Returning after Injury
 

My player goes in for a layup is fouled and lands on his hand. I tend to him, make sure he is OK. (probably 1 min.) He gets up, official tells me I have to take him out. Sub misses first shot, makes second.

When can I put him back in the game, or did he even have to come out?

He has to come out, since you came onto the floor. He can come back in after the clock has started.

You could have requested a TO to keep him in the game.

I was trained to tell the coach that they have a choice ... bring in a sub or call a timeout to keep him in. That said, since you brought in the sub, the clock must start before you can bring the player back in.

That is not totally a bad idea, but I think coaches should know some rules without us telling them everything. And I think timeouts are so valuable I would rather the coach make that request. But then again, I am not opposed to giving them that option, just not something I have been told to do.

Peace

You're right. The official doesn't have to do this as the coaches should know the rules. But sating simply "coach I need a sub" could incorrectly suggest that there are no other options.

I usually say "coach, we need a replacement unless you want to take a timeout." If they don't immediately request a timeout, then start the replacement interval.

When you are beckoned onto the court by the referee, tell them you want to take a timeout. The referee will then grant your request. At that point, you have the length of the timeout to get your player ready to play.

Alternatively, you can just walk out, once beckoned, and then replace the injured player. The substitute will shoot the free throw/s. The replaced player is eligible to re-enter the game as soon as the next opportunity for substitute presents itself, after the time has started.

I am not so sure we should grant the request for the timeout until the injury or the injured player is taken off the court. Just like you would not start the time to replace a player until the player has been "carried" off the court.

Peace

That's correct. I excluded those details, my bad.