You make some good points. But in this league, the top averages on each team MUST play each other all 3 games, the second highest averages on team team MUST play each other all 3 games, etc. The ONLY place bias can come into the process, is when two teammates have the exact same average. That's when a coin flip comes in as the most fair way to decide who plays who.I didn't read all of it but this is what I see.
1st be a captain. Don't flip coins, pick each match up intentionally. Your the captain make a decision, people will respect that more.
2nd when you start the season decide if your team is there to win or have fun.
If you want to win YOU decide every match up every night to give you a chance to win. No wishy washy coin flippin b.s.
If your there for fun hell, flip coins for every match.
This was a unique situation where the other team's top player was WAY better than the second highest average player, and with only 2 weeks in the season left, whoever got to play the weaker player was pretty much a sure thing to take at least second place in the league.