Drawbacks

I'm fascinated by the idea of stats which have no maxima.

By this I mean that any value along the stat range has advantages and disadvantages. I've done this ever so slightly for the Size stat in Unangband, where increasing Size lowers your Agility, but this is too easily overcome (by having high Strength) and to make it more significant would require a redesign of the whole class and stat system.

A clearer example of this is the Body Type characteristic in Brink. In that game, you can have either a character with high hit points and the widest selection of weapons, but moves slowly and unable to climb obstacles effectively (the Heavy body type) or a character with lower hit points, much more restricted weapons, but high speed and maximum movement choices (the Light body type) or one in between.

Now you can simulate a stat system with no maxima by having a fixed number of stat points you can allocate to various stats, and provide no way of increasing the number of stat points you have. There are three problems with this: two obvious and one subtle.

The first obvious problem is the fallacy of stat equivalence: that is, increasing your strength stat by one point is equal to increasing your intelligence by one. In a system with stats with no maxima, you have to explicitly balance the drawback with the advantage; in a system with a fixed pool of stat points, you loss the ability to have improvements on a bell curve or inverse bell curve, as people will inevitably min-max by dropping points from stats near the middle range to pump one or more stats into the interesting edges of the curve (or vice versa).

The second obvious problem is psychological: people are not good at moving numbers around multiple stats, but when you make explicit trade offs instead of implicit ones, they are much more able to make correct decisions instead of vascillating between multiple seemingly unimportant choices.

A more subtle problem is that you miss out on systems which have interesting but hard to define drawbacks: an example of which is the Luck stat. Having a high luck means you get the widest variation of dice rolls against you (good and bad), having a low luck means you get fixed results every time. Having a low luck and therefore low variation emphasises skill (think TF2 servers with no randcrits and no damage spread), having a high luck means you occasionally overcome overwhelming odds (and therefore have more chance of having fun), but also can perform below par.

Now the question I have, is it possible to design a system in which you have every player characteristic defined by stats with no maxima?

The first example I can think of is Belief. If you have high Belief, you have powerful spell casting abilities, but are also vulnerable to magic being used against you; if you have low Belief, you are highly resistant to magical effects applying against you, but are unable to use magical effects reliably.

Any suggestions for other stats which could operate this way?