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We have to have "stats". There's not really any feasible way (or practical reason why) we would avoid it. But I propose the following:

  1. Inner workings of stats are "hidden" from the player. The player can see them, sure, and see when they increase. But how they increase should be a mix of a variety of different factors that takes effort to figure out how to manipulate it. For instance: we don't level up in life, and there's no reason to think that hacking 20 enemies to bits with a sword will make you better at magic--and it's impossible that hacking 20 enemies to bits with a sword will make your friend better at magic. And if I go to the gym in real life, eventually my strength will increase: but other factors (fatigue, effectiveness of workout, diet, companionship, timing) come into account, too, and I can't control all of them.
  2. Stat increases are based predominantly on the actual activities that you do, and not just bashing enemies. Why shouldn't walking around increase your endurance (albeit slowly)? Maybe that'll be some motivation to keep walking after you've gotten the "airship". Speed can increase if you practice running away: but you can't do it if you're carrying a lot of stuff--you'll be increasing your strength instead (i.e. Elder Scrolls, although not necessarily with so many skill options).
  3. Stats increase individually, not based on "levels". Levels may be necessary, but each stat (as well as element) is given it's own "level" (as in Quest 64, only without the lameness).
  4. Battle Skill Confidence: The more often a character makes contact with an attack (be it melee, missile, or magic), the more confidence he gains in that battle skill. If a character misses, he is still improving in that skill, but if he makes a hit, the rate of improvement becomes greater because the character gains some confidence in that skill. If a character misses after making a series of hits, his confidence will decrease; however, if a character suddenly makes a hit after making a series of misses, his confidence will increase. It may be possible for a character to gain too much confidence, becoming overconfident (status = "cocky"), and though that character may execute some devastating attacks, he will leave himself open to opposing attacks that he would normally evade or block; on the other hand, a character could become unconfident (status = "cautious") after losing too much confidence, and though that character may struggle to make a hit, he will block and evade more opposing attacks than usual.

All this to increase the reality of the game enough to make it interesting, dynamic, and mind-increasing.