Mostly, when we do things, we perform only within a fairly narrow band of ability. Slightly under our skill level, equal to our expectations, or slightly better than we expect. Exceptional luck either way is rare.
I've been wondering how to reflect this in a game, d4-d4 does this pretty well and I recommend it as a pick-up system for your odd little ideas but it doesn't quite work for me in some ways in regard to this question.
What about coin tossing?
The scale would need to be compressed, probably a 1-5 scale, to make it work but if the protaganist and the challenge each tossed a coin that either increased their level by one (heads) or decreased it by one (tails) that would give you the right range.
Dirk is an Average (3) Warrior, fighting an Average (3) opponent.
He flips and scores Heads raising his ability to 4.
The opponents flips and scores tails, taking his ability down to 2.
Dirk defeats his opponent.
Complications would be hung off that to increase the granularity of the system and to describe specific instances and special cases, but that would be about right.
Over The Edge or HeroQuest style trait descriptions would probably suit best.