As of 8/1:

Assuming the Rangers, Angels, and Mariners maintain their current win percentages, the Athletics need to go 42-12 in the remaining games in order to make the playoffs.  

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As of 7/28:

Assuming the Rangers, Angels, and Mariners maintain their current win percentages, the Athletics need to go 44-14 in the remaining games in order to make the playoffs.  

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As of 7/27: 

Assuming the Rangers, Angels, and Mariners maintain their current win percentages, the Athletics need to go 46-13 in the remaining games in order to make the playoffs.  

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As of 7/26:

Assuming the Rangers, Angels, and Mariners maintain their current win percentages, the Athletics need to go 48-12 in the remaining games in order to make the playoffs.  Let's go, win 5 of every 6!  

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Previous fucked up math:

So it sounds like most people have given up on this season pretty much, which is understandable.  The A's are currently sitting 12.5 games back, and the situation looks pretty dire.  I was just sitting at work thinking about what it would require to make the playoffs this year, and I made a little spreadsheet model.  

Assuming the Rangers, Angels, and Mariners maintain their current win percentages, the Athletics need to win __ of the last __ games.  Obviously that would be insane, but I still like to have a number to look at.  Of course, the other teams probably won't win at the exact same percentage for the remaining games.  Texas has been on a tear recently, so maybe (hopefully) they will cool off.  

I am just thinking of it as winning ___ games remaining.  Obviously it is not a reasonable goal, but hey, a man can dream.