behind the glory: hand rankings

[emp1346]

so i understand that certain starting hands are better than others, but how is this determined (and supported) mathematically?

forget that it just is, but why is AA better than other hands?

also, i'm not interested in a hand vs. hand comparison (i.e. AA is better than KK because...) but instead a generic AA is better than ?? because...

i can see how doing a heads up comparison of all starting hands can produce these results, but is there something easier?