Venix wrote:
You can read everything here https://osu.ppy.sh/wiki/Performance_Points
Personally, I think that many examples and how it works in practice should be added there. It could be explained better.
I don't know, if normal players can edit wiki, but if they do, then maybe I will try to contribute something in future
_Toxi wrote:
Faustas156 wrote:
you basically got 181 pp and earning much less pp gives you less pp, as the weight drops for pp.
So PP is weighted from how far it was from the highest amount of PP earned, not how high it is on the ranking?
Yes. We can say that all your scores are sorted by PP, from highest to lowest.
First score is 100% (or multiplied by 1)
Second is 95% (multiplied by 0.95)
Third one is 0.95*0.95 = 0,9025 (so you already lose almost 10% from weighting)
Each next score is multiplied by another 0.95, so n-th score will have weight 0.95^(n-1).
11-th score is 0.95^10 = about 0.5987 (59.87%)
21-th score is 0.95^20 = about 0.3585, so it's just slightly more than 1/3 of it's base pp value.
51-th score is 0.95^50 = about 0.07694 or 7.69%, so it almost doesn't matter at all.
Now, how to we understand these numbers? if you add 1+ 0.95 + 0.95*0.95 + 0.95^3 + ... then with more and more scores, the sum of weights will be converging to 20. So, if you had thousands of scores (or in theory: infinitely many) and all of them would be equal, then you would have 20 times your average score + bonus points (let's ignore bonus points for now)
So, having many scores with an average score of 55pp would result in about 20*55 = 1100 pp.
But let's go back to this 51-th score. If you compare its weight (~0.07694) to the sum of all weights (20), then you will get that it's actually weights 1/260 of all pp. Very small, isn't it?
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Now, what happens when a new score is added?
Many people are asking things like: "I just did 40 pp score, but get only 2pp, why?", but the answer is quite simple. This is how it works:
When you make a new score, its pp is calculated and the scores is added to the list of your sorted pp,
pushing down all the lower scores.
Then it effectively works like if all the differences between scores were being weighted and summed up.This one maybe sounds complex, but let's look at this example (I will round some numbers).
Let's say your top scores are
100pp *1
90pp *0.95
85pp *0.9025
72pp *0.8574
70pp *0.8145
63pp *0.7738
50pp *0.7351
all the lower scores are 50pp and there's thousands of them,
so we ignore them (they are equal, so no additional pp from pushing them down)
Now, let's say you set 87pp score. It jumps on the third position (when 85pp is), pushing 85pp on 4-th position.
72pp that is 4-th is pushed down to 5-th position, when 70pp was. Etc.
So, because you have
87pp *0.9025 instead of
85pp *0.9025, you are gaining
2*0.9025=1.805ppBut that's not all! On every position below you have now a better score than you had before, so every single one of them will give you pp!
You have
85pp *0.8574 instead of
72pp *0.8574, so you gain the difference
(85-72) *0.8574 pp, which
11.146 pp!!
The you gain
(72-70) *0.8145 = 1.6290 pp, and so on, i.e. difference between the previous and new score, multiplied by the weight.
Because you have more scores now, then if you had just few scores, the last score would be added fully, with next weight, as there was zero pp before that. But as we have 50pp scores all the way down there, we ignore this.
The new scores, weights and
+pp table will look like this:
100pp *1 +0 pp
90pp *0.95 +0 pp
87pp *0.9025 +1.805 pp
85pp *0.8574 +11.1459
72pp *0.8145 +1.6290
70pp *0.7738 +5.4167
63pp *0.7351 +9.5562
50pp *0.6983 +0 pp (there already was 50pp score here)
all lower scores are 50pp
So, by getting 87pp score and pushing all the other scores down, you gained about
29.5528 pp!
But this is because:
(1) the score was so high, so the weights are big enough
(2) the differences between scores are big
So, if the differences between scores were small (like many people tend to have big number of similar scores at the lower bottom of their top 100 scores), you would get much less PP from this transition. Just look how some of the shifts gave about +10pp, while others only about +1.5 to +2 pp.
Also, as you see,
what you really gain is weighted difference between new and old score, including all the scores pushed down by it. So, it the score is around top 50 and instead of *0.7738 you have something like *0.077..., then you get 10 times less from this score. Including the fact that the difference between scores will probably be small down there and the next scores will have even smaller weights and probably differences too, you gain almost nothing.
Whatever you push down there, it will be almost meaningless in comparison to score getting into your top 10 and pushing down many, many scores with bigger weights and differences between them.
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I hope that it will help you understand better how PP system works
Sorry for poor formatting, but it's 3:15 a.m. and I am so tired... xD- - - - - - - - -
P.S.
Bonus score is additional PP added to sum of your weighted pp from scores. It is equal to:
416.6667*(1- 0.9994^Number_of_scores).
There was a table on the old wiki, but I can't find it on a new one. Doing math quickly, you need:
213 scores for bonus
50 pp 458 scores for bonus
100 pp 744 scores for bonus
150 pp 1090 scores for bonus
200 pp 1527 scores for bonus
250 pp 2121 scores for bonus
300 pp 3054 scores for bonus
350 pp 5346 scores for bonus
400 pp for memes:
10727 scores for bonus
416 pp 