So it's definitely true that players will have different skill levels with different factions. But even with 20 factions I'd be worried about getting enough dat

So it's definitely true that players will have different skill levels with different factions. But even with 20 factions I'd be worried about getting enough data on for individual player/faction combinations to converge to the real values. That's especially true if the game doesn't allow a player to specialize in just a couple of factions, but realistically will be playing 10+ different ones. Maybe the thing to do would be to have three components instead of the current two; generic player skill, faction power, and faction-specific player skill. One thing I do is track how much games with each faction contributed to each player's rating. But that's just for amusement value, there's no feedback from these faction breakdowns to the ratings as a whole.