What rating system should I use for a team-based webiste? My website has a few thousand users, and they play in teams pitted against each other, i.e. 5v5. I want to implement a system whereby each user has an individual rating that adjusts whether they win/lose, depending on the skill rating of the other players involved. For instance, if a player on your team is really bad and you lose, then you won't lose as many points as if your team was a good one. I was thinking of averaging the ratings of each team, and using the ELO rating system to adjust ratings. But as far as I know the ELO rating is optimized for 1v1 games such as chess, and I'm not sure how mathematically suitable this rating system is for group matches. Excuse me if I sound like a math noob, but thank you in advance for answering this question

A rating system is just a function $r(u,v,w)$ where $u,v$ are the ratings of the competitors and $w$ is the result of a match. In the ELO system, it is assumed that $u,v$ are scalars. But if you look at the math, there is no barrier from generalizing to vectors. For instance, if you assume $u,v\in\mathbb{R}^5$ (which is your case) then just replace scalar multiplication with the dot product and other similar changes to obtain the analogue for vector rankings.

Actually, performing vector rankings has been studied extensively and there is really nothing new over the scalar case.