# How to design rating (leaderboard)

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?

Thanks.

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I'd probably ignore these scores and make a rating similar to the Elo rating system.

In short:

• Have an invisible rating number for each and every player. They start at some fixed number, like 100 or 1000.
• You then try to determine how good the player will be (either against other players he's playing with/against or simply "how many questions he'll answer right").
• Once that's done, you let them play.
• After the game compare the real result to the expected result calculated before.
• The bigger the discrepancy, the bigger the change in the Rating will be. For example, you expected the player to guess 50% of the questions correct. If he did better (and wins), he's gaining points based on how good he was (only slightly better? -> less points; a lot better -> more points). In case of a lost game, you do the same - just reversed.

For a highscore or ranking, you can now compare these ratings. You could do things like "highest rating overall" or "highest gain last week". To avoid people stop playing to Keep a good position you simply lower their score over time if they don't play at all.

Just find a good name/system to actually visualize this. Just don't display raw numbers, as this might get People into number crunching, trying to manipulate it, etc.

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I'd say definitely not the perfect answer, but still way better than the system the asker was using. – o0'. Feb 10 '13 at 10:21
Yeah, it has ist flaws, esp. given with the vague question, as we don't know how the actual quiz works. – Mario Feb 10 '13 at 11:06
Yeah. I felt compelled to write this comment as a compromise: I (personally) really hate ELO-like systems, but this deserved a +1 anyway. – o0'. Feb 10 '13 at 11:12