I'll be applying the "if you see a good idea, see if you can make it work for you" principle here.
In this case, This idea is very similar to what Zechnophobe described earlier.
My housemate plays Heroes of Newarth (HoN), and they seem to have developed a semi-decent automatic team balancer which people trust enough to use. I'm going to describe it briefly, list out the (IMHO) important ideas, and then talk about how we can apply some of these ideas to Demigod.
A Brief Description of the HoN System:
1) It's not perfect, and it's algorithm has some funny edge case behavior (equating 3 strong players and 2 weak players as being only slightly more powerful than 5 medium players)
2) It uses a player's "skill ranking" which seems to be derived from the 1600 "chess" point system (I say that b/c that's where I've seen it before, I don't know if the chess meisters developed the system or if it predates them). The system is transparent, and lets the players know their potential gains/losses from a match based on the team balance before the match starts.
3) The amount of points each player stands to gain or lose is modified by the percieved balance of the teams (the Automatcher is used to create this balance and predict odds, the odds then modify the points gained/lost from the match)
Some ideas from this:
1) A numerical, and therefore amenable to a auto-balancer algorithm, way of measuring player strength is the end-goal.
2) HoN does this by using chess-like player skill rating algorithm, and it seems to be working out alright for them, though their autobalancer doesn't handle some specific edge cases very well. This algorithm takes *only* the results of games played into account based on the relative difficulty of the opposition, using some forumula to formulate a "team strength". This player skill rank is independent of hero played.
Great, I'm done talking about HoN lets talk about Demigod!
Now HoN is not Demigod, so you can't just port the system over wholesale. For one thing, they choose their heros/demigods *after* team selection is finalized, in a draft-pick manner -- we don't do that in Demigod. To adapt a point based system to Demigod, I think it would be important to have that number represent that player's *skill with the Demigod they have currently chosen*.
1) We should be able to differentiate between a player who is awesome with Oak but dabbling with QoT today, and the player who is awesome with QoT, and is playing QoT today.
Win/Loss ratio doesn't seem to be working out that well right now, and dividing it out onto the various demigods alone won't fix that. This is primarily (IMHO) b/c Win/Loss ratios would not reflect the difficulty/level of the games played.
Avg Favor Points Earned is another possibility, but I don't think it will be able to reflect, the same as Win/Loss ratios, the relative difficulties of the match; eg. do you avg. awesome favor with Unclean Beast b/c you're slaughtering a bunch of newbies with him, or are you actually that awesome?
2) A Player's number, which is used to balance teams, should reflect not only the matches they play, but the relative skill level / difficulty of those matches as well.
Both of these ideas keep bringing my thought process back to the chess system that HoN/Chess/WoTC (Wizards of the Coast) use to rank their players. For a competitive ladder, that's the sort of thing we're looking for I think, with casual play as the bottom of the ladder and with all the hypercompetitve players duking it out at the top of the ladder.
Now, if you're really set on using avg. favor or something like it, I think there's a good way to deal with Colonel_Jessup's point:
However, as Wallstop already mentioned some support players won't get the amount of favor points they deserve. QoT averages at 56 favor per game atm (4495/80), Sedna 67, while UB is close to 80 and Erebus gets 84 favor per game on average. Favor might need a little tweaking before it really represents a players skill.
that being to normalize favor earned based on demigod, and present this "normalized" score. If you do use that idea though, please make it completely transparent eg. make it so that a Sedna who averages 67, an UB who averages 80, and an Erebus who averages 84 all present a "Normalized Average Favor Per Game" of 75. Or, grab a academic grading system from somewhere that uses a letter system, and rate each of those players as a "C Sedna, or a C UB, etc.", and then publish the normalization scales somewhere (or automate the whole system to map to the "average" score of each demigod over all games played).
Giving the host the ability to move players from one team to the other sounds good but I'm pretty sure it won't solve the real problem: a few players will simply try to join the team they think is stronger. The idea is good in theory but it opens up new ways to grieve and I don't think it will help with the problem in the long run. Butterskin385 will simply move back or leave and probably crash the lobby.
If we can develop a good player-strength number, an auto-team-balancing button would probably help out with this problem.
Just my 2 cents, volumnious as they be.