Long post to come later today with more detailed thoughts and examples (I hope), but some quick initial thoughts are:
1. Please drop the "G" from everything.
Since I can't think of anything better, may I suggest we call it CCWM with Opposing Alliances, or CCWMOA?
2. As other's noted, CCWM and CCWMOA aren't well suited to the 2015 FRC game because there's virtually no defense and thus virtually no benefit to looking at winning margins over just final offensive scores. Can we look instead at 2014, which had a lot of defense?
3. I'm wondering if the method may be doomed due to insufficient data? With CCWMOA, we only get 1 data point per match, while OPR and CCWM get 2 data points per match. In Ether's example tournament, there were 40 teams and 80 matches, so CCWMOA is trying to use 80 noisy data points to find 40 values, while OPR and CCWM are trying to use 160 noisy data points to find 40 values. Comparing CCWM and CCWMOA, I argue that CCWMs data values are noisier for reasons that I said in my first post, but maybe fitting with 160 noisier data points still gives you a better result than fitting with only 80 data points that are cleaner?
This is like trying to find the slope of a line that you know goes through the origin using 2 noisy points vs 4 noisier points. Which one is better will depend on the ratios of the noises. I hope to think about this more and comment more further with some data to back it up, but I'd be curious to hear the thoughts of other folks too.
Thanks everybody for the discussions!