[alter_ego_trip]

Double points nights wouldn't be affected at all. You're still averaging all the games played, and those games would just get doubled thus raising the average.

You might set up different weekly bonuses. For example you might have a bonus for the team that has the most players in a room that week, or the most games played throughout the week, or the team that has the members with the highest points for a given night, etc. For each weekly bonus you can award that team a 100 point bonus which would increase their average.
Just throwing out ideas.