Replace Bonus pp with Change to Make pp Scale Logarithmically

[Xexxar]

Hello!

NOTE: IF YOU ARE SEEING THIS FOR THE FIRST TIME, UNLESS YOU LIKE READING, GO TO THE THIRD POST, AS IT CONTAINS THE LATEST INFORMATION ABOUT THIS SUGGESTION. THE FIRST TWO POSTS ARE BEING LEFT IN TACT FOR RECORD KEEPING AND TRANSPARENCY

Introduction:

A thread was posted on Reddit recently on the topic of bonus pp and whether or not it was time or change it or outright remove it. I have had ideas on this subject for a while and thought it was time to formally present the idea with documentation. The core purpose of bonus_pp is to incentivize new players to play more maps. Unfortunately, as evidenced by many of the comments on the thread: lots of people, especially new players, don't even know of it's existence. The value is exceedingly small for each score, and as a result: it serves little to no purpose and it's existence is nearly completely disregarded by the community.

But it doesn't have to be this way. At it's core, the idea of a system that incentivizes players to play more maps and different songs is one that keeps the health of the game alive. It is for this reason that I am proposing a change to the way pp is calculated in an effort to improve the game and the system as a whole.

Current System

The current system is quite simple, a users total pp is defined with the following formula:

score_pp = sum(scores[n] * .95^n) ;where n is the index on your scores sorted by pp.

bonus_pp = (416.6666) * (1.0 - pow(0.9994, scores.size())); 

pp = score_pp + bonus_pp

While this system does have advantages, there are also a number of disadvantages that I want to highlight:

• Over half of your score pp is determined by your top 13 plays. This means players almost always have to set scores in this range if they want to progress their rank. It also makes farm maps highly incentivized, because if a player can get 13 scores on farm maps that are on average 20% overweighted then they gain 10% raw pp.
• A player has no reason to set a score outside of their top 50, as no matter how many scores they set outside of this range, they can never gain more than 7.5% of their total pp from this region.
• The bonus pp system is based off just playing maps, rather than trying to set good scores.

Proposed System

The core of my new solution revolves around combining the desire of incentivizing people to play new maps as well as work to set top scores. Performance points are a measure of what you have accomplished, so why would a player who has set a lot of good plays be outranked by someone who's set only a few marginally better plays. My solution attempts to address this is as follows:

score_pp = sum(scores[n] * .95^n) ; where n is the index on your scores sorted by pp.

total_pp = sum(scores[n]) ; aka the sum of all your pp.

pp = constant * score_pp  * (log(total_pp) / log(score_pp))

Here is a desmos that illustrates the base concept with a slight re-balance, halving the default bonus ratio:

https://www.desmos.com/calculator/ghzb14pqqr

NOTE: this is just a test build and balancing can be worked out with assistance from community feedback and pp committee.

For those who really want to tinker, here is a way to play with balancing using a and b as constants: https://www.desmos.com/calculator/dqq51rhdxs

Conclusions

The advantages of this system are numerous:

• Players are incentivized to play a variety of maps and go for the best scores they can get on them.
• Players who aren't able to set top plays for whatever reason can still gain pp by getting scores on other maps.
• There is no arbitrary cap to pp. Players are always capable of gaining pp, no matter how small.

Many people have expressed a dissatisfaction with the idea of a player being able to out rank another player just based on the fact that they have set more scores than the other. Obviously though, this has its limits. Even Momo, the number one score farmer, would only see to gain 1100 pp with this current implementation, subject to balancing. As such, this isn't really an issue, rather, it's the point. It takes skill and dedication to set scores on a variety of maps, and having a way to reward players who do play more in the game's competitive scene is of the same idea as to why bonus pp was added in the first place. This system de-emphasizes setting only top plays, and instead brings a great harmony between trying to set top plays as well as just setting good scores in the first place.

As far as implementation is concerned, all that is needed is that we add total PP as a database value that updates properly when scores are set, as well as the small additional calculation overhead for the logs in the equation. As it stands, it has very few draw backs to me and lots of benefit.

Thanks for reading,

Xexxar

[Xexxar]

For what it's worth, I'm also playing with the idea of just summing pp by using a 1/n sum. (consider this a ppv3 proposal)

sum (scores[i] / (i + 1)) ; sorted scores sum by index / 1+index (assuming starting at index 0).

This would make it so your top scores are defined by

100%
50%
33%
25%
20%
...
...

While at first this might sound like it would create the same problem where your top plays influence your overall rank too much, the difference with this situation and original ppv2 scaling is that every additional score will always help you. In the old system, where your pp can never be greater than 20*your top play, players are incentivized to tunnel vision and shoot for the highest scores they can get on the maps that are worth the most pp. This new system would still require players to improve their best scores to rank up, but that wouldn't be the only way.

Instead of only being rewarded when you're playing your absolute best, players would also be able to gain rank by setting good scores on maps they don't already have good scores on. Playing new or previously failed maps and would be encouraged, even if the score wouldn't make it onto your top plays list. Every good score set, even if it's someone's 250th best, is a small improvement to their history of performances, and would contribute to their rank.

As someone who used to play back during ppv1, I can't help but be reminded of that system. Not only is the top pp of players around 7000 using this system (unless you scale it), but the emphasis on requiring players to set good scores on a variety of maps is something that I'm very fond of.

Perhaps it's not an idea that would be accepted by most, but it is definitely something that would bring in a breath of fresh air to the game. I'm sure I'm not the only person who has grown tired of the toxic system that always demands you play at your best to feel gain any meaningful sense of progression.

TL;DR:

Old system:

• It pushes new players to play outside of their comfort zone instead of playing more maps and learning fundamentals
• It forces players to always try and set scores at the absolute top of their skill level to improve their rank
• Doesn't consider plays outside your top 100 in any meaningful way

New system:

• Encourages players to set good scores according to the pp system on a wide range of maps
• Considers every play you've ever set
• The player with the best cumulative performances is the best player

NOTE: It's also probably worth expressing that there may be a better algorithm such as using 3/(n+3), ie. 3/3, 3/4, 3,5 etc. i just went with this since it more closely mirrored live, but perhaps a split method could be used where the first 100 scores are weighted using some slightly less harsh fraction such as above and then the rate of decrease could increase to the 1/n used in this example. That way pp could be noticably more weighted by your top 100 than what is outside your top 100. either way the core rests on using y/x type sum.

