I think characters like Michael Corleone or Tony Montana from Scarface are better representatives of anti-heroes or tragic heroes. Sure Vito wasn't Superman, but really, he wasn't tragic or evil, he just existed in his world and succeeded.

There is a formula for tragic heroes I learned in Grade 10 english class. I can't remember...

Something like:

1. Hero of great importance
2. Has tragic flaw
3. Flaw effects several other people
4. Flaw destroys hero
5. Hero dies.

Something like that...