Martial arts ranks are a quantifiable ranking measure of ones skill level in the unarmed arts. They are representations that are also labeled in a literal way like you'd see on a character sheet (and in some game systems, literally are).
No, those are purely
subjective measurements that are unique to a given martial art form/tradition. Game stat ratings are
objective ratings, each rating point signifying one 6-sided die to be rolled (for the Shadowrun game system, in this instance).
For instance, I hereby found the martial art of "Janessa-Fu," and I decree that it has 313 ranks. Why 313? Maybe I like prime numbers, maybe I just drew it out of a hat.
But a quick check of Wikipedia tells me that Taekwondo, for instance, has "color belts" of: white, white yellow, yellow, yellow green, green, green blue, blue, blue red, red and red black.
Sounds like their ranks wouldn't translate well to Janessa-Fu ranks (and prospective students must memorize the 313 unique color shades before advancing to Rank 2 - yes, there
will be a test later). And how would either directly translate to the Shadowrun game system?
They don't.