Backcourt violation?
 

A1 is shooting second free throw of a 1 and 1. Shot is missed and rebound tips off A2's hand (no possession/control) and heads toward out of bounds line. A3 leaps from inbounds and smacks the ball in the toward midcourt while he is in the air heading out of bounds. Ball goes into backcourt and A4 retrieves it. Backcourt violation?

No.

The key is whether you judge A3's action to be a :smack" (as described; no player control) or a "throw" (player control).

the first is not a violation; the second is.

In this play, I'm defaulting to no control unless it's clear that A3 held the ball.

It was not a "smack", the player leaped, secured ball with one hand and threw it back toward midcourt. I guess the question is, can a player gain control of the ball while not touching the court?

And if the "smack" is with a closed fist it would be a violation.

Yes.

You just changed the play -- that changes the result.

It happens all the time, that's why there's an exception built into the backcourt rules for throw ins.