https://drive.google.com/open?id=19b5XVjZtsFfY_V-MAzWpyBWf2IXw23Nn
You clearly see two peaks indicating that one can indeed distinguish between games with different alliances.
Unfortunately I cannot resolve fights up to a certain round, since the logfiles are a bit inconsistent or I am just too bad at coding , so i define alliances as:
There is a Greyjoy-Lannister Alliance if: Greyjoy fights 4 or more times vs Stark and 2 or less vs Lannister
There is a Greyjoy-Stark Alliance if: Greyjoy fights 4 or more times vs Lannister and 3 or less vs Stark
Here are the winrates
Greyjoy-Stark Alliance:
https://drive.google.com/open?id=1z1gZNwudlDdWKrbetMnsEpHlH3PtatWX
Greyjoy-Lannister Alliance:
https://drive.google.com/open?id=13QtOJruiHtt5q5NVZy6IPLOr6l_8MDEB
For comparison here again the general winrates in my set:
https://drive.google.com/open?id=1jW71ErXMav9UpT2_ijWwOexADohbvMX9
Interesting I found also the games where Greyjoy fought 8 or more times vs Lannister (4 or less vs Stark):
https://drive.google.com/open?id=1Yl7YUHTY-LnhtIFIp_7k0vV2hqlBL8l3
Let me know what you think!