[Xexxar]

After some more investigation using the concepts laid out in the previous reply, I wanted to explain my final proposal which was decided on by results as well as elegance in the mathematical solution. I also want to clarify some of the statements I made which probably are miss leading and might be confusing.

Q&A Over Some Misunderstandings

• Q: Does this system mean that if someone farms 50pp plays endlessly that they could become ranked number 1?

• A: No Because in order to accomplish this, they would need to get 50 pp on over 4.345*10^3300 maps. If that doesn't make it clear, there aren't anywhere near that many maps in the game, let alone atoms in the universe, or nanoseconds in a lifetime. For the record, setting 50 pp on every ranked beatmap (90000) would only award you 1366 pp, which is long shot from 22600 (the old system would give you 1000 pp for this accomplishment. When factoring in the 416.66 bonus pp, this player would actually be nerfed using this new system).

• Q: We already have score. Why should the pp ranking also be a score ranking?

• A: This equation has nothing to do with total score, number of scores, or the number of plays a player has made. The only numerical value that is a part of this equation is pp, and the way it's being totaled is the only change (that and the removal of Bonus pp). The only way in which this new proposal is similar to score is that it is unbounded, meaning that every additional pp you earn will have some measurable effect on your total pp value.

• Q: If every score I set has an effect on my total rank, doesn't that just mean that someone who sets more scores will be ranked higher than someone else?

• A: This proposal uses a curve which has the effect where your top scores are much more significant in weight as compared to scores farther down your profile. If someone with a fresh account set 100 scores worth 600 pp each, and another player with a fresh account decided to try and acquire the same amount of pp as the first by only setting 500 pp for each play, they would need to set 1237 scores worth 500 pp each to be able to match the total pp of the other player.

• Q: The person who set the 600 pp plays is clearly better, why should the person setting only 500s be able to be ranked equally to the other?

• A: The point of this pp is to weight the performances of both players against each other. While it is true that the raw skill of the 600 pp player might be higher in that they were able to achieve individual scores that are worth more than the other person, the consistency and ability to perform well enough to acquire 500 pp on over 1237 maps is also a feat in it of itself. Just because we're used to seeing PP only be affected by a persons top 100 plays does not mean that the current system is better, nor does it necessarily mean that the one I'm proposing is any better either. It is simply bringing attention to an alternative as a means to address some fundamental problems laid out earlier.

• Q: Why remove bonus pp with this update?

• A: This update solves the problem that bonus pp was trying to address: which is to encourage players to play more maps. The problem with bonus pp is that it requires simply playing a new map, rather than setting a good score on new maps. This solution fixes it by removing anything that is not related to pp from your pp total, but keeps the original intent of bonus pp alive by making setting high pp plays something that will always push your rank forward.

With that out of the way: The final proposal

Final Proposal

After playing with some of the algorithms laid out previously, I arrived in a dilemma of wanting to weight scores in the top 1-100 region more than using log(1/x), but not wanting to use something like log(5/(x+5)) due to it having too high of weighting on scores outside of the top 100 (NOTE: when I refer to log here, its because the sum of your scores divided by the index of your score is the same curve as a log function). These two graphs can be visible here: For these: x = number of scores worth p performance points, y = your total profile pp. Some constants were used to keep the graphs somewhat similar. The black curve is old pp, the red is the new concept.

Tail matters too much: https://www.desmos.com/calculator/fyz4yjmtg2

1-100 scores don't matter enough: https://www.desmos.com/calculator/wsdq9nzgv5

Because of this, I tried to come up with a mathematical way to combine them, and the result can be seen here:

The Proposed Solution: https://www.desmos.com/calculator/5nnbpx0fjp

Here, we have the same idea: x is the number of scores worth p performance points, y is the total profile pp. Black is the original curve, and red is the new proposal. This curve has some great properties.

• It is unbounded. Every performance a player does contributes to their total pp.
• It is well distributed in the 0-100 region, while remaining slowly scaling in the tail region.
• It is well fit with the old system. A player can expect nearly identical levels of scaling from the old and current system up until 20 scores is reached, and which point the systems diverge.
• There are no arbitrary max's or mins, and only one balancing constant is used (similar to how .95 is used with the old geometric sum method).

Some additional curves can be seen here: https://www.desmos.com/calculator/tzbtwcf9jt

This graph shows some extra data, specifically, the amount of pp awarded for each play. The black curve is the old system and the purple is the new. This helps me visual some of the differences, so I thought I'd include it.

PP Values

Website is available here. It uses the dataset dump from sept 1st so it only factors in scores set before September 1st, and it only includes the top 10k. If you're not in this group, you can't see your PP right now (sorry).

https://pp.huismetbenen.nl/rankings/players/xexxar_total_pp

Closing Comments:

I kind of rambled more than I needed to throughout all three of these posts. I was sort of spitballing from the get-go and probably should have just spend more time theory crafting before posting, but the post itself was the jump start that launched into all of this in the first place. I think it's in a good place now and I hope people who may have shut down the idea initially will be willing to give it a more critical look with this final version. In a world where Mrekk is getting to the point where setting a 1k pp play has almost no effect on his overall performance, I hope people will see this more as a way to move forward rather than pushing us back.

Thanks for reading,

Xexxar

NOTE: due to some sql bug, the actual constant to be suggested is 120, not 145.

[OliBomby]

For people who do not read the whole thing:
I think it should be re-emphasized that this change is not meant to improve the accuracy of total PP representing the skill of the player. The intention is to redefine total PP to more represent the total achievement of the player.

