I was a chess player for many years. I held a decent FIFA rating.
Mohawk could do worse than to use a rating based off of international chess ratings. The games online could be rated, or non-rated, based on the player's wishes. If I wanted to try out Scientific, I wouldn't want my rating to be compromised during this test game.
So...the key here is to also give us primarily single players the ability to be ranked as well. A game won against the easiest AI should give you a point or two...with more points as the AI opponents get tougher. The key here is to see how the very hardest AI stacks up to average human opponents...and base your ranking in that fashion.
If you play a noob like me, over time, you would be given points equivalent to a lower level AI opponent...as this is where I see myself today, after just two hours in the game.
If you beat the hell out of Soren, clearly, you would gain more points, or your average would increase, etc.
Would you base your ranking on total points, or average points, or somewhere in between, or a combination of the two? A player with 600 wins and 550 losses should rank highly...and should gain respect for his game total. Conversely, how highly would you rank someone that was 15-2 against weak opponents? Higher than someone whose record was 32-20 against much tougher opponents?
The analysis of the parameters used can get fantastically complex.