Example:

Str based skills should check STR for skillups (parry/possibly weapons/etc)

INT based - int

dex based dex

etc/et al.

My rationale is, I was a nerd in highschool - I was not good at sports. I couldn't play defensive tackle even if I wanted to, sure with a LOT LOT LOT of practice I could overcome the fact that in H.S. I was a 130lb bean pole soaking wet, but it'd take me longer than someone with the "recommended" physical attributes.

Elves should not advance quickly in parrying, because they suck at it.

Giants should, as physical based fighting is 2nd nature.

I don't think that there should be 1 stat to rule them all when it comes to skill learning.