Well that pretty much explains it all. With overhang you are probably cutting out a quarter of the energy you could collect, but even on a clear day, 3/4 of what you could collect can still add up to a strong signal. But when the atmosphere cuts the signal strength, and your overhang cuts it, it drops to zero. Loss of energy due to overhang is probably greater than loss due to rain on the dish, but oh well. I don't have anything left in my arsenal to prove or disprove the rainx stuff. I give up.
Oh, but by the way, division by zero is undefined. It's not equal to zero.