# Looking for input on this performance points algorithm/idea

Since it has recently been brought to everyone's attention, the current mania rating system is flawed and it is undergoing changes as we speak (Tom94 is working on a new and improved star rating calculator currently). Along with the star ratings having to be fixed is the pp obtained from songs being fixed, because there's a huge difference in pp gained between 700K and 800K runs but not 900K and 1mill for example. Myself and some others thought it would be a good idea to increase the pp gained exponentially as the scores obtained increase. After gathering some opinions, I'm thinking that the algorithm should have an 800K run at around 70-75% of the total possible pp that can be obtained from a song. The algorithm I'm using that is based around 800K being 75% total pp is (e^(score/591716))/e^(1.69). Below is the % of total pp that you would expect to gain from a song depending on your score using this algorithm:
500K = 43% of total possible pp
600K = 50.9%
700K = 60.2%
800K = 71.3%
900K = 84.5%
950K = 91.9%
980K = 96.7%
990K = 98.3%

I'd like to hear from everyone else how steep they would think that the exponential curve on pp gained should be.
In addition, I'd also like to consider that a VERY slight bonus pp should be awarded, also exponentially, for scores above 990K. As Bobbias said in a different thread, this bonus should be small for low sr songs, while being a little more noticeable for higher difficulty songs. The algorithm I'm about to show for this bonus is based around the star rating system that Tom is working on, where most of the songs will be a lower sr than they are currently, as 6*+ songs in this calculator would be considered overjoy difficulty maps.
(e(1+(amount of score score over 990K / 10000))-e(1))*(e(rating)/10)
So let's say under Tom's star rating system that someone scores 996K on a 5* map. The bonus gained, in addition to the amount already gained through the previous algorithm, is (e(1.6)-e(1))*(e(5)/10) = 33.17 bonus pp
Here's the results of this algorithm used with a 5* map by every 1K points over 990K:
1K over 990K = 4.24 pp
2K = 8.93 pp
3K = 14.11 pp
4K = 19.84 pp
...
10K = 69.32 pp

The bonus will gradually increase as the score above 990K increases. The bonus is low enough for low star rating maps that it cannot be farmed and high enough with higher star rating maps that it is actually effective but not overpowered. Your thoughts?

Now that I think about it, 600K giving 50% is overpowered and I'll have to nerf that, or someone can help me with that.
just so you know 600K giving 50% is what we have right now

#### Aqo wrote:

just so you know 600K giving 50% is what we have right now
Nope, IN2006 lunatic would give around 450 pp for 600K then, but it only gives around 280 pp now iirc
Just to clarify, when I first came up with the idea, I didn't mean that the 990k-1m was bonus PP above with the calculation says the max PP for a song would be. The idea was that it was a part of your PP% calculation. I suppose it's easier to just treat it as separate bonus, but when I came up with it, I just considered it a separate region of the %PP calculation.

Anything that rewards players for achieving near perfect scores absolutely NEEDS to consider song difficulty. If song difficulty is ignored, it ends up encouraging players to play for accuracy rather than improving their overall skill, which is something we definitely do NOT want here.

#### Bobbias wrote:

Just to clarify, when I first came up with the idea, I didn't mean that the 990k-1m was bonus PP above with the calculation says the max PP for a song would be. The idea was that it was a part of your PP% calculation. I suppose it's easier to just treat it as separate bonus, but when I came up with it, I just considered it a separate region of the %PP calculation.

Anything that rewards players for achieving near perfect scores absolutely NEEDS to consider song difficulty. If song difficulty is ignored, it ends up encouraging players to play for accuracy rather than improving their overall skill, which is something we definitely do NOT want here.
Yeah the only reason why I kept it as a seperate bonus is because it's easier lol. Maybe I can just make that into seperate region of the %pp calculation like you said
mmm right more like 660k for 50% ok
Not directly responding to your inquiries, rather generally speaking about this pp re-re-revamp. I'd like to share a little knowledge on the subject to give people a better idea about what's exactly at play here.

