Composure as a stat

I've played a few games that have a 'Composure' trait or something similar.   I think more systems should have this.

Think of it this way - most likely your character has a strength score or something along those lines.  This is how the group can all have an idea of how strong the character is, and there's a way to adjudicate what he/she can do.  "I bash the door down" -  not with a four in strength, buddy.

So what about when the group meats a 30 foot tall, fire breathing dragon?   Or is involved in a firefight with bullets whizzing by?    Its super easy, from the comfort of your game table, to declare that Bob the Bad Ass shrugs off care or concern and advances grimly to meet his foe.  We don't get the quiver of fear in our stomach, or the paralyzing terror from having someone else try their best to kill you.

Granted, when we sit down to play these games, we want to be heroic.  And this can still work.  We also want to be ridiculously strong and have awesome abs.