Ok, so I just played a game that, for lack of being modest, I destroyed. Now with a score on 
of 11/0/4 with 61 cs at 20:33 where the enemy team surrendered, AND I had the most gold on the team and in game, how in gods name did I get an A-, where my teammate 
had a score of 7/1/1 and 137 cs and he got an S-. Please, someone explain this to me.
You're compared to all other performances on that champ in that role, not necessarily any particular absolute numbers, so good enough for one champ/role isn't necessarily good enough for an S on a different champ/role, as the grades work on a percentile basis.
While you may have done well, apparently a sufficient number of other players have done better. (Also, more goes into your performance than just kda/cs, theres stuff like warding and objectives and so forth as well.)
cs number sadly always is taken into consideration, so you might have rekt hard, but you haven't farmed enough to "deserve" an S Rank, according to the system..
I find it easy to get S's with support champions. I got an s with janna on my 2nd game. And i took zilean top, went 3/1/3 in a 20 min game and got an S. But for assassins it is quite hard to get an S. I like assassins, and I haven't gotten a S on any assassins yet. So if you wanna farm chests play less common/"brain dead" champions where it is harder to get kills.
your cs at 20 min was bad, if you were at 120-130 you would have got an s-, cs plays a bigger role than your score unless you go 18-2 in like 25 min.
edit: I say this because I've had plenty of games where i was negative score and still got s- I'm talking like 4/6, but like someone said it compares you to other cockroaches jungle assuming you were jg, if you had played him mid and got that score you might have got an S because hes is rarely played mid so your comparison pool is lower.
