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IIRC, a simple approximation of that horrendous formula is : (positive)/(positive+negative+1) It rewards items with more ratings. Basically, you initialize th

IIRC, a simple approximation of that horrendous formula is : (positive)/(positive+negative+1) It rewards items with more ratings. Basically, you initialize the number of negative ratings to 1 instead of 0.

raldi 5y ago
This is a decent approximation. It handles all the common hazard cases: +10/-0 should rank higher than +1/-0 +10/-5 should rank higher than +10/-7 +100/-3 should rank higher than +3/-0 +10/-1 should rank higher than +900/-200
akamoonknight 5y ago
Very interesting, seems your remembering looks correct to me. x / (x+y+1) :: https://www.wolframalpha.com/input/?i=plot+x+%2F%28x+%2B+y+%2B+1%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot+x+%2F%28x+%2B+y+%... horrendous formula :: https://www.wolframalpha.com/input/?i=plot+%28%28x%2F%28x%2By%29%29+%2B+%28%281.96%5E2%2F2%29%2F%282*%28x%2By%29%29%29+-+%281.96%2F2%29*sqrt%28%28%28%28x%2F%28x%2By%29%29*%281-%28x%2F%28x%2By%29%29%29%29+%2B+%281.96%5E2%2F2%29%2F%284*%28x%2By%29%29%29%2F%28x%2By%29%29%29%2F%281+%2B+%281.96%5E2%2F2%29%2F%28x%2By%29%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot+%28%28x%2F%28x%2B... Much less prone to typos.
- anthony_r 5y ago
  And the distance between the two, specifically formula - x/(x+y+1): https://www.wolframalpha.com/input/?i=plot++-x+%2F%28x+%2B+y+%2B+1%29+%2B+%28%28x%2F%28x%2By%29%29+%2B+%28%281.96%5E2%2F2%29%2F%282*%28x%2By%29%29%29+-+%281.96%2F2%29*sqrt%28%28%28%28x%2F%28x%2By%29%29*%281-%28x%2F%28x%2By%29%29%29%29+%2B+%281.96%5E2%2F2%29%2F%284*%28x%2By%29%29%29%2F%28x%2By%29%29%29%2F%281+%2B+%281.96%5E2%2F2%29%2F%28x%2By%29%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot++-x+%2F%28x+%2B+y...
gowld 5y ago
The main flaw in this formula is that when positive=0 the negative votes have no weight.
- rdlw 5y ago
  A heuristic I use when looking at products with low numbers of reviews is to add one positive and one negative review, so (positive+1)/(positive+negative+2). This basically makes the 'default' rating 50% or 3 stars or whatever, and votes move the rating from that default.
6gvONxR4sf7o 5y ago
This is another way of moving towards a bayesian lower bound instead of a frequentist one. As your formula shows, in this case the bayesian formula is super duper simple. (positive + constant1) / (positive + negative + constant1 + constant2) For more details see the beta distribution.
nullc 5y ago
This is like the "add one smoothing" the is commonly used for entropy / population diversity statistics. (class1 + 1)/(class1 + class2 + 2). (effectively, initialize all counts to 1). https://en.wikipedia.org/wiki/Additive_smoothing https://en.wikipedia.org/wiki/Additive_smoothing https://en.wikipedia.org/wiki/Rule_of_succession https://en.wikipedia.org/wiki/Rule_of_succession

raldi 5y ago

This is a decent approximation. It handles all the common hazard cases: +10/-0 should rank higher than +1/-0 +10/-5 should rank higher than +10/-7 +100/-3 should rank higher than +3/-0 +10/-1 should rank higher than +900/-200

akamoonknight 5y ago

Very interesting, seems your remembering looks correct to me. x / (x+y+1) :: https://www.wolframalpha.com/input/?i=plot+x+%2F%28x+%2B+y+%2B+1%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot+x+%2F%28x+%2B+y+%... horrendous formula :: https://www.wolframalpha.com/input/?i=plot+%28%28x%2F%28x%2By%29%29+%2B+%28%281.96%5E2%2F2%29%2F%282*%28x%2By%29%29%29+-+%281.96%2F2%29*sqrt%28%28%28%28x%2F%28x%2By%29%29*%281-%28x%2F%28x%2By%29%29%29%29+%2B+%281.96%5E2%2F2%29%2F%284*%28x%2By%29%29%29%2F%28x%2By%29%29%29%2F%281+%2B+%281.96%5E2%2F2%29%2F%28x%2By%29%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot+%28%28x%2F%28x%2B... Much less prone to typos.

anthony_r 5y ago
And the distance between the two, specifically formula - x/(x+y+1): https://www.wolframalpha.com/input/?i=plot++-x+%2F%28x+%2B+y+%2B+1%29+%2B+%28%28x%2F%28x%2By%29%29+%2B+%28%281.96%5E2%2F2%29%2F%282*%28x%2By%29%29%29+-+%281.96%2F2%29*sqrt%28%28%28%28x%2F%28x%2By%29%29*%281-%28x%2F%28x%2By%29%29%29%29+%2B+%281.96%5E2%2F2%29%2F%284*%28x%2By%29%29%29%2F%28x%2By%29%29%29%2F%281+%2B+%281.96%5E2%2F2%29%2F%28x%2By%29%29%2C+x%3D0..10%2C+y%3D0..10 https://www.wolframalpha.com/input/?i=plot++-x+%2F%28x+%2B+y...

gowld 5y ago

The main flaw in this formula is that when positive=0 the negative votes have no weight.

rdlw 5y ago
A heuristic I use when looking at products with low numbers of reviews is to add one positive and one negative review, so (positive+1)/(positive+negative+2). This basically makes the 'default' rating 50% or 3 stars or whatever, and votes move the rating from that default.

6gvONxR4sf7o 5y ago

This is another way of moving towards a bayesian lower bound instead of a frequentist one. As your formula shows, in this case the bayesian formula is super duper simple. (positive + constant1) / (positive + negative + constant1 + constant2) For more details see the beta distribution.

nullc 5y ago

This is like the "add one smoothing" the is commonly used for entropy / population diversity statistics. (class1 + 1)/(class1 + class2 + 2). (effectively, initialize all counts to 1). https://en.wikipedia.org/wiki/Additive_smoothing https://en.wikipedia.org/wiki/Additive_smoothing https://en.wikipedia.org/wiki/Rule_of_succession https://en.wikipedia.org/wiki/Rule_of_succession