Basically the rating system is a bunch of such and such, and that seems to be especially true in ARAM. Not uncommonly some player will absolutely carry the team, not get S (of course they get too many deaths if they are carrying a weak team to victory in a long ARAM game; for S rank you have to have low deaths, no exceptions to that as far as I have ever seen), and some player that contributed very little to the overall team effort but managed to keep a low death stat (by avoiding participation in most team fights, such as when we are trying to save inhibitor) gets an S rating. As far as I can tell K/D/A is the only thing that matters in ARAM -- or at least any other factors are insignificant by comparison.
When I play Soraka in ARAM i sometimes do more healing than any other champ in the match does damage (and almost always do close to it), but never get S because I don't get enough kills.
Another function of this is that it is almost impossible to get S rating in an ARAM game that ends quickly. If you steamroll the other team that hard, you don't have enough time to get k/d/a numbers up to what is required for S rating. For example, 8/0/15 will not get you S rating regardless of length of match (as far as I have witnessed), but if you get 15/2/20 you will almost certainly get S rating.
For the same reason it is quite hard to get S rating in an ARAM game that goes on too long, because you will get too many deaths if the match lasts that long.
Take an example: your team is badly outmatched early, they take your two towers and inhibitor in the first ten minutes, you fight hard, rally your team, grow, make a bunch of clutch plays, and by hook or by crook you claw your way back into the game. Everyone in team is like, "Thank you," because you are carrying them and they know it, the match should be over already. Eventually your team grows, you outscale the enemy, and make a late comeback to win a game that was nearly certainly lost in the beginning. You pretty much did the hardest thing to do in this game carrying a weak team from the brink of defeat to a late victory..... GUARANTEE YOU WILL NOT GET S RATING FOR THAT, lol. 100% guarantee. You cannot get S rating if it is a hard match and you are in the fights, because you have to have very low deaths to get S rating.
Does it reward coward play that screws your team? Absolutely. Coward play that screws team but cleans up after team fights and gets good K/D/A at the end can totally get S- or better rating in ARAM and pick up that champion chest even though they lost and pretty much ensured their team would lose. I've seen guys on losing teams that do nothing to stop every objective from being taken except stay as far away as possible and poke --- get S many times. Then of course they blame their team who actually tried to defend objectives for "being crap". For example, Lux player will save up ult, not participate in team fights, just use ult for sniping kills once team gets enemies to the brink of death --- even though she contributed very little and was a main contributor to the team loss by avoiding participation and always staying out of reach of danger regardless of circumstance, she will have a good k/d/a at the end (unless team got totally steamrolled so much that she doesn't have enough time to snipe enough kills from out from under the teammates who have actually done the damage and taken the damage necessary to secure those kills) and will get the S.
Actually, I didn't think of it before because it is so moronic that it should even matter, but "kill stealing" is a great strategy to get S scores in ARAM. Just save your ult and such for when your teammate almost has the enemy killed, stay out of danger, jump in and get the last shot... repeat. Actually now that I think about it that is what a lot of people I see in ARAM do, lol. So sad. The fact "kill stealing" is even a concept in a team game like this is pretty pathetic, Rito.
Ok, as you can see, this thing with the ratings really irritates me. I'll stop. All the yo-Rito boys can come in and contradict me to say how perfect the rating system is now. Maybe they even believe it.