them seven and a half games behind the Sox, and two games ahead of Baltimore and Cleveland for the second wild card (two and a half in front of New York).
Coolstandings.com has been taken over by FanGraphs, so you can now see their coin flip simulations, their simulations using seasonal record to calculate team strength, and simulations using FanGraphs projections (ZiPS and Steamer RoS, with human input playing times). Here are those three playoff projection systems, along with Baseball Prospectus's PECOTA. For a full explanation, along with an appearance by DRB community member baltar (I agree with you, btw), read here.
Note that while the Rays have very little chance of beating out the Red Sox, stranger things have happened (we've seen them happen). Also note that the projection systems that use more advanced estimations of team strength like us much more than those that use record (and emphasize recent record). Now is the time to hope that the "stat-boys" are right.
*I bet there's someone out there thinking about telling me that I have the combined playoff odds wrong. You're going to say that I/FanGraphs am/is valuing winning the division as much as making it to a one game playoff. If that's the number you want, just use ((Wild Card)/2)+(Division).
Here's my problem with that, though. It assumes that making the play-in game is worthless, and that the playoff payout only comes when you make the "real playoffs." Yes, one possible goal is to win the world series, but it's not the only one. Making the playoffs makes teams considerable amounts of money. That's why a team on the brink of the playoffs should be willing to spend more. They make money from ticket sales, from TV (I think, but correct me if I'm wrong), and from renewed and continued fan interest in the form of merchandise sales and future attendance. Some of these obviously apply far less in a one game playoff, but they don't disappear, and I flat out don't know to what extent they exist.
That's why for these purposes I'm categorizing "making the playoffs" as not stopping playing baseball on the last game of the season.