Throw In
 

After a made basket A1 runs the base line and when he is behind the backboard he attempts a thrown in that hits the back of the backboard and comes directly back to him. This ball has never touched inbounds. Do you have anything?

OOB violation/Throw-in violation

I agree that I'm going to probably make the same call, but what rule has been violated?

Actually an out of bounds violation. I guess technically you could say a throw-in violations as well, considering that you did not complete the throw-in properly.

Peace

I can bounce the ball out of bounds and I can turn around and bounce the ball off the back wall. Why can't I bounce the ball off the back of the backboard as long as I complete my legal throw in within 5 seconds

Because the thrower released the ball toward the court as he's required to do within 5 seconds...once that happens, the thrower can't be the first to touch the ball. He also needs to release the ball and cause it to touch another player.

The player has 5 seconds to release the ball INTO the court. The back of the backboard is not part of the court. Once the ball rebounds to A1 he would still have the opportunity to throw the ball to A2 who is on the court.

No you can't.

2013-14 Case Book 9.2.2 Situation A

Thrower A1: (a) causes the ball to carom from the wall behind him/her, or from the floor out of bounds and then into the court; (b) caroms the ball from the back of the backboard to a player in the court; or (c) throws the ball against the side or the front face of the backboard, after which it rebounds into the hands of A2. RULING: Violation in (a) and (b), since the throw touched an object out of bounds. The throw-in in (c) is legal. The side and front face of the backboard are inbounds and, in this specific situation, are treated the same as the floor inbounds.

No of those 3 things has happened in the OP

The back of the backboard is out of bounds by rule. The throw-in touched this object that is out of bounds and therefore it is a violation. Whether or not it is a "run the endline" throw-in or whether the ball comes back to the player is irrelevant—it's a violation. I'm not sure how that case play has nothing to do with the OP. Plus you said that you are allowed to throw the ball off the wall on a throw-in and obviously that's not true.

I think there is a difference between throwing the ball off the back wall and catching it and then throwing it into the court, and throwing the ball off the back wall and letting it bounce into the court without touching it again.

7.7.2
ART. 2 . . . The throw-in starts when the ball is at the disposal of a player of the team entitled to the throw-in. The thrower shall release the ball on a pass directly into the court, except as in 7-5-7, within five seconds after the throw-in starts. The throw-in pass shall touch another player (inbounds or out of bounds) on the court before going out of bounds untouched. The throw-in pass shall not touch a teammate while it is on the out-of-bounds side of the throw-in boundary plane.

He violates in two ways, (1) His pass did not go directly into the court, and (2) the throw in pass did not touch another player on the court before going out of bounds untouched.

The case play references the ball touching out of bounds and then going into the court. My situations are bouncing the ball, off the backboard, floor or back wall and having the ball come straight back to A1. A1 can 100% without a doubt "dribble" the ball while standing out of bounds. So the question is what makes it illegal to throw it against the back of the backboard and have it rebound back to A1 while still out of bounds?

On an end line throw in, we have to determine the intent of the throw. 99% of the time, or more, the intent is obvious. This is one of those times. The intent was to throw the ball onto the court, thus making it a throw in pass. Once that throw in pass touches OOB before touching a player, it is a violation for having a TI pass go OOB before touching a player.

This is the correct understanding and reasoning.