Despite its issues, it is hard to argue with the success of the hit point mechanic in D&D. (That’s a post of its own.)
I think what makes it so great is that it spreads an outcome over several die rolls, and it gives the player several points at which to decide to cut their losses or press their luck. And it doesn’t simply function that way in one combat either. Combat and many of the other hazards encountered in the dungeon will deplete hit points. It’s a press-your-luck mechanic for the entire expedition.
Compare this to what has become a more conventional mechanic. The big burley fighter with the 17 strength (part of the top 1.4% of the world’s strongest people) walks up to a door. The player rolls 1d6...one. The door doesn’t open. The mage’s player then rolls 1d6...six, and—bing—the door opens.
Now, I’m not sure what the best mechanic for opening doors is, but I’m beginning to think that if anything is worth rolling for, it’s worth heading more in the hit points direction than the open doors direction.
Spells in Sovereign Stone have a casting threshold. Each round, the caster makes the appropriate die roll and adds its result to a running total. When the total exceeds the casting threshold, the spell is cast. That sounds much better to me than those games I played where a single die roll determined if my spell was cast or failed.
The AGE system from Green Ronin generalizes this into advanced ability tests that can be used for anything.
(I’m certain there are other systems with similar mechanics. I’m just listing the ones that come to mind.)
I think a reversal of this could be interesting. Say a party heads out on a stealth mission. The GM sets several thresholds at which the alertness of the place being infiltrated steps up. X failed rolls means that the denizens are suspicious. Y failed rolls means they know something is up and are actively searching. Z failed rolls means the jig is up, and the PC’s have been found.
Much better than a single failed stealth check by a single player killing the whole mission. Plus, the players have a chance to change tactics midway through depending on how things are going.
Perhaps the ultimate expression of generalizing the hit point mechanic is Robin Laws’ Dying Earth. The die rolls are a straight d6 with the same chance of success or failure (or exceptional success or exceptional failure) every time. The player can then spent points from their attributes for a chance to reroll. I found it very off-putting the first time I read it, but now I’m thinking that I need to give it a chance.
Plus the system of trumps in Dying Earth is great too.