Probability that each baseball team will make it to the postseason, according to Baseball Prospectus:

Pretty much a lock
Cardinals 99.9998%
Braves 99.3%
Yankees 98.7%
Dodgers 97.1%
Red Sox 93.3%
Twins 93.3%

Probably
Athletics 86.0%
Cubs 63.7%

Still a fighting chance
Giants 20.8%
Angels 16.0%
Padres 10.5%

Barely in it
Rangers 5.7%
Astros 4.6%
Indians 3.8%
Marlins 3.8%
White Sox 2.6%

Mathematically alive, but there's no hope
Tigers 0.2%
Phillies 0.04%
Mets 0.0001%
Pirates 0.00008%
Reds 0.00003%

Now you might be wondering why the Red Sox (who have a 4.5 game lead on the Angels and a 6 game lead on the Rangers) are just as likely to make the playoffs as the Twins (who have a 9 game lead on the Indians and a 9.5 game lead on the White Sox).

It's because these percentages were calculated by doing a million simulations of the rest of the season. The Twins play the Indians 7 times and the White Sox 6 times, while the Red Sox won't play the Angels or Rangers after this weekend.