[Xexxar]

Yeah this is very accurate Olibomby. While pp will always be skill based because it takes skill to set good scores, it takes the focus away from pp being a numerical representation of your skill (which it has for a long time struggled to do), and brings it back to it's original definition: pp being a numerical representation of your performances. Considering pp's purpose was to replace ranked score, I think this would be a great move. It would certainly reduce the toxicity that surrounds pp while still being a competitive skill based metric (as opposed to score which is largely a metric of time invested).

[Rekunan]

This and bonus pp as a whole is fundamentally flawed.

The pp system is meant to be an objective metric that measures difficulty. Adding features for the sake of incentivizing players to play more undermines that goal and causes it to lose it's already somewhat shaky value in the community's eyes for being able to perform its purpose in the global rankings. This incentivization can also backfire, as players will realize that they don't need to improve to progress through the global rankings, they just need to be able to repeatedly perform at their current skill level, thereby abusing the system even more than it already has.

You also bring up some points which are ill-guided at best:
The majority of your pp being based upon only your highest top plays is important, as it disallows someone from climbing the rankings by just settings tons of similar pp scores. Instead, they have to improve and be able to set higher pp plays.
You also bring this up, that they have to set over 1237 of the 500pp scores in order to overcome a player who has set a couple of 600pp scores. Even despite the seemingly high count, that doesn't justify them being able to overcome a player who's shown to be objectively better than them. You say that the consistency of being able to do so is a feat in it of itself, but how will you respond when someone inevitably abuses this fact to climb the global rankings, surpassing Momo, -GN, DigitalHypno, etc. just by setting enough 500pp plays?

One of the few good points brought up in this discussion is that bonus pp in its current state is a flawed and useless system. However, this is not the way to go about reworking or replacing it. It should instead be abolished, as it undermines the goal of and years of work that went into making an objective metric for difficulty.

[Rekunan]

@smoogipoo It's an objective fact that cs5 is harder than cs4, which can be measured and taken into account in the pp system. Same with other diffstats and other objective facts you can think of. With something like AR, that requires more work into considering the overlaps, note density, how patterns change, etc. but is still possible to be objectively measured.
I believe something you will agree with (and possibly what you were trying to say) is that we should have a different method of summing up total pp, one where it displays/uses the different skills, like -GN recently mentioned on Twitter. I can see the logic and reasoning behind this and am interested in seeing how this could happen, though my support of this may change depending on how this is implemented.

@Xexxar that doesn't change the fact that when I go on a profile, there's a possibility that a profile that only shows 500pp plays in their top 100 and is ranked higher than a profile that has some 600+pp plays (which is obviously bad UX). I didn't bring this up because I didn't think of this before, but if you want something like this to work, you'll need to be able to give visibility to all, or at least way more, scores on a user's profile, and I'm not too sure if the servers are ready to handle that, esp considering full score dumps on https://data.ppy.sh are only available for the top 10k players.
Regardless, the fact remains that the player who has set 600+pp scores has shown themselves to be higher skilled than a player who has only set 500pp scores, and should therefore be higher ranked. I could use the same argument and say that the person who has only set 500pp scores should just play more and improve to be able to set higher pp scores.
I will also say that the current system isn't using an arbitrary subset of the plays a player has set. I know a lot of people, including myself, who don't remember anything past their top 25, let alone top 50 or 100. Whether that means we should shift the weighting or even visibility of top plays is a whole other discussion (personally I think it's fine as is).

[Xexxar]

Rekunan to Smoogi: It may be an objective fact that CS5 is harder than CS4. But it's a subjective evaluation to state that a certain level of jumps are harder than streams, or that spaced triplets are harder than spaced streams. Smoogi's point isn't that there is no such thing as objective difficult, but rather that the game isn't one dimensional.

For every skill or aspect of the game, there is a spectrum of objectivity that exists on it, but the second you cross that spectrum into another, ambiguity arises. Aiming will always be a distinctly different form of difficulty from tapping, and to suppose that there is an objective way to quantify the difficulty between them is to claim that there is an objective way to qualify their differences, which isn't possible because every player has their own subjective opinions that they form about those two different aspects of the game.

Rekunan to Me: This is a problem with UI and is not related to whether or not the metric of summation is fundamentally flawed. We don't visibly show bonus pp on peoples profiles and it hasn't been a problem before. Perhaps we can just add a "PP from scores outside of top 100" that is visible on peoples profiles at the bottom of their scores list. In regards to DB complexity, I will defers to the devs on whether or not that would be problematic. My best guess is that they would already be summing every score since the performance benefits would be minimal since regardless your scores would need to be sorted when you set a new play.

And again, by your logic, would a person who has set one 600 pp play be objectively better than someone who has only set 500 pp plays? What qualifies your basis that 100 600s is enough to know that they're better than someone who has over a thousand 500 pp plays. Would 50 suffice? 10? 5? It's entirely subjective no matter how you slice it. My solution at least makes it less subjective in that every play matters, which is better than what the old system can say.

[Rekunan]

Smoogi part: That's a fair point. In response, I turn to the -GN tweet and what I've said about that in my reply.

Your part: Fair point.

But also, allow me to slice this objectively. Yes, a player who has set one 600pp play has shown themselves to be objectively better than someone who has only set 500pp plays. This is clearly shown with the higher pp value, which again, is meant to be an objective metric that measures performance (I realize now this is the better term instead of difficulty). Even if the latter player could thousands of 500pp plays, they haven't shown themselves to be objectively better, despite the former player having only set one 600pp play, because again, 500 is lower than 600.

Now, having said this, I realize this may come off as me suggesting that we should just switch to only using the #1 top to sort global rankings. I will clarify that this is assuming the former player has a good amount of 500's and 400's in the rest of their tops, and taking into consideration what was mentioned earlier in Smoogi's part about trying to compare different skills, it's better if we were to focus around the best 50 scores from a player (like how it currently is), and perhaps lower the number when we can have some sort of skill splitting, where then there could be perhaps the best 5 plays focused for each skill, to then be all summed up for 1 total, used for global rankings.

I also realize that it may seem arbitrary to focus on only around the best 50 scores (like how it is in live). This is in part due to again not having some sort of skill splitting, thereby requiring a relatively large number, but also not too large to the point where your skill is significantly less represented accurately, getting into the territory where it's very easy for the player to set that level of scores.

