Association quality is definitely determined based on best 14 players in squad.
Even if a team has worst 11 on pitch, if you check the Association overview, you would see his best 14 average stars.
My guess is that, the 2 important factors in the draw are:
1. The overall average quality of the association determined using the best 14 in each team
2. Last X weeks results.

We had a season where we facing monster associations, 1 after another.
The season before that, we had 4 out of 4 wins in association tournaments.
So there is definitely some history which affects the draws.

Plus, there is the obvious rule that all draws will be made between teams in same association division.
GOLD1 will not face a GOLD2 division team.

All the above "rules" are based on my observation.
Not written anywhere
So, they may be right, may be wrong.