Troy has known Max for quite some time since they were young. When he was a child, he attended Max's fourth birthday party where he seen McGoogles (a Scottish frog character) on TV and in person (Mr. Keeble in disguise) and was automatically afraid of it and it became his greatest phobia, even as he got older. But later in his teenage-hood, he grew out of his fear and came to accept McGoogles as just a harmless and imaginary character thanks to the school counselor.
Initially, Troy was a friend of Max's.
However, as he grew up, Troy became a bully at school, developing a love for picking on and torturing the kids that are younger and smaller than him. His main target is always Max. He would always write the name of his victims on a plain white T-shirt. He even partnered with another bully, Dobbs, to torment Max on the school parking lot. At the end of the film, the kids had finally got back on Troy and Dobbs by throwing them in the dumpster.
It is implied that he had learned his lesson and reformed.