A couple years ago, I read The Design of Everyday Things by Donald Norman. It's about the psychology of the design of practical everyday items, like door knobs and door handles, water faucets, telephones, and car dashboards. One element he addresses is affordances, the components of everyday objects that enable us to act on them. There's a psychology to the shape of active components: buttons want to be pushed, levers want to be pulled, knobs want to be turned. One bad design mistake that rises again and again is making the shape of a control component suggest one kind of action -- turning, for example -- when the control requires a different kind of action entirely, like pulling. Another element the book addresses is the way the interface, especially the part that reports the results of actions, must either match the mental map of the people using the interface or give enough clues to let the users figure out the correct mental map. You don't place two buttons one above the other, but map the interface so that the top button lowers the temperature or volume; it's confusing.
The book made me rethink RPG design and inspired me in several ways. For one, it inspired my various mechanics that use the position of dice rolled on a character sheet or "dice map" to generate results. For another, it made me reconsider whether RPG design should be mainly about game design or interface design. But it's also been useful in considering why different games take different approaches to generating a particular result, and which approaches are best under which circumstances. If an ability score table notes plus and minus modifiers, the player expects to add and subtract these modifiers to and from something; it's an affordance. If you see a dice notation like "3d6", you expect to roll the dice.
OD&D had descending armor classes, 3e/4e have ascending armor classes. Both have you roll a single die, modify the result, and compare that to a target number. Which is better? From the new school perspective, it's better to use the AC as your target number directly than to look up a target number using the AC as a guide, so for a roll-higher mechanic, ascending ACs make more sense. But it's been pointed out that an old school shortcut is to add the AC directly to the die roll, along with a level modifier, and beat a fixed target number of 20, which is actually a little easier than having a variable target number. Clearly, math isn't the issue.
What's being neglected is the different mappings. In OD&D, the armor classes were originally fixed, non-overlapping shorthand descriptions of armor types. There were no modifiers to AC: Chainmail +1 adds +1 to your opponent's target number to hit, not to your AC. There were no AC 1, AC 0, or negative AC monsters. Since there were no negative ACs, and since the target numbers for the tables were derived from subtracting AC from 20 and modifying for character level, it made more sense to use a descending AC, especially if you used a house rule that made movement rate equal to AC. Under an OD&D "to hit" table approach, almost all modifiers are included in the table already, so there are only three things to be added or subtracted from any number in combat:
- magical weapon bonus (+1 or +2,) added to the die roll;
- magical armor bonus, added to the target number;
- situational bonus of +/- 1 or 2, based on a DM's ruling.