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.

The simplest I can think of is this: always hit. It's on the defender to evade the attack. Then it's a simple "roll a random number and see if it's within my evade parameter" check. As far as I know, this is how the Final Fantasy XIII games work. See the damage calculations here: http://www.ign.com/faqs/2010/final-fantasy-agito-xiii-damage-calculation-guide-1085648

The only example that I can think of that has "official" documentation is from Dragon Age II (from the Wikia site http://dragonage.wikia.com/wiki/Attributes_(Dragon_Age_II)#Dexterity): "Your attack score is your chance of successfully hitting an enemy with a basic attack. The takes your attack percentage (derived from your primary attribute) and subtracts the enemy's defense and displacement percentages (if applicable). Attack scores are also modified against enemies of higher rank (-15% for a lieutenant and -30% against a boss). The final sum is the likelihood of success. If you fail to make your attack, you will strike a glancing blow that does 10% of your character's base damage."

Hope this helps!

There's also a good document about Final Fantasy X's Accuracy vs Evasion stats here: https://www.gamefaqs.com/ps2/197344-final-fantasy-x/faqs/31381

Also, Final Fantasy VII's Defense% stat: http://finalfantasy.wikia.com/wiki/List_of_Final_Fantasy_VII_stats#Defense.25

Side note: I promise I play more than just Final Fantasy and Dragon Age, I just happen to know where the places for their damage calculations are

When combat in RPGs where is not dependent on the motor skills of the player, I believe the combat comes down to resource management. Your main resource that you're trying to maintain is your Life Points. The various means that you have at your disposal to reduce your opponents life or support your own may have some limited number of uses or require consideration for the time it takes to implement their use (for example, you get one attack per turn).

A "To Hit" chance would then in effect become a rate of depletion, particularly on the Life Points.

In balancing a game, a designer's job is to determine expected rates of depletion for life points and other resources as the player moves his character from one location to another where presumably an opportunity will be provided to replenish resources and plan for the next leg of the journey.

Character progression in some ways increases the resources and options available to the player and thus opens the player to a number of ways to resolve combat, making it more interesting as the player progresses. However the balancing of the battles between two points is still about achieving the same effect which is finding a good rate of depletion of player resources as he progresses from one point to another.

The second Final Fantasy document has the sort of thing I'm looking for, although unfortunately it's full of special cases and hidden variables so it's too complex for my needs. I guess 10 iterations of a series will tend to do that...

Any other examples?

I'm sure I can find others. It might be a few days, though. Stupid Irma.