Reposting this here, since yesterday, I've started to model the rest of this season every time the standings change.
OK, here's what I've got for today. I wound up at about 5.9%.
Maybe ESPN's odds are playing out the tiebreaker game, in which case I'm closer to what they have than baseball prospectus.
If we win out, then as of right now we're 50/50. If we lose one game, we're at about 14% (but that obviously will go up or down a lot based on what our opponents do).
Right now, 2 losses puts us somewhere above 1%, but its hard to tell if that was a fluke or not, because I only have 4 events to support that.
It is mathematically possible for us to make it with 3 losses, but after thousands of simulations now, I have not yet hit that event.
edit: Adding on to the above: A simple way to estimate getting past the 163rd game (maybe even a 164th game) and at least reaching the wild card game can be done by giving half credit for 2-way 2nd wild card ties, one-third credit for 3-way 2nd wild card ties, and 2/3 credit for 3-way 1st wild card ties. (all others get full credit)
If you do that, we're at about 3.1% to reach at least the wild card round, which is very close to ESPN's odds.