I've been playing with a concept over on The RPG Site the last few days. The idea is that how a system handles skills can be quantified along certain axes. The axes we seem to have settled on in the thread are:
For the purposes of this discussion, anything that functions as a skill is covered. For instance some games use Professions or Classes as skills, in that they are what supplies the character's target number - or the character's part of the TN - for a test. This does not cover actual interpretation of how skills are handled by a GM, which is impossible to quantify for all GMs.
Player/Group-defined<--->Designed is a continuum from a game whare all skills are player or group defined and/or created to one where all skills are designed into the game by the designer. Example: Risus allows players to create their own Cliches - the functional equivalent of skills in that game.
Broadly-defined<--->Narrowly-defined is a continuum from a game where all skills are defined so as to cover a great deal of circumstances to a game where each skill is defined so as to cover a very limited set of circumstances. Example: A skill such as Science is generally broadly defined, where a skill like Hydrodynamics is generally narrowly defined.
Edge-defined<--->Center-defined is a continuum from a game where all skills are defined by their limits to a game where all skills are described by their central focus, with the limits being left vague. For example, GURPS skills are generally defined with a statement describing in a fair amount of detail what is and is not covered by the skill, whereas in Risus a Cliche like Lion Tamer is defined as "Stuff that has to do with Taming Lions."
Overlapping<--->Discrete is a continuum from a game where different skills may apply to the same situation to a game where the problem dictates the skill used. For Example, one game may allow you to use your Rifle skill to operate a pistol - either as is or with a modifier, while another game may force you to use the Pistol Skill, perhaps with a default.
Nested<--->Stand-alone is a continuum from a game where all skills start out as root skills which can in some manner be specialized into several other skills to a game where all skills are essentially unrelated. For Example, in Ringworld, you can take a root skill of Physics, which can be specialized into Physics: Astrophysics and/or Physics: Plasma etc.
The endpoints of these axes are essentially theoretical - such paragons seldom exist in the real world - but they are none the less effective. As to the gradations, make them however fine you want to make them. Strongly - Weakly - Neutral - Weakly - Strongly works fine, or 1 to 10, or -9 to +9 for that matter. However you feel comfortable.
Some combinations are more common than others I'm sure you can supply dozens of examples for some combinations, and none for others. Breaking down how one can handle skills is a useful tool, either in design or in nailing down why one reacts the way one does to a particular game, thus allowing you to apply that to other games.
How many times have you heard "I can't stand games with over X number of skills!"? On the surface, this makes no sense - there is no cutoff switch in the brain where when X is reached no more information can be processed. However, maybe they are actually disliking Narrowly-defined and/or Discrete and/or Edge-defined skills, all of which are associated by custom and usage with long lists. If you can address that, you have gained something.