I will also respond to where you say that your system is less subjective by making every play matter. What about determining the value of c in your formula? The only justification I can see is that it's similar to how it was in live, but that also seems subjective, especially since you say that live is more subjective than your proposed system.

[Xexxar]

While I agree that being able to sum skills separately and then add them up after would produce better results as far as a skill measurement is concerned, there is a substantial amount of database and logistic refactoring that would be involved with that. DB, UI, pipelines, etc. Considering you have said that a player with one 600 pp play is better than a player with thousands of 500s, I don't really think there is much more to discuss on this subject. The pp system does not produce results that are that objectively certain when it comes to plays. That's why we have farm maps and underweighted maps. I don't think and I imagine you would not think that a player capable of FCing Zanei HDHR SS is necessarily better than someone who can get a 1 miss on with a dance number DT (or insert your favorite underweighted play less than 560pp). If you claim that the pp system is just wrong on those cases, then you're not being consistent with your statement that pp is the objective metric of performance, and your point falls apart.

Yes. I agree that I used the constant of 120 in a way that's arbitrary, but this is not a unique case. This is done all the time, even in the pp engine itself which you have claimed is the arbiter of objective difficulty. These constants exist because, again, subjectivity is a necessary part of the system. The reason I said that my version is less subjective is that my system considers all of a players plays and then weights them accordingly, your system considers some arbitrary subset of a players plays and then weights them accordingly. There are two points at which you're applying a subjective restraint on the quantification of skill, rather than just the one that I am. Perhaps that's my bias, but I think if we can consider all the plays a player has done, then we ought to consider all the plays a player has done. The more information we have when making a some kind of logical deduction, the better the result is. That is just a normal facet of life.

Also: I went and checked, and there are only TWO players who have more than 1000 500 pp scores. they are Mathi and Rizer, who are both top players with skill exceeding both 600, 700, and even 800 pp ranges.

[Rekunan]

I agree, the pp system can be inaccurate, massively even at times. However, I will bring back to my point in my first response about pp being an objective measurement of performance. This is in fact a goal, not a current fact about the system, which is fueling the currently ongoing work from multiple pp devs, even spawning massive projects such as stat pp and the delta rework way back around 2019.

I will also repeat myself and say that the only reason you've only been able to find Mathi and Rizer to fit the criteria is that no one has any reason to do so, other than extrinsic ones like for fun. If this were to be pushed to live, there will be a new intrinsic reason, which is that players can climb the rankings without improving in their skill, thereby causing pp and global rankings as a whole to lose their already somewhat shaky value in the community's eyes to perform their purpose.

However, I do also agree that there isn't much point in continuing this discussion. It seems that we have two opposing perspectives, on how and what total pp represents, that are unwilling to change.

(i realize mentioning a WIP rework might spark curiosity for some people, so for anyone wanting to follow the dev progress on the aforementioned stat pp rework and others that are currently WIP, here's the invite to the pp dev discord: https://discord.gg/aqPCnXu)

[Myonpasu]

One property of the current method that could be nice to preserve is the linearity of overall pp. For instance, if I double the pp of all my scores, then it would be intuitive if my overall pp would also double.

Just replacing the 0.95^n in the current formula with any choice of decreasing function f(n) would do, and could potentially be a simpler change, while still achieving the same goals with regards to bonus pp. The proposal in the second post is of this form with f(n) = 1 / (1 + n), but what about trying some other kinds of f?

Testing choosing f to be the survival function (1 - CDF) of a few different heavy-tailed distributions might be worth a shot. The Lévy, log-logistic, and beta prime distributions spring to mind (with appropriate parameters/scaling for balancing of course), but there are also many others.

[Xexxar]

That property is preserved with the function I suggested, so I am not really sure what the advantage would be in using a different distribution than the one I laid out.

[Myonpasu]

Sorry, you're quite right. I was getting mixed up with the log stuff in the initial post which does not preserve it. Still, it might be useful to keep in mind if you decide to make any further changes.

[Xexxar]

AH true. My bad. In hindsight I wonder I should have just rewrote the post from the ground up every time I had a brain blast.

[stanriders]

I will reiterate here:

Current summation is indeed kinda flawed, making only the toppest plays significant, BUT considering 100 scores (with like 50-70 significant) is more than enough for total pp. Average player (assuming they're not completely washed up which pp can't and shouldn't measure) can easily set scores below their top-50 because they are either below or at their level of skill. Top 100 scores is a good representation of players overall skill, anything past that is not significant and does not show that player is any more skilled. Having infinite significant scores inflates the total pp value for no reason.

An alternative to this proposal is changing the curve to have more significant scores, for example something like this (courtesy of Ilmeria):

100 is chosen as a cutoff point because it's the amount of scores visible in players' profiles, but can be adjusted if there's any data to support it. Final pp value needs to be divided by 1.65 to keep values at the same level.

[stanriders]

People perform more than 100 plays, yet the ones showing their skill are usually just within the first 100 or so. It does not take any effort or skill to perform way below your skill level, why should you be awarded for that?

[Xexxar]

That seems like a very subjective opinion to claim that your 99th best play takes skill and effort but your 101st doesn't. I know I have some scores outside my top 100 which I consider to be some of my best, and they certainly did take effort and skill to set.

[stanriders]

That's why there's a curve, not just a cutoff. 99th would have 0.01% significance, 101s would have 0%, or whatever the value is. If you have scores outside your top-100 that you consider one of your best - this is a diffcalc issue, not a pp summation issue. Total pp summation shouldn't be a way to fix difficulty calculation flaws.

[apollo-dw]

The change here is certainly contentious as I think we've all found out. If the developers are interested in this direction, then I would recommend getting input from the pp committee for each respective gamemode: holding a discussion and a vote or something like that. I'm assuming that was going to be the plan anyways, but just putting it out there.

