first of all I'm not in any way a mathematician, so be kind ;)
Our current routine: The game is a card game. At the end of each round cards still in your hand are summed up and make your points. The winner of the round gets zero points. After four rounds (one "game") points of each round are summed up and the player with the lowest score gets three points, the second two points and the third one point. Over a year there is an unknown amount of "games" (aka 4 rounds each). At least three players must attend but there can be more. There is a (small - currently 7 people) distinct set of players, each player plays at least once but not all players have the same amount of games over the year.
The problem: Currently our algorithm (I don't know it) is suboptimal. I think it is set up so players who can't (or don't want) to play very often still get chance to not drop into insignificance. Meaning that whenever they play it doesn't change anything as others have played so much. On the other hand this means that a player having not played for a while, can even rise in positions whilst that and then if he plays once drop again.
At the end of a year usually everyone is so close that every game changes the scoreboard (which is good on the one hand) but only the last game seems to actually decide who wins. So you could as well not play the whole year and just at the last game.
The goal: I'd like to have an algorithm that will reward you for playing as much as possible but leave a chance for people who simply can not play that much. The algorithm should get rid of strange changes in the scoreboard (aka I did not play but suddenly I'm on the first place).
Can you recommend an algorithm for this? There is no need to keep our current counting system. But due to the setup of the game: - we still need to play 4 rounds - points have to be related to numbers of the cards still in your hand at the end of each round
I thought of an algorithm that respects the amount of games you played but keeps the players close to each other on the scoreboard. So if playing often you would be higher than someone who does not play that regularly even thou you might only loose in those games. Yet not playing often you still have the chance to catch up to the lead by just playing more often, with the need to win more of course.