Now, sadly, it's time to do almost the opposite calculation--how many games do the Angels have to win in order to catch the Rangers and force a 1-game playoff for the division?
This assumes that the Angels and Rangers win and lose games at the right time.
First, I've heard rumors that the Rangers have a tough schedule coming up over the remainder of the season (excluding games against the Angels, apparently). Let's assume they go .500 over the remaining games. That brings their total record to 91-72 for the season. In that case, in order to also go 91-72 for the season and tie the Rangers, the Angels must go 26-14 over the final 39 games--a .654 winning percentage.
The Angels have done that before. At this point though, with the steadily flailing offense and messrs. Mathis, Wells, and the suck-of-the-week it looks like a pretty tall order.
Now let's assume the Rangers just bomb out the rest of the season and have a 1995-esque collapse, going, say, .400. That brings their final record to 87-75. To beat that, the Angels have to go 22-17, or .554, over the remaining games. That is slightly higher than the Angels's current winning percentage of .526 and so seems somewhat doable. By that same token, if this is what the Angels do and the Rangers go .500, then the Angels will finish something like 4 games out. Just bad enough to miss the playoffs for the second straight year but maybe not bad enough for Arte to step in and say enough is enough.
Finally, what happens if the Rangers keep on their current winning percentage of .577? In that case (depending on whether I round the calculator down to 57% or up to 58%), the Angels have to go either 28-11 or 29-10 to tie the division. That's a .724 or .734 winning percentage. In other words, the Angels have to catch absolute fire to win this thing in that case.
Perhaps at some point I'll look at these calculations for getting the wild card. As for winning the division, however, it looks like the Angels could conceivably win the division but that it will be pretty ridiculously difficult for them to do so. Sorry to be the bearer of bad news--let's hope the Angels can pull out all the stops and win this thing!