I'm currently working on a gaming site where users will submit virtual players for different games, like Chess, Nash, Backgammon, Go, etc. The idea is that users don't compete themselves, but through their virtual players. There will be leagues, tournaments, and other competition formats.

The question is which would be a good rating system for users in this environment. Take into account that every user may have many different virtual players playing in many different games. As a general guideline I would like to guarantee the following properties:

• Users who have a lot of mediocre players should not score higher than users with a few very good players.
• A user with a high rating should not be penalized if he adds a new bad player, until he has had enough time to improve his player.
• Users who don't play often should not score higher than users who play every day.

Thanks in advance.