An accurate system would have to consider that a map's difficulty curve (difficulty vs score) is far from linear. But since this isn't the case here, I'll walk through this subject to see the alternative solutions.

Taking 3 random maps (we'll call em A B and C) of the same difficulty range, it's more than likely that you'd end up with a case where although map A is easier to 90% than map B and C, B can still be easier to 95% than A and C, and C easier to 100% than A and B.

If you decide to rank their difficulty towards how hard is it to 90%, an FC on map A and a 90% on map B and C would be underrated. You would end up with inflated PP for 90% on map A.

If you decide to rank their difficulty towards how hard it is to 95%, you would end up with inflated PP on map B.

And if you decide to rank towards 100%, FC on map C becomes inflated.

A great example of this dilemma is Utakata. Many people come to the simple conclusion that it's difficulty is inflated but that isn't "truly" the case. Maps with big chords are generally rightfully hard to the ones who aren't ready for em, but once you can hit the chords, the accuracy is usually very easy to obtain. You end up with a difficulty curve that just jumps from hard to easy at a certain point. If you were to come with the simple solution to nerf maps with big chords, you'd be underrating a great many scores from people who still find themselves on that "hard" spectrum of the difficulty curve.

Some map's difficulty are linear, some are the exact opposite and most are completely irregular. Realistically, no matter how accurate a linear difficulty system ends up being, there isn't a single way to regress PP rewards accordingly in a way it won't produce over and under-rated maps at given scores.

Take the first picture into focus again. This time I roughly regressed a line through to simulate how a linear difficulty system (assuming perfect accuracy) would rank them.

Our current PP system "focuses" greatly around the 92% range as Aqo has pointed out in a separate thread. At this 92% range, the "true" difficulty spread of the maps are from easy to hard, A-B-C. Unfortunately, that doesn't match with what the linear difficulties are showing, which is A-C-B.

What you're suggesting and has been suggested is to change the PP systems "focus zone" upwards in hopes of getting more accurate results. But really, you will end up with the exact same problem. Take the 98% range, the "true" difficulty spread is C-A-B while the linear difficulty spread is showing again, A-C-B. You will get the exact same problems with overrated and underrated maps even if the linear difficulty algorithm is completely perfect.

Now there are still ways to make a linear system "mostly" accurate, but they aren't very appealing. One being to model the difficulty algorithm towards the difficulty of the map at the PP system's "focus zone" (instead of regressing an average difficulty) and to completely disregard scores that are outside of that zone because they are subject to inaccuracy. EX: rank difficulty according to how hard a map is to SS and only accept 99%+ for PP. Like I said, not very appealing. The other solutions are also knacky with massive short-commings, I don't really feel like enumerating more than one considering this post is long enough.

Finally I just like the people reading this to keep in mind; although I said "same difficulty range" for the example maps, they can be preeeetty far apart and still produce the same results, especially between the S and SS range, specifically the range that's being asked to focus on. What do I suggest we do to remedy such a dilemma? Nothing really, just passing through providing some food for thought.
Drace you're a god.
I was wondering when someone would finally make some graphs.

To me, the problem boils down to this: assigning a single difficulty number to an entire map where the difficulty changes can never give a true representation of the actual difficulty of that song. When you boil that much information down to a single value, you lose a lot of information about the map.

However, even though this is true, I do not see peppy or tom deciding to completely abandon the idea of rating songs by a single difficulty number here. Technically, you could use the difficulty graphs generated by the new system to create a PP reward curve for each song, while using star rating as a simplified representation for the player. But I don't see that being something they'd want to do either.

The reason I don't think they'd really consider that as an option is consistency. Players expect the rewards for their scores to be predictable and consistent between songs. If the PP reward were to be implemented this way, you'd be getting players complaining that the PP they get for something doesn't make sense all the time.