My current thoughts are that after setting enough XXXpp plays, setting another play of the same value or below becomes effortless and unequivocably free. This doesn't seem to line up with representing skill nor player accomplishment. This sentiment has been echoed by multiple players to be clear in the pp dev discord, where the discussion has been... ongoing

[mk56-spn]

Since this potentially decides in principle the direction of pp as a whole not so much specific values ( ie knowledge on pp isn't as key to understanding if you want it as simply knowing what you want the system itself to represent ) I see no reason such decision should be held by the pp committee. It would make much more sense for it to be a general community polling.

[stanriders]

General community polling is a must, however pp committees may have a better view of the direction the system is going, as well as overall expertise in the matter.

[mk56-spn]

General community polling is a must, however pp committees may have a better view of the direction the system is going, as well as overall expertise in the matter.

you are missing my point, yes the pp committee has a better view of where the system is going because they mostly decide where it is going on a day to day basis, no one is really denying that, what im questioning is if the pp comitee should decide where it is going on a more abstract level such as this. deciding whether 10 or 100 or 1000 scores are considered when accounting for the total value is not really similar at all to deciding values

[smoogipoo]

If the developers are interested in this direction

If by developers you mean me and peppy, we don’t decide these things. The reason this discussion exists is in the hopes that an amicable decision can be reached between Xexxar and the community most interested in the issue before anything else.

[Xexxar]

If the developers are interested in this direction

If by developers you mean me and peppy, we don’t decide these things. The reason this discussion exists is in the hopes that an amicable decision can be reached between Xexxar and the community most interested in the issue before anything else.

This decision should really not rest entirely on the community, even the pp community, since it deals with the definition of what pp is and how the system is supposed to work at large. I know that ppy has shut down the idea of removing bonus PP before because it quote "is the purpose of pp," so some direction from the developers on this seems needful. Plus: this change is a very broad change in that it covers all gamemodes, not just standard. Having a consensus from such a wide group would be very difficult.

[Xexxar]

I implemented a new curve based on feedback that weights the top plays we're a little too weak, and that tail end weights were a little too strong. You can find that version now on the website and the graph for this new version here:

https://www.desmos.com/calculator/4qwnj8v4jk

It should be labeled appropriately. Hope people think this looks better. Website is updated at https://pp.huismetbenen.nl/rankings/players/xexxar_total_pp

[Doxxz]

Total pp is a representation of how good you are at getting pp. While setting pp plays take skill, it is skill mostly only relevant to solo gameplay. Say the top 200 and the top 400 were to 1v1. The first is above, but the second could win just as well.

I believe what Xexxar has in mind is for total pp to represent how skilled you are against other players, because if his changes come to be, users will be incentivized to play a lot more maps (and by extension, a greater variety of maps), therefore broadening their skillset. Someone that has two thousand 500 pp plays is probably way more versatile than someone with a hundred 500's and a couple 600's, and well rounded players are more likely to win in a match, assuming the usual tourney map pool, which grades many different skillsets.

Thus it is a battle between "rankings should represent who is better at player vs player" vs "rankings should represent who can get the highest pp plays"

Perhaps in the future we could have an elo system to measure pvp skill, but keep pp around as it is to measure who is better at breaking limits.

[stanriders]

pp is about solo skill and only that, it can't represent multiplayer/tournament skill. Versatility is not really something that can be covered by total pp - it does the opposite in fact. To truly measure different skill there has to be multiple metrics, total pp squashes them all into 1 value.

[Rekunan]

What's stopping someone to just farm the same type of anime aim map +DT to get two thousand 500pp plays? Sure, maybe it's not possible right now (I wouldn't be surprised if it already is), but what about in the future?

Adding on to what stanr said, if anything, the second player would be more likely to win a match against the other due to the former not performing at anything above a certain difficulty level, thereby getting skillcapped.

I also agree with stanr, this would be better solved using some system of skill splitting, where instead of focusing on around the top 50 plays (like how it currently is) we'd only have to focus on around 5-10 for each skill (such as aim or reading).

This is not a battle between pvp vs highest pp plays, this is a battle between rankings staying true to the goal of pp, and rankings being used to incentivize players to play more, to the point of not wanting to improve since they don't need to.

[Doxxz]

What's stopping someone to just farm the same type of anime aim map +DT to get two thousand 500pp plays? Sure, maybe it's not possible right now (I wouldn't be surprised if it already is), but what about in the future?

Lack of maps. While this person waits for more maps of this trope to be made, someone else could play hundreds of other varied maps .

Adding on to what stanr said, if anything, the second player would be more likely to win a match against the other due to the former not performing at anything above a certain difficulty level, thereby getting skillcapped.

Would player two really be able to perform better at the 600pp level at every skillset given that they only have two 600 pp plays and less experience at 500?

This is not a battle between pvp vs highest pp plays, this is a battle between rankings staying true to the goal of pp, and rankings being used to incentivize players to play more, to the point of not wanting to improve since they don't need to.

In my opinion, this change actually incentivizes players to play more. Because it changes the gameplay loop from "playing well at the limit of your skill to get rewarded" to letting you play anything you want and still get rewarded. You can also practice a skillset which you can't yet perform at the necessary level, and still gain something for it. Sure, you could also do those on the current system, but the reward is worthless or non existant.

I also agree with stanr, this would be better solved using some system of skill splitting, where instead of focusing on around the top 50 plays (like how it currently is) we'd only have to focus on around 5-10 for each skill (such as aim or reading).

I can also agree with stanriders on that point, but that doesn't mean this rework doesn't measure that at all. It does a better job at measuring versatility and experience than current pp. The reason I mentioned all that pvp stuff is because these traits are very good to have in tournaments.

It is a matter of what the playerbase wants; for total pp to represent your skill and experience/versatility (this log pp), or for it to represent your skill only (current pp).

[Rekunan]

Lack of maps

Even if it isn't possible now (which I'd argue it is), it will be in the future, which fundamentally undermines your idea.

Would p2 really be better

Maybe not every skillset, but enough to the point where if they played a hard enough pool, they'd more than likely get at least a close win against p1.

