The Wave is all about types, and Robert Billings is no exception: he's the school loser, to use the novel's rather cruel terminology. Ben thinks that part of Robert's problem is that he's living in the shadow of his ultra-popular brother, who used to attend Gordon High. But keep in mind, we never get confirmation of this from Robert himself. (As we discuss in "Narrator Point of View," the narrator never reveals Robert's thoughts.)
Even though we might feel sympathetic toward this guy at the beginning of the novel, things quickly go downhill. He gets super involved in The Wave, threating Laurie behind her back. The narrator even implies that he actually stalks Laurie at school after hours, and that he has something to do with spray painting "enemy" on her locker.
We have to assume that this didn't all appear out of nowhere. Robert has some seriously bad ideas going on in his head that were probably in there before The Wave even existed. At the same time, his tears at the end of the novel suggest that he's a sensitive, vulnerable young man who is simply struggling to belong. Once again, we've got a problematic character. Score!
In the beginning of the novel, other students are afraid to ruin their own images by hanging out with Robert. He's totally isolated at school and isn't successful on either the social or academic front.
When The Wave comes along, he seizes the opportunity to make a change. For a while, it seems to work: Robert's grades improve and his social life actually comes into existence. In The Wave, Robert doesn't just find a way to relate to his peers, he finds a way to actually have power over them. As Ben's bodyguard, he creates an image for himself of someone who is not to be challenged.
At the end of the novel, we're led to believe that Ben will take Robert under his wing. And you know what? We really, really hope this happens. Robert has some big issues, and his experience in The Wave might make things even worse if he doesn't have somebody to talk to about it. Ben is in a position to make things up to Robert, to right the damage he did by exposing Robert to The Wave. We hope Ben takes advantage of this opportunity and helps Robert get involved in things that can highlight the unique talents and skills he most certainly has.