When will a guy risk rejection to ask a girl out?

when he makes a fool out of himself, or when he annoys her. girls need time to think about it unless they actually already like a boy. make it sort of romantic or more simple, that will have to depend on what type of girl you are asking out. you should try to get to know the girl abit better first and let her know that you like her.
Hope that this will help.

How old is he?

When he is pushed by friends and/or really, really likes that girl. He will probably go for it if he knows that he will still be friends with the girl even if she says no and that the friend relationship will still go on unchanged.

Pretty much after he's slept with her...