Looking for simple attack roll or skill roll mechanics

I'm writing a short article on game balance, specifically dealing with typical combat attributes, combat resolution systems, and how those values tie in to game balance, character progression, etc. What I want are some examples of the "to hit" rolls, or skill checks, or other similar contests or evaluations (there must be a word for this!), so I can compare and classify them, along with their balance implications. It's important that the mechanic is documented or otherwise known, rather than just being an opaque "68% To Hit" or whatever. They don't have to be from computer games; alongside some simple classic ones from Civilization and Age of Wonders, I'm also looking at the d20 attack roll from Dungeons and Dragons, a couple from Warhammer, etc.