Opinion that it incentivizes play more

This is not an opinion, it's a fact. The question becomes why should players be incentivized using the pp system? Its entire goal is to be objective at measuring performance. Combining that with the global ranking system, in most cases, higher ranked players are more skilled than lower ranked players. With this change, that no longer becomes the case. Players will be able to grind 500pp scores and climb the rankings without needing to improve their skill, surpassing players that have 600's. Even if you need thousands, the fact remains that it's possible. This then completely removes the already somewhat shaky value in the community's eyes for being able to perform its purpose in the global rankings. All to just get an incentive to play more.

that doesn't mean this rework doesn't measure that at all

This rework doesn't even change anything with pp calculation. All it does is allow players to climb ranks without needing to improve. Most if not all gimmick skillsets are still underweight, and there's still all of these issues: https://twitter.com/NateIytIe/status/1570486304621854722

It's a matter of what ppl want

Do people want the global ranking system to be accurate and objective in determining who has more skill, or do they want a fundamentally inaccurate system with loopholes and exploits, just to get an incentive to play more? The former is the current goal of the pp system + skill splitting, and the latter is this current proposal.

[iSimpFor]

maybe name the pp gained from this method "consistency pp" or something like that? the name would communicate its purpose

[Rekunan]

if you want a name it's "incentive pp"

[Xexxar]

Its not really about incentives. It's about properly weighting and assessing the total history of a players performances.

As far as the original idea here: I think people will just need to adjust how they think about pp. Perhaps for a while it would be referred to as pp beyond peoples top 100, until the system becomes normalized and people are used to it. After all there is only one metric and no extra systems or variables that would need to be labeled.

[Xexxar]

I'm going to appeal again to devs as this will never be a decision that can be concluded without developer insight. All that needs to be answered is: what do performance points represent and what is the purpose of the pp system in osu?

I know smoogi said they don't intend to comment and instead they will leave it up to us. If that's the case it'd probably just be best to close the discussion, as I cannot see anything beneficial coming from it. Arguing over definitions will get us nowhere.

Fwiw: the wiki definition:

Performance points (or pp for short) is a ranking metric that aims to be more contextually relevant to a player's progression in osu!.

It aims to shift the focus of skill progression from the amount of time played to an actual representation of the player's skill. This is attained by the calculation of a unique score known that is based on the difficulty of a beatmap and a player's performance on that beatmap.

[stanriders]

Please do not appeal to anyone and stop trying to halt the discussion. Any comments here show what people in the community think about it, having it closed just makes you free from acknowledging counterarguments.

[Xexxar]

As long as there is a disagreement in definitions, counter arguments will continue to boil down into "pp is a measure of skill, not a measure of accomplishments." For reference, the below post made me reiterate my appeal, due to its completely disrespectful tone and statements.

Do people want the global ranking system to be accurate and objective in determining who has more skill, or do they want a fundamentally inaccurate system with loopholes and exploits, just to get an incentive to play more?

This isn't a discussion. This is complete closed mindedness and borderline hostility. When people are at the point of unsubstantiated repetitive arguments, I'd rather just close the discussion because its doing no one any good to respond to a post like this which is misinformed at best, malignant bait at worst. There is nothing that can be said to someone who calls the entire point and intention of the post and suggestion, 'fundamentally inaccurate with exploits and loopholes.' It again just boils down to definitions which cannot be decided via arguments.

[Fr0stium]

Had a small discussion on the pp dev discord regarding this change and was asked to put my thoughts here. My apologies if some points were reiterated already.

Right off the bat, I do not think that a sum of the player's performances that grows logarithmically is appropriate for total performance. More generally, any summation of a player's performances that grows to infinity is not appropriate.

The primary reason is because if a player repeatedly sets scores that are worth at most p, it's quite clear their performance has maxed out at p. Their total performance should therefore be kp for some positive constant k, which is what the current geometric sum (and any finite sum) does. It makes no sense for their total performance to grow without bound when all their individual performances are below some constant.

If your definition of total performance is different, then the meaning behind total performance is now further detached from individual performances, despite total performance being directly made up of individual performances. Not a good direction forward. The existence of bonus pp has already detached the two to some extent, and an unbounded sum worsens it.

One of the counterarguments I heard is that a geometric sum for the aim skill is a bad idea, so the geometric sum for individual performances is a bad idea. This is a false equivalence between the two.

Let's say we have a map that is n notes long, and the player's goal is to hit all n notes. The player must repeatedly hit every note without fail. If they fail to hit a note, they fail to FC, and the player must restart from scratch. As n grows larger, the probability of FC decays exponentially, so the skill required to FC grows without bound. Therefore, a geometric sum of strains, which approaches a finite number, is indeed inappropriate for aim SR. A sum that grows indefinitely would be much better. This is also true for any constant amount of misses, but I won't go into that here.

On the other hand, let's say the player's goal is to set n scores, where each score is worth at least p performance points. The key difference now is that if the player fails to set a score worth at least p, they do not immediately fail to meet their goal; they can repeatedly try again until they set a score worth at least p. Unlike the FC case, where missing renders all previous hits irrelevant, failing to set a score worth p does not render all prior performances irrelevant. The player does not have to start over like in the FC scenario. For these reasons, as n grows larger, that does not necessarily mean that the player is performing better.

It's kind of like if the player misses a note, and the game allows them to go back and try again until they can hit the note. The circumstances are clearly different. Therefore, a geometric sum of individual performances is much more appropriate here, and an unbounded sum is not.

Summary of this countercounterargument.

Additionally, when dealing with the shortcomings of this proposed system, I've heard the excuse "just play more maps" and that is a bad excuse. Shortcomings should be fixed with a better system. If players that have a few high-pp scores become underranked, it should be fixed, not chalked up to "just set more scores to really prove yourself."

[Rekunan]

The justification is the same. Sure, there may not be 5 or 10 ways to split aim, but it's enough to show that a player has a aim skill. Going back to the plays in my proof, only one is needed to show s stamina, and will be added to tapping, along with others such as sp speed and r rhythm. Perhaps there could just be one play used for stamina, speed, etc. Again, this depends on the implementation of skill splitting. However, your claim, that my restrictions (skill splitting & live/current system) are subjective, has no ground unless you're able to refute my proof(s) and/or explanation(s).

