One thing that has -- for, I think, complex reasons -- largely fallen by the wayside is the equality of opportunity naturally producing inequality in outcomes determined by the combination of player skill and chance.
Even starting (as, for instance, in The Fantasy Trip) with the equality of resources in a character generation system utterly lacking a random factor, one in which what you get is no more nor less than what you pick, the courses of subsequent careers are bound to vary greatly. Some characters survive and thrive; others achieve relatively little; some perish in their first ventures.
That provides a key part of the context in games (such as the original D&D) in which options are so different from each other as to make "equality" nonsensical and the "balance" one of very disparate factors. Risk and reward figure, some choices being more conservative and others more daring.
It also puts into perspective the variation in starting conditions due to chance, a feature familiar from such other forms as card games. There is a range in which the effects of those largely wash out once the vagaries of actual play are brought to bear; "stat" rolls serve mainly to shape selection of strategies.
The importance of ability scores increases when significant bonuses and penalties kick in closer to the average score. When there is little game-mechanical difference between a score of 7 and one of 14 -- as opposed, say, to a difference of 4 points on attack and damage rolls -- the chief function is to inform the shaping of a persona for role-playing.
"Stats" of all sorts become more important as using them becomes more centrally the means of play. When they are often bypassed in favor of a direct correlation between dialog about a situation as cause and change in the situation as effect, they do not matter so much. When, regardless of the action taken in the narrative of events, success or failure ultimately depends on a skill rating or the like, those ratings count for a lot! (So much, indeed, that it can sometimes be like pulling teeth to get some players to engage the narrative at all.)
In Traveller, for instance, skill ratings -- production of which is the immediate object of the involved, heavily chance-driven character-generation system -- tend in my experience to serve mainly a persona-portrait function. Lack of expertise is easily made up by hiring experts. The course of events depends much more on the choices players make, especially their navigation of the social milieu. If one considers the similarity of that to our current real world, the reasons why are not too hard to discern!
A high rate of character mortality (as is common among low-level characters in old D&D and some other games) broadens consideration to a sum of many histories. A practice common in my experience is the keeping of a "stable" of characters in a campaign (although typically only one is played in a given session). That is due in part to the tracking of time, which may leave Character X either "elsewhen" or indisposed when Character Y undertakes an adventure. (I note, though, that the custom was addressed most explicitly in Tunnels & Trolls, which does not emphasize accounting of the calendar as does old D&D.)
I raise these points to give some historical perspective to consideration of older (and today largely obscure) game-forms, and their related rules sets, by folks unacquainted with them. Different goals naturally tend to call for different arrangements!
