The Cubs are 7 losses clear of the Giants and 6 losses away from the Cardinals. In a very real sense, the Cubs are closer to the division than they are to falling out of the Wild Card. However, that doesn’t mean that the Cubs are really all that close to getting there.
BP has the Cubs at 4.7% to win the division, and 6.3% to miss the playoffs altogether. Those seem right, and looking at how many games are left, it’s easy to see why. First, let’s see what San Francisco must do to catch the Cubs.
If the Cubs play .500 ball the rest of the way, they are 91-71. That means the Giants would need to go 26-12 over the rest of the season to overtake them. That’s a better 38-game stretch than the Giants have had all season (though they did go 21-7 to open May). Plugging the Giants’ .5323 winning percentage into a binomial calculator would give them a 4.2% chance of having a 26-12 or better streak to close the season: and keep in mind, this is if the Cubs go .500, the chances of which are pretty low to begin with (the same binomial calculator gives the Cubs an 81.4% chance to exceed 20 wins the rest of the way)! All told, it’s really likely the Cubs make at least the second Wild Card, with the obvious caveat that a catastrophic injury or an unlikely surge from another team gets in the way.
The math is much more bleak for catching the Cardinals. The Redbirds are 78-45, which give them a .6341 winning percentage. If we assume the Cardinals go .500 the rest of the way (and win the last game, so 20-19 – the probability they win 20 or less is 8.2%), they win 98 games. The Cubs would need to go 27-13 the rest of the season just to tie them and 28-12 to overtake. The Cubs lose the head-to-head matchup unless they sweep the last 6 games against the Cardinals, so I assume they need 28 wins: the chance that happens is 8.6%.
This is all just to tell you that you should steel yourself for a 1-game WC date with Pittsburgh (or St. Louis – don’t forget, Pittsburgh could still win that division pretty easily).