How do stats affect to-hit percentages?

My soldiers have an Aim stat and a Defense stat. Sometimes, I've got things like smoke grenades which claim to give you +20 defense and the like.

What does this actually mean in terms of chance to hit? Is a point of aim or defense worth 1% to hit, or some such?

Solution 1:

Aim and Defense are pretty simple. As you suggest, they're simply lacking a % sign.

Aim is your base chance to hit. A rookie's starting 65% Aim means a 65% chance to hit.

Defense is also pretty simple: 10 Defense means 10% less chance to hit.

In this way, you can think of Cover as providing Defense, and standing in a smoke cloud makes you 20% less likely to be hit, hence, 20 Defense. (Incidentally, 65% base Aim and -20% for low cover is why most Rookies have a 45% chance to hit sectoids in your first couple of missions).

Additionally (thought not a stat per se), different weapons get different range bonuses, which increase or decrease your chance to hit. Shotguns can get up to 37% bonus chance to hit at point blank, and Sniper Rifles actually get a penalty if you're too close.