I have a quiz online game. For each game there is a prize (number of scores). Now I have three ratings: top for the last day, top for the last week, total top (based on the sum of scores). Sum is not bad, but there is an issue: the more you play (even with bad results), the higher you are because more games leads to more points. I want to build a new rating, that takes in account not only sum of scores, but performance in games to. Just an average prize is not a good idea for me, because it means that winner of a single game will be higher, than a person who won 9 games and got not-maximum score in the last one.
Do you have any ideas/experience, what formulas could be used?