I think of area runners who I would classify as hardcore. You will not ever find them at races yet if they were to line up, would handily win.
For some, the greatest competition doesn't involve any other person they need to look no further then themselves to find their greatest competitor.
I would have to second GTF's comment. If we're talking about the internal fire for competition, how do you compete against yourself without having a baseline? Maybe someone you haven't beaten or a certain race performance or something like that?
I also don't know of a single competitive person for whom a race atmosphere doesn't provide something extra. Maybe just the adrenaline of head to head competition or maybe people to chase or maybe a million other things. Whatever it is, though, everyone who lines up seems to be affected.