Also, I do agree that skills don't exist in a vacuum, at least in almost if not all the ranked section, however,

encourage to rank hyperfocused skill farm

Personally, I believe this to be very unlikely. One is that it is very rare to find a song that fits this type of mapping, while also still being rankable. Two is that there have been many methods and abuses open for creating farm maps, such as length bonus and diffspikes. Despite this, there hasn't been any creation of farm maps recently, in fact you could say that it is dying, perhaps even already dead. There are just maps like Zan'ei, which will be fixed. This is compared to back in around 2018-2020 when the creation, of farm maps, was constant and common, with most of them still in the top playcount rankings.

However, let's say this does happen. Then the plan is the same: make changes and reworks so that the farm maps are no longer farm. You say that this will massively increase the work on the system required, but this is not the case. Any issues that arise would've arisen regardless of skill splitting.
Let's take your example you bring up. Yes, it is true that PP+'s tapping leaderboards (https://syrin.me/pp+/l/scores) are filled with Hidamari no Uta. However, this is not due to this being a worse system. It is due to 2 other factors:

1. PP+ reaching end of life (not as big factor)

In the 2 years since end of life, the scene has had massive changes. More speed maps ranked (trio cup, slowmotion, etc.), plays set (end time DT, the whole top9 of aricin's plays, etc.), and more players and boundaries being broken.

2. Speed acc scaling (big factor)

It's known that Hidamari is a doubletappable map. If you look at the Hidamari plays beyond the top20, you will notice that almost all of them have <93% acc and >10 50's. That's not to say that it's necessarily a result of doubletapping, but considering they place higher compared to arguably more impressive speed scores, speed acc scaling needs a rework. This fact has been known around the time since the 50's band-aid nerf was thought of, probably even before then. This was not known because of PP+'s skill leaderboards. They may have helped in displaying the issue, but were not the sole cause of knowledge being spread of it.

Similarly, we know about the Zan'ei angle abuse, or the trio cup burst abuse, or many other problems listed in Natelytle's thread https://twitter.com/NateIytIe/status/1570486304621854722 all without having skill splitting. If anything, skill splitting will help in detecting/noticing these issues, or at least bring them to light more widely, just like how combo scaling rework really enhanced the length bonus issue. But again, these issues exist without skill splitting, and is why we don't have "to balance every maps subskills against every other maps subskills."

[MaxKruse]

Short reply, but can we go away from entertaining skill split when the topic at hand is about changing how bonus pp and score weights works? This doesnt help at all.

[Rekunan]

Oh, but it actually is a massive help. Skill splitting has been mentioned multiple times during this discussion here and on the pp dev discord to prove why a large bounded number of top plays is required and justified in live/current system, and why we shouldn't just use top1 play.

Allow me to explain again.

My proof shows that we only need one play to show that a player has s stamina, anymore would be redundant and in fact detrimental to the global rankings due to the abuse that exists in not requiring to show improvement to climb them, despite the whole goal of rankings is to show who is the better player, combined with pp being an objective metric that measures performance. This may lead people to believe that we should just use the top1 play. However, using only the top1 play neglects skillsets not represented in the top1 play, as is natural when considering the majority of the ranked section. Therefore, we must use a large number to be accurate. Here, I will say live/current system focuses on around 50ish plays for ranking purposes. This is justified for 3 reasons:

1. Again, so that we don't neglect skillsets not represented in the higher tops.
2. This is around the number where many, including myself, start to forget many plays.
3. Anymore, and the plays would be easily replicable/duplicatable.c

Now let's say skill splitting was a thing, then we wouldn't need to consider 50ish plays for each skill, like how it is in live/current system. We'd only need to consider 5ish (or even lower depending on the implementation) for the same reasons:

1. Don't neglect what's not represented
2. Forgetability
3. What's easily replicable/duplicatable

If you still believe that this adds nothing to the discussion, well at least my first part of the reply wasn't entirely about skill splitting.

Also, and this goes to anyone, it's fine if your reply is short. I'm happy to continue discussion, and perhaps even educate, no matter what your reply contains. Don't feel intimidated by these essays, you all have the capability to contribute. Just make sure to think before you hit reply, and remember that the edit button exists.

[Xexxar]

Your proof hinges on stamina because stamina is a skill that is the hardest to fluke out or get lucky with (although a player can still get lucky with their accuracy or with their mash allowing them to hold combo). Even still, as you address, skill sets are not so one dimensional as to be able to be defined by one map alone. Does a play that has 300 bpm streams for 256 notes have more stamina requirement than a map with 250 bpm streams for 1024 notes? What if one map has triplets and 5 note bursts predominantly where the other is a constant stream?

There are many ways to demonstrate s stamina, as laid out above. You acknowledge the problem with only using one map, which is that it only works by assuming that s is measured in some type of quantitative vacuum where the skill can only be demonstrated one way. Unfortunately, every skill, even stamina, isn't that one dimensional. This is why it is necessarily to look at more scores. My position is that it is most advantageous to use a system that looks at every score you've done in a meaningful way.

This really shouldn't be as controversial as you're making it out to be.

What if two players have the exact same 5 best plays in a skill, but one player has many many many more examples of top skill plays whereas the other has none. Why would we consider them to be the same skill? How is it that this is not clear that this system is flawed?

[Doxxz]

pp is linked to the leaderboards. A leaderboard's purpose is to show who is better than who. If we can agree that a player is getting better by playing more maps then it makes no sense for it to not be reflected on their rank.

But if we can't agree on that, what if this formula was changed to have a steeper tail? As it is right now, as far as I can tell, it reaches a point around 10k plays where you need 100 plays to get ~5 pp. Maybe this "soft cap" could be reached earlier on, so players that never aim for higher pp plays start to decay in rankings. If 5pp is too much, it could even be 1pp/100 plays (I would make an example myself if i had any idea how to implement these changes).

That way it better represents the total achievements of the player while still requiring you to improve (in the sense that Rekunan is reffering to) to get ranks.

edit: pressed ctrl + enter by accident instead of shift + enter.

