Did Coriolanus play league?

Possibly one of the most surreal conversations I've had in recent weeks was in a debate with a PGCE student, naturally enough about the respective merits of union and league. (We're talking rugby here. If you didn't get that, don't bother reading on.) His main line of argument was 'Macbeth would have played league.' Then he upped it to 'Coriolanus. Coriolanus definitely played league. So did Titus Andronicus.'

Union or league is not really the question.* The real question is what position did they play? Macbeth's a hunky warrior to start, but turns out to be a bit of a flash in the pan, with power going to his head. Sounds like a centre to me. Macduff, slogger, slow to start, but makes it in the end? Classic prop behaviour. Julius Caesar, live fast, die young? Must be a winger. This is definitely my new favourite game. Along with the 'what would any given Shakespeare character be listening to on his iPod?' game.

* Because of course, the answer's union. No-one has ever seen the Aire Valley FM dancing girls in a Shakespeare play, and it's not a rugby league match without dancing girls in jewel coloured lycra and furry yeti boots.