Player rating for game with random teams

I am working on an algorithm to score individual players in a team-based game. The problem is that no fixed teams exist - every time 10 players want to play, they are divided into two (somewhat) even teams and play each other. For this reason, it makes no sense to score the teams, and instead we need to rely on individual player ratings.

There are a number of problems that I wish to take into account:

• New players need some sort of provisional ranking to reach their "real" rating, before their rating counts the same as seasoned players.
• The system needs to take into account that a team may consist of a mix of player skill levels - eg. one really good, one good, two mediocre, and one really poor. Therefore a simple "average" of player ratings probably won't suffice and it probably needs to be weighted in some way.
• Ratings are adjusted after every game and as such the algorithm needs to be based on a per-game basis, not per "rating period". This might change if a good solution comes up (I am aware that Glicko uses a rating period).

Note that cheating is not an issue for this algorithm, since we have other measures of validating players.

I have looked at TrueSkill, Glicko and ELO (which is what we're currently using). I like the idea of TrueSkill/Glicko where you have a deviation that is used to determine how precise a rating is, but none of the algorithms take the random teams perspective into account and seem to be mostly based on 1v1 or FFA games.

It was suggested somewhere that you rate players as if each player from the winning team had beaten all the players on the losing team (25 "duels"), but I am unsure if that is the right approach, since it might wildly inflate the rating when a really poor player is on the winning team and gets a win vs. a very good player on the losing team.

Any and all suggestions are welcome!

EDIT: I am looking for an algorithm for established players + some way to rank newbies, not the two combined. Sorry for the confusion.

There is no AI and players only play each other. Games are determined by win/loss (there is no draw).

Provisional ranking systems are always imperfect, but the better ones (such as Elo) are designed to adjust provisional ratings more quickly than for ratings of established players. This acknowledges that trying to establish an ability rating off of just a few games with other players will inherently be error-prone.

I think you should use the average rating of all players on the opposing team as the input for establishing the provisional rating of the novice player, but handle it as just one game, not as N games vs. N players. Each game is really just one data sample, and the Elo system handles accumulation of these games to improve the ranking estimate for an individual player over time before switching over to the normal ranking system.

For simplicity, I would also not distinguish between established and provisional ratings for members of the opposing team when calculating a new provision rating for some member of the other team (unless Elo requires this). All of these ratings have implied error, so there is no point in adding unnecessary complications of probably little value in improving ranking estimates.