Re: Poll: How often do you actively slap the ground with your arms/hands when you fall during aikido training?
Secrets of Judo, from 1959, has a nice explanation on it. This might be the resource that someone was referring to about a formula (they have one in the book).
Most of the arguments I've heard against slapping is that in real life someone's hand got injured when they did it. Well, what if they didn't slap? I'd much rather have my hand broken than my head or vital organs damaged.
Having the hands and arms out and ready, instead of one behind the head, also makes it easier to block/attack in real life if someone decides to attack you after you fall. If you fall but have one hand behind your head and I jump on you, I don't think your hand behind your head will do you much good.