[MaxKruse]

To give my input, even if its not very high brain usage:

I like the idea of deatching bonuspp from unique submits (which also virtually infinitly scales because of deminishing returns) and instead attach it to actually trying to set good scores.

How i see it, it moves "bonus pp farm" (if that even is a thing) from spamming random low diffs for that extra 1-2pp depending on unique scores to playing at a constant higher level. I am aware nobody actually does this, but with enough tweaking this can be tuned to factually not affect anyone that plays semi-regularly.

The only people getting fucked by this are people that have relatively low unique scores for their total pp (mainly "peak" pp farmers or banned/reset accounts). Anyone else gains the ability to have an incentive to actually play the game more and enjoy themselves, being able to play slightly lower maps and still have a small but visible chance to get pp when you play well.

This rework in total would give less pp than any other difficulty or map related reworks usually do. I dont get why people are upset about this. Everyone except a small subset of people have everything to gain.

[Xexxar]

Yeah. For what it's worth, I'm a player who loses around 200 pp with this change. To me, this isn't surprising at all. If you look at my completion, you can see just how few maps I really played, let alone set a score I was proud of.

Number of scores on ranked maps in each year
2007 | 00.567% | 2/353
2008 | 00.632% | 12/1898
2009 | 00.650% | 28/4308
2010 | 00.630% | 40/6345
2011 | 02.529% | 124/4903
2012 | 04.131% | 224/5423
2013 | 11.399% | 511/4483
2014 | 07.438% | 326/4383
2015 | 06.125% | 383/6253
2016 | 03.390% | 187/5517
2017 | 00.674% | 36/5341
2018 | 00.241% | 21/8705
2019 | 00.078% | 7/9027
2020 | 00.082% | 7/8546
2021 | 00.117% | 13/11151
2022 | 00.024% | 2/8442

In total I have 500 FCs of 2500 scores. (about)

Generally I just played a few songs I liked and would cycle them endlessly trying to get 'tha FC', which makes sense why when I lose my bonusPP I am nerfed slightly. With this system in place, I would have benefited much more from venturing out of my comfort zone of maps and would have likely tried to set good scores on maps that I could actually do (instead of just fixating on scores just outside of my reach). I think it would have helped me from burning out probably as well, and I might have honestly improved as a player from having to play different maps more often as well.

It is as you say, every player has everything to gain from this change. The only people who don't gain from this are the people who literally do not want to play the game.

[Xexxar]

Helix has updated the website with two bugfixes:

• The website was running every score without respect to maps, meaning that the same map would process with multiple mod combinations. This has been fixed so that now only the top score for each difficulty will be summed.
• The old pp used to be based off the live data, meaning that the old total would be affected by new scores whereas the new total pp would be back dated to September 1st. This means it could give the impression that players were losing more than they actually were (if they set a lot of scores after 9/1). This has been fixed so that now the profiles old pp is calculated from historical scores available on 9/1 so that it matches the new total pp calculation.

Again you can see this at: https://pp.huismetbenen.nl/rankings/players/xexxar_total_pp

[unholyghosttyper]

What the hell is this whole discussion... damn!
Guess people mostly conserned 'bout farming of lesser pp scores.
But it seems like nobody sees that with Xexxar's system every next score still be scaled down like in original.

So let's get this stupid argument 'bout hundred 600pp and 1237 500pp giving the same pp and think a little.
If first guy gets one more 600pp score, how much 500pp maps should second guy farm more? Hundred? More?
It's log() so it scales pretty fast.
Those guys who scream about all-powerful low pp farmers most likely just aren't skilled enough to play couple more same pp maps as their top 100 plays.

Anyway.
Don't understand why only top 100 plays should be considered for PP.
And bonus PP is kinda pointless and shouldn't exist.
Xexxar found a method to solve all this without any damage.
And did a great work with all that math.
Even more. It doesn't remove anything from the game and just adds something besides mindless pp farming for people to enjoy.

I want to click circles with maps that i enjoy the most.
And with this addition i will be rewarded for enjoying my time including difficulty and not just map count.

Also i like the term "Consistency Bonus"

Where should i sign for this being added to game?

[r9bina]

I like this change and this is actually could be breath of fresh air for some players. These changes are minor and won't affect many players, but it's a nice bonus for score and not PP farmers. I see only 1 downside of this - an even bigger difference between top nomod/hr and dt players. Even now we have 5x less (and even more FARM) nomod/hr 700+pp maps compare to dt and i think with this change it would be much easier for dt players to go for many scores. I understand this is not a problem of this specific change, but a problem of the established meta but still i see someone like mathi for example can easily go for another +100pp(total) by playing and someone like rupertion can't, because there are just 0 maps for him on this range.

[Xexxar]

Any updates on this? It seems that conversation has died. Would love to get more feedback if theres anyway this can be improved further.

[unholyghosttyper]

Also still waitin'
Dunno who's responsible for pp system right now but i would like an answer.
Something competent like "No, we cannot do this 'cuz ..."

[smoogipoo]

There's a lot of things happening simultaneously right now, please wait.

[Xexxar]

Hate to just bump always but it's worth a shot since it's been over a month. Hopefully things aren't as busy.

[ghost]

I think this would be healthy for the game and I don't think it's nearly as controversial as people make it out to be. Of course initially the rankings might seem somewhat imbalanced, but very few people are going to have a profile that's optimized for a system that hasn't been implemented. I don't think PP committee should be the deciding factor in whether or not it's implemented, because it's more of a decision surrounding the future direction of the game and community. If the community agrees with this direction, but the initial rankings change is too steep, I don't see why you couldn't just implement it gradually over a longer time period (Calculate top 150 plays, then top 200 etc.) to allow for players to adjust to the new "meta".

Allow ordinary, intermediate players to easily see what their and their friends' profiles would look like and I think you would get some valuable feedback. Perhaps something that would make it more easily understandable for players and make it easier for them to give feedback is a standard calculator, "In order to reach X rank, you would need to set Y plays worth Z PP." Then it's less of a theoretical for people and they have the hard numbers right in front of them.