1k, 2k, 3k, 4k, 5k, 6k, 7k, 8k, 9k, 10k, 12k, 14k, 16k, 18k
These are the keymodes osu! currently has. How much harder is one keymode than another, and how much does an extra key add to the difficulty?

How I see it, there seems to be a split in playstyle as such: 1k, 2k, 3k .... 4k, 5k, 6k, 7k .... 8k, 9k, 10k .... 12k, 14k, 16k, 18k
Between those splits, I imagine a difficulty jump by some amount, but not sure. I also think difficulty can vary by setup, especially 10k+, but also not sure. That's why I am asking, help me understand how this works. By how much does the stamina and finger flexibility of one keymode relate to another?

I was gonna write a big post, but instead, I'm just gonna say this: trying to compare key modes is a terrible idea and will do nothing but result in a bunch of people arguing over whether 4k is easier/harder than 7k. IMO this thread is pointless.

Bobbias wrote:

I was gonna write a big post, but instead, I'm just gonna say this: trying to compare key modes is a terrible idea and will do nothing but result in a bunch of people arguing over whether 4k is easier/harder than 7k. IMO this thread is pointless.

And if this is important in guiding me to get a general picture of how to correctly determine the difficulty for the keymodes for osu!skills since this strawpoll shows players want the keymodes separated?

abraker wrote:

Bobbias wrote:

I was gonna write a big post, but instead, I'm just gonna say this: trying to compare key modes is a terrible idea and will do nothing but result in a bunch of people arguing over whether 4k is easier/harder than 7k. IMO this thread is pointless.

And if this is important in guiding me to get a general picture of how to correctly determine the difficulty for the keymodes for osu!skills since this strawpoll shows players want the keymodes separated?

if they would be to be separated, they shouldn't fall under the same unit/graph/plane, different keys have different ways to calculate difficulty. Taking taiko and ctb for example, you can't really say that the #1 player of Taiko plays better than the #1 player of CTB, vice versa. Basically you will have to treat them as separate game modes if you were to calculate them, there's no general consensus that [x]k is harder than [y]k

if you're going to link them somehow using stamina/flexibility relationship good luck lol, i find that only 0.1% of the maps i play in 7k made my whole arm tired and 0.1% of the maps i play in 4k felt awkward to play

Evening wrote:

if they would be to be separated, they shouldn't fall under the same unit/graph/plane, different keys have different ways to calculate difficulty. Taking taiko and ctb for example, you can't really say that the #1 player of Taiko plays better than the #1 player of CTB, vice versa. Basically you will have to treat them as separate game modes if you were to calculate them, there's no general consensus that [x]k is harder than [y]k

if you're going to link them somehow using stamina/flexibility relationship good luck lol, i find that only 0.1% of the maps i play in 7k made my whole arm tired and 0.1% of the maps i play in 4k felt awkward to play

This, basically.

When it comes to speed in rhythm games, difficulty in keymodes is divided into two distinct categories: reading difficulty and physical difficulty. Doesn't really take a rocket scientist to find out which key mode is harder in terms of reading difficulty. In a combination of 4 1/4 intervals, there are exponentially exponentially more combinations present in 7K than 4K. Likewise, there are more combinations present in 12K than 7K. So theoretically speaking, if the overall skill level of a 4K and a 10K player are the same (and you somehow manage to measure the holistic skill level of a player through voodoo), you would expect the 10K player's reading skill to be far far better than the 4K player.

That's also another thing I want to emphasise though, reading difficulty of a higher key mode will only be ultra prevalent in high levels. At skill level 0, no key mode is harder than the other. Therefore you can say that with higher key modes, the potential reading difficulty will be higher. Direct relationship.

As for physical ability, given that a person is using a conventional one finger to one key setup, the lower the keymode, the higher the potential physical ability demanded - inverse relationship. To give an example - take a 180 BPM stream in any key mode. In 4K, if no minijacks are created, each finger is hitting notes at 3 notes per second (180BPM / (60sec * 4 beats) / 4 fingers), equivalent of 45BPM jacks - it could potentially be higher, but it's unlikely to reach something like 7-8 notes per second for one finger. As for 1K, you cannot spread out the notes in any way, so you will be doing 12 notes per second on a single finger for a sustained period. While that is definitely within human capability by a decent margin, it's still much much harder to do physically than what most streams in 4K expect you to do.

The reason why key modes can't be compared is because you cannot meaningfully compare and quantify "reading difficulty" and "physical difficulty" in the same type of measurement. Any claim of saying that a keymode is harder than the other is irrational because people are unable to measure their absolute skill level in a certain key mode. Yes, this also means that relative comparison is not a good measurement either. There are certain keymodes where are played more often than others, so the perceived "best player" in a particular keymode (say 3K) might be, in reality, not all that great if 4K players decide to play 3K, since there's a high possibility that there's a better "3K" player in the 4K community since so many people have played 4K.

I don't think there's necessarily a key mode that's harder than any other when it comes to speed, at least. The difficulty of any chart can reach infinity, regardless of keymode.

Other than reading difficulty however, I would say that accuracy is the only other thing that is objectively harder in higher keymodes. You build much more muscle memory in higher keymodes with different fingers, and as a result there's a much higher chance of making timing errors with keymodes that require more fingers. In addition to this, the average strength and flexibility of a finger in a higher key mode (e.g. 9K) is much lower than say, 4K. This also creates a higher chance for more timing errors.

If you want to measure difficulty of any keymode, it's best to keep them separate and ensure that they have their own scale of difficulty. Creating a difficulty system is a completely new can of worms altogether, and I don't think it'd be a good idea to post about how to measure difficulty in a certain key mode accurately because it'd take eons to write and a million factors to account for.

You also have to remember that a difficulty scale can only be so flexible and robust. It is not possible to create a perfect difficulty system, the best thing you can create is a difficulty scale that exceeds human perception bias (i.e. 10/12 people will say something like "this chart is definitely overrated") and for one particular playstyle. You would need completely different variables