by mrchad9 » Mon Jan 14, 2013 10:16 am
I've got the formula Matt!
This wasn't easy, and unfortunately isn't the sort of thing that I can sleep over, but figured it out. And it works. I do hope you consider it.
There are variables that can be tweaked which we could discuss, such as the starting score and how quickly page scores approach 0% or 100%. These are very easily adjusted. Currently the starting score is 70%, and it takes 28 10/10 votes to reach 90%, 68 to reach 98%. This is a bit fast, unless folks really start using the 6-9 range. If most votes remain 10 I would adjust the formula.
Implementing this completely resolves people's voting issues and minimizes the risk of any unintended side effects (which is why I kept using the result of a percentage score for each page).
The formula... it looks complicated but is should be easy to implement and calculate.
Page score = 70 + 30 * [1-1/e^((x-5.5)*y/5.555555)]
e = 2.718281828459
x = simple weighted average page score between 1 and 10 based on voter weighting (if all voters give a 10 then this average is a 10)
y = total number of votes for a page
It works very well. Also note that while the score allows some members to be weighted more than others (seperate discussion) it does not affect the page score itself (i.e. if members with low weightings vote on one page and high ranking on another, but both pages have the same number of votes, then they get the same score. Member weighting only affects how your vote is considered versus another member voting on the same page).
Here are some examples...
One 10/10 = 71.18%
One 6/10 = 70.13%
Ten 10/10 = 79.89%
Twenty 10/10 = 85.62%
Thirty 10/10 = 90.96%
Thirty 10/10 and one 6/10 = 91.00%
Thirty 10/10 and one 8/10 = 91.16%
Thirtyone 10/10 = 91.32%
One hundred 10/10 = 99.451%
One hundred 10/10 and one 6/10 = 99.453%
Ten 8/10 = 75.98%
Thirty 8/10 = 84.60% (same as 17 10/10 votes)
Thirty 6/10 = 73.74%
Thirty 6/10 and one 10/10 = 74.77%
Ten 4/10 = 65.72%
Twenty 2/10 = 44.11%
The key is basically that multiple votes of 6 or 7 etc are equal to fewer votes of 9 or 10 (as in the above example 30 votes of 8 = 17 votes of a 10). The score will gradually but continuously approach 100% as long as votes are anything equal to or above 6.
I think this is much closer to realizing the desired A, B, C, D, F page scores people are inclined to think of, and under ALL circumstances a 6, 7, 8, 9, or 10 will increase a pages score (and a 1-5 will lower it).
What do you think? If you want to discuss or play around with the variables you have my contact information...