The leveling concept is an RPG idea that I think needs to die a quick death. They borrowed it all from D&D where things like stats were needed because you used your imagination.
Actually, knowledge of stats isn't required in table-top gaming either. That's not the problem. Recent incarnations of D&D do suffer an emphasis on statistics -- but they are somewhat ironically derided as being like video games!
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In typical old-school tabletop gaming, even though stats for items exist they are often not revealed to the player until they are discovered through trial and error. The same is done in some video games, and it can be done well.
Instead how about we drop all the stats stuff completely.
Well, you can't -- completely. The computer needs metrics internally. But you can definitely take the focus away from them, and/or not present them to the player.
Incidentally, it's a good idea but not a new one. The trick is figuring out how to present what the stats measure in an immersive fashion.
Here is one of the first 3D "RPG" videogames ever written, and it does not use stats at all. The graphics are primitive by today's standards, but it is a very immersive game compared to modern "RPGs":
http://en.wikipedia.org/wiki/Dungeons_of_Daggorath
Video of first dungeon level:
http://www.youtube.com/watch?v=sQKQHKdWTRs
If you can find it in emulation and try playing it, you'll see precisely what I mean. (If you can't, you'll look at the primitive graphics, scoff, and not understand...that's ok.)
It isn't done now because they can still get away with using things that were designed for paper and text games.
Again, you're barking up the wrong tree here. The problem isn't emulation of paper and text games, which can be done well or poorly. The problem is an emphasis on stats, which can occur in any sort of game.