A1 is to throw the ball inbounds on the baseline. B is pressing. A1 throws the ball in, and B1 bats the ball out of bounds and it hits A1 before it hits the floor.

As I read Rule 7, section 2 (I think it is), a player who is out of bounds when the ball touches him or her caused the ball to go out of bounds. In which case, it's B's ball.

I think we touched on this last week, but I don't believe I was comfortable with the explanation, so I'm asking again, and asking for your indulgence. Thanks.

You are correct also see casebook play 7.2.2 it covers your sit exactly