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Math Help - Weighted rank equation for sorting movies. Need explanation or new equation.

  1. #1
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    Weighted rank equation for sorting movies. Need explanation or new equation.

    IMDB (Internet Movie Database) has a top 250 list of movies. Movies enter this list according to a weighted rank.

    I downloaded a copy of the database from an ftp site that imdb.com pointed out for personal use and within this file I found the following:

    Code:
    weighted rank = (v/(v+k))*X + (k/(v+k))*C
    where:
        X = average for the movie (mean)
        v = number of votes for the movie
        k = minimum votes required to be listed in the top 250
        C = the mean vote across the whole report (currently 6.90)
    I plugged this in to recreate the top 250 list and it works fine. But I've been trying to understand how it works for some time and I can't get it.

    I want to create another type of list. This list will be called top_recent_movies. The equation above should include the following new parameters.

    a = age of the move in years
    m = maximum age to be considered (currently 3 years)

    If I had to give it a go I would probably do this but I know it's wrong:

    Code:
    weighted rank = (v/(v+k))*X + (k/(v+k))*C + (m/a)
    where:
        a = age of the movie in years
        m = maximum age to be considered (currently 3 years)
        X = average for the movie (mean)
        v = number of votes for the movie
        k = minimum votes required to be listed in the top 250
        C = the mean vote across the whole report (currently 6.90)
    I mean would there be any difference between (m/a) and (1/a)

    Any help, please?
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  2. #2
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    Re: Weighted rank equation for sorting movies. Need explanation or new equation.

    I made a little progress last night after about an hour and 6 pages of trying to work out how the original equations works, and I actually got it, I think...

    (v/(v+k)) + (k/v+k) = 1.0

    As the number of votes increase, the weight of the mean vote for the movie increases, by a decreasing amount.

    So to introduce m and a and still keep the rank in the range of 0.0 to 10.0 I did something similar. It penalizes movies that are old, by a decreasing amount.

    Code:
    ((v/(v+k))*X + (k/(v+k))*C) * (m/(m+a))
    where:
        a = age of the movie in years
        m = maximum age to be considered (currently 3 years)
        X = average for the movie (mean)
        v = number of votes for the movie
        k = minimum votes required to be listed in the top 250
        C = the mean vote across the whole report (currently 6.90)
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  3. #3
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    Re: Weighted rank equation for sorting movies. Need explanation or new equation.

    Ok so I tested it out and the weird thing is is works just as I want it to. It includes movies from current and previous year. Although when I adjust m (maximum age) it makes no difference whether m = 3.0 or m=10.0

    will maybe try something like

    ((v/(v+k))*X + (k/(v+k))*C) * ((m*5)/((m*5)+a))

    --- edit ---

    I don't know, the equation seems right but still, adjusting m doesn't change the result. Yet when I print the figures they do change. May have something to do with the list itself. Am satisfied with this for now.
    Last edited by russ123; February 25th 2013 at 10:39 PM.
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