What do you think about a system like that :
At the beginning, you earn only 50% of your distinctions. (if your medals allow you to win 100 distinctions, at this moment you will earn only 50 distinctions)
After each game finished, you win five more %. For example, after 5 games, I will earn 75% of the distinctions. And after 30 game, I will earn 200% (and this is the maximum, so you can't earn more than 200%). And so now, if your medals allow you to win 100 distinctions, you will earn 200.
Each time you finish the bg with 2 medals, you lose 10%.
If you finish with only one medal, you lose 15%.
If you finish with 0 medal or if you don't finish, you love 25%.
So, in this case, if you leave, you will be able to play but you will earn less than an other player.