I agree that favour points aren't a good measure of skill. But they are a good indicator of a person's experience, if all favour points ever accrued are the currency used, as well as being accessible by the current statistics tracking system (i.e. no need for a redesign.)
The more games played, with as indicated in your re-direct cosmoe, the more favour someone is going to have. The more games played, should equal more experience.
Perhaps a modified version of what my memory remembers of the old fairly useless vanilla starcraft rating system. It had a star system, each half star earnt by winning two games. Whilst pretty useless as 10 games wasnt much indication of experience, you oculd always look up a persons stats too.and see the actual stats.
So for demigods case, an easily identifiable system could be half a star earned for every 1000 favour points accrued in the players lifetime?
If 40 is the minimum favour for staying in a game and losing, then itll take at least 25 games till you earn that one half star.
For custom, its only use would be say bragging rights and indication of experience, nothing more.
For new demigod players, theyd have some idea who to play against.
So in a potential ladder, you could compete against the players at your star rating in order to work your way upto a 5 star rating. Would give players something concrete to accomplish, as well as allowing for skilled players to compete in a ladder vs other likedminded skilled players.
In terms of identifying random teams, if team play isnt organised, the % played on team sounds like a great idea.