Backward pass
 

NCAA rules:

4th down and 3 for A at the 50 yardline. A1 throws a backwards pass toward A3 who muffs it beyond the LOS and the ball rolls out of bounds at B's 46. By rule a backward pass is not a "fumble", so does that mean we leave it at B's 46 and give team A a first down? Or do we bring it back where the backward pass was thrown from? Or is it brought back to the spot where A3 muffed it?

It is a backwards pass & therefore 4th down fumble rules do not apply. A's ball 1st & 10 at 46 yd line. Clock will start on the ready unless in the last 2 minutes of either half. (As a side note, wing guys need to explain to coaches & R may want to turn the mike on & give a quick explaination as most folks, even the TV talking heads, don't understand.)

same situation, but instead of a pitch, A1 attempts a handoff to A3. the exchange is botched, and the ball becomes loose.

4th down fumble rules apply, right? but who has fumbled?

I've heard different things. Some say only A3 can legally recover and advance the ball. But others say A1 is the fumbler. Because if the problem occurred during the exchange (say they bumped into each other, or the ball came out as soon as A1 put it in A3's belly), then that means A3 never had possession, so therefore he can't have fumbled.

Interesting. From memory, a fumble is defined as a loss of player possession other than by a bunch of things, including handing the ball. Does the definition of handing the ball encompass attempted handoffs? Or does another player have to gain possession in order for handing the ball to have taken place?

What if A1 is holding the ball and making no apparent attempt to hand it, and A2 strips it from him rugby style, like a stolen ball except by a teammate, but the ball becomes loose instead of A2's gaining possession of it? There I'd have to say it was A1's fumble. It can't be A2's muff because the ball wasn't loose until he made it so.