Criticker is designed to be fully transparent. Every calculation that we use to generate recommendations for you is exposed. If Criticker guesses that your probable rating for a particular film will be 85, you can see exactly how that number was generated.
Everyone has a different rating style, and Criticker strives to accommodate them all. For some users, a rating of 70 is fairly bad, while others will consider a 70 to be decently good. Some users only use a scale of 0-10. Some only use 50-100.
Because a rating of 75 can mean something different for each user, comparing ratings is not good enough for Criticker. Instead, we compare the percentile rank of a rating. Percentiles are defined as "the value below which a given percentage of observations in a group of observations fall" [wikipedia].
Let's say you have 250 ratings, and you give a new film a rating of 85. Criticker looks through your ratings, and sees that you've given ratings less than 85 to 195 of them. You have a total of 10 films rated with 85. That means that the percentile for your new rating is 79. Here's the calculation:
percentile = floor((num_lower + (num_matching / 2) / total_ratings) * 100)
79 = floor((195 + (10/2) / 251) * 100)
Note that the number of ratings has increased from 250 to 251, because you've rated a new film. Also note that it's impossible to acheive a percentile rank of 100, because a rating can never be lower than itself, and we use the floor as opposed to rounding the number. Percentiles can therefore range from 0 to 99.
In order to generate percentiles at all, you must have at least five distinct ratings. That means, if you give every film a rating of 1, Criticker will not build percentiles for you. For Criticker to work, there needs to be at least some variation in your ratings.
TCI - Taste Compatibility Index
If my percentile for Miller's Crossing is 68, and yours is 85, that's a difference of 17. The TCI is simply the average of all such differences, across titles which we both have rated.
Criticker stores your top 1000 TCIs (or 2000 if you're a sponsor). These are the people whose tastes are mathematically closest to yours.
For TCI generation, Criticker will only consider users with whom you have at least 10% of your titles in common. So, if you've rated 251 films, you have to have at least 25 ratings in common with UserX before generating a TCI with them. You can adjust this "minimum" anywhere from 10% to 50%, on your profile.
On any other user's profile page, you can see the math behind the TCI generation.
PSI - Probable Rating Indicator
Let's say 229 of your top 1000 TCIs have seen The NeverEnding Story. Criticker gathers the top 10 of them, and looks at each of their percentiles. The average percentile is 46. In your case, that means a PSI of 72.
How exactly is that guess being produced? Criticker is simply translating percentile back to rating. In your list of 251 ratings, 46% of them (or 117) have a rating less than 72. So, Criticker predicts that you'd give The NeverEnding Story a rating of 72, based on the ratings of your most similar users.
PSIs can only be built if at least 3 of your top 1000 have rated the title in question.
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