User blog comment:Neppudere/The verdict on the LAW/@comment-3204627-20151005153315/@comment-26340448-20151006060027

FWIW, I've never seen anyone with a "high" damage (say >10m) getting an N card, but most of the UR drops in my alliance go to people with "low" damage (say <30m).

So maybe you get more R's/USTs/Arcanas over N's as you deal higher damage (better rewards as per the help file), but UR drop rate favors players with low damage as well :P