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Bayesian Rating

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Manick
Post #529875
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11:51 pm, Jul 20 2007
Posts: 2213


We have a new rating system... series are now ranked by the bayesian system. This will hopefully provide a fairer ranking for all series (weighted by the number of votes now).

RilleL
Post #529876
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12:02 pm, Jul 21 2007
Posts: 172


So how does this bayesian system work exactly?

ares6
Post #529877 - Reply to (#529876) by RilleL
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1:59 pm, Jul 21 2007
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yes....what's the difference between Average and Bayesian Average?

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RilleL
Post #529878 - Reply to (#529877) by ares6
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2:05 pm, Jul 21 2007
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Of what i've figured out, the number of votes is now relevant too. For example, if two manga have the same average rating but one of them have more votes, the bayesian rating would be higher.
I'm curious on how the bayesian rating is calculated though. Can someone write the formula please?

lambchopsil
Post #529879 - Reply to (#529878) by RilleL
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2:49 pm, Jul 21 2007
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Only Manick can do that, and he's at Otakon...Wait until Monday or so.

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G. Zeus
Post #529880 - Reply to (#529876) by RilleL
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3:53 pm, Jul 21 2007
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To give you an idea of how it works, you could check out the Anime News Network's top 10 lists for anime and manga titles. They have lists of series rated according to the weighed average and the bayesian estimate. I think that it's a better idea to keep tabs on both since it makes it possible to compare the data and guess which ones are merely winning by popularity, which ones are the hidden gems, and which ones are "blips" (very high but very few votes, such as "Arigatou" which is currently taking up the top spot despite having only 8 votes).

http://www.animenewsnetwork.com/encyclopedia/rating s-manga.php

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RilleL
Post #529881
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7:12 pm, Jul 21 2007
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Quote
Bayesian rating = (v ÷ (v+m)) × R + (m ÷ (v+m)) × C
where:
R = average for the movie
v = number of votes for the movie
m = minimum votes required to be listed
C = the mean vote across the whole report


Looks awfully complicated... :S
(No i'm not an idiot, i do understand why the formula looks like it does. Kind of...)

RilleL
Post #529882 - Reply to (#529881) by RilleL
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7:12 pm, Jul 21 2007
Posts: 172


Opps, replace "movie" with "manga".

Sosseres
Post #529883 - Reply to (#529881) by RilleL
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9:37 pm, Jul 21 2007
Posts: 186


So average is adding all values and dividing by the number of values?

Midrange (Mean?) is taking the highest and lowest votes, adding them together and dividing by 2? Considering any series with a lot of votes will get both 1's and 10's it means almost all series will have a 5.5 value here...

Taking a median approach to mean would give a decent picture though I guess.


Just curious by what the ambiguous terms average and mean stands for in this case. smile

RilleL
Post #529884 - Reply to (#529883) by Sosseres
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11:48 am, Jul 22 2007
Posts: 172


Average should be the "old" rating we had before.
I'm not sure what "mean" is, but at animenewsnetwork the mean is currently 7.8065.
My guess is that "mean" is the average or median rating of ALL the series. That would explain why the mean is 7.8065 at ANN since the rating for series is usually between 6-9. It's also logical for series with low votes to be pushed towards the "general" rating.
Through the formula I can see that [b]if the average rating is higher than the "mean", the bayesian rating is lower than the average rating. The oppsite apply[b].
You could say the bayesian rating adjust the average rating to be closer to "C" (mean), depending on how many votes you have.

I've been trying to figure out the mean value for MU but since i don't know "m" (minimum votes required) it's kind of hard. I've used m=4 for my calculations and gotten different values for "C" (mean). For Claymore i got C=4.925, for Naruto C=7.0125.
Taking a first look at the different values i got for "C", one can say that the difference is too much. A closer look at the formula shows that the bayesian rating aren't affected too much from "C" since (m ÷ (v+m)) is really small. For Naruto it's 0.0084.
More important would be the average rating so unless i get a more exact value of "R" and the value for "m" this is as close as i can get.

Oh, i just figured out that i can calculate a more exact value of the average rating myself, but i'm too lazy to do that...
Manick come here and answer!

RilleL
Post #529885 - Reply to (#529884) by RilleL
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4:37 pm, Jul 22 2007
Posts: 172


I need to correct myself here. When i said that the bayesian rating wasn't effected much about "C" (mean) and used Naruto as an example i was wrong.
In fact, that is exactly how the bayesian rating works! "C" is almost irrelevant in Narutos case because it has a lot of votes.
Bah, formula analysis can be tricky...

Manick
Post #529886 - Reply to (#529885) by RilleL
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9:10 pm, Jul 22 2007
Posts: 2213


I got the equation from here:

http://www.thebroth.com/blog/118/bayesian-rating

yoannjuan
Post #529887
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11:27 am, Aug 4 2007
Posts: 4


Well, the result of this system is that now each serie get a 7 or an 8 :s

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