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We have this current list of top games on our website:

http://www.scirra.com/arcade/top

As you can see the formula we currently use (based on IMDB's) is:

Weighted Rating (WR) = ((v ÷ (v + m)) × R + (m ÷ (v + m)) × C) × E

Where:
R = average for the game (mean) = (Rating)
v = number of votes for the game = (votes)
m = minimum votes required to be listed in the top games (currently 1)
C = the mean vote across the whole report (currently 3.2)
E = 1 if the game isn't an example, 0 if the game is an example

We also have a StackExchange type reputation system. Each user who votes will have some rep, ranging anywhere from 0 to tens of thousands. What I would like to do is add the reputation into this formula as another weight. People with more rep who vote on the game have more of an impact!

An exagerated example, if 10 accounts with 100 rep vote 5/5 for the game and one account with 100,000 rep votes 1/5 for the game it should heavily weight the game towards the lower score as we trust this vote far more. The purpose of this is to help stop people signing up dud accounts to inflate their games rating.

Currently the range this weighted rating returns is 0-5 which is good as this falls into the range of the voting options (users can rate a game 0 - 5, five being the best). So I would also like it if this rep weighting also results in a weighted rating in that range!

We can make use of variables such as:

  • Sum of rep of users who voted on a particular game
  • Sum of rep of distinct users who voted on any game
  • Min/max rep of voting users total/per game
  • etc etc, basically anything that can be useful we could do

I'm not especially great at this sort of maths (but find it interesting), if any answers could also show how I can adjust the influence easily it would be appreciated also.

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Try multiplying each voter's rating base 10 logarithm of the rep of the voter, then finding the weighted rating, then dividing by the mean of the base 10 logarithms of the reps of the voters. Change the base from 10 to something like 2 if you want heavier weighting. –  Angela Richardson Dec 25 '11 at 7:16
    
@Angela thanks for the comment, please treat me like an idiot because I'm semi lost there, can you write it in maths? I'd be able to translate that easier I think –  Tom Gullen Dec 25 '11 at 8:36

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