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I'd love to see an update here that:

* Included a graph of the resulting ordering of the two dimensional plane and some examples

* Included consideration of 5- or 10-star scales.



They have an article about K-star rating systems [0] which uses Bayesian approximation [1] [2] (something I know little to nothing about, I'm just regurgitating the article).

There's a whole section on their website that has different statistics for programmers, including rating systems [3].

[0] https://www.evanmiller.org/ranking-items-with-star-ratings.h...

[1] https://en.wikipedia.org/wiki/Approximate_Bayesian_computati...

[2] https://www.evanmiller.org/bayesian-average-ratings.html

[3] https://www.evanmiller.org/ ("Mathematics of user ratings" section)


The formula still works for scales of 5 or 10, you just have to divide by the max rating first and then multiply by it again at the end.

For example a 3/5 stars turns into 0.6 positive and 0.4 negative observation. Following the formula from there will give a lower bound estimation between 0 and 1, so then you just multiple by 5 again to get it between 0 and 5.




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