I would like to add a rating for online version of a board game. In this game there are many game rooms each normally having 3-4 people.

So I expect that player's rating adjustments (RA) should depends on

1. Rating of opponents in the game room
2. Number of players in game room and final place of a player
3. Person gets rating increase if he plays more games and more frequently
4. If a person leaves a game room (disconnect) before the game ends he should get punished with a high rating decrease

I have found two related questions in here

Developing an ELO like point system for a multiplayer gaming site

Simplest most effective way to rank and measure player skill in a multi-player environment?

Please, let me know what would be the most appropriate existing rating model to refer.