One of my great frustrations with playing this game in puglandia is team damage. It drives me nuts. Here is an idea to at least for a weekend, make people focus on minimizing team damage.
Have your standard match score based event(say 150 match score gets you a grab bag item) Place a large penalty on team damage. For example, your match score is 175, but because you had 35 team damage points, you subtract 2X team damage from your match score(35x2=70) 175 minus 70 equal=105. Now you don't qualify for the prize.
I want a stinging penalty for team damage!