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On the user profile page, there is a list of 50 Top Ranks which each has a PP score:
The scores are weighted, as you can see on the right. I assume this weighted PP score is what goes into the total PP calculation.
The question is: How is this weight determined?
I have noticed at one time that the first score was weighted at a 100%, and the second was 98%, but it has changed since then. It seems like the weight gets smaller faster when the scores are higher?
From the wiki article on Weightage system:
For transparency on how your final pp is calculated, pp gained from the beatmap is given along with weight (% of eligible pp to be gained for final pp). Only your highest pp score's beatmap gives you full pp. Other scores' pp values will be multiplied with decreasing percentage. The percentage is always rounded to the next whole number for displaying, but for calculations it is not. For example a score can be weighted by 0.48% despite the display saying "0%". If n is the amount of scores giving more pp than a given score, then the score's weight is 0.95^n .
It follows, that your total pp is computed as follows. Let PP contain each score's pp value. PP[i] denotes the ith score's pp value, sorted decreasingly, where i goes from 1 to n, and n is the amount of scores you have.
Total pp = PP[1] * 0.95^0 + PP[2] * 0.95^1 + PP[3] * 0.95^2 + ... + PP[n] * 0.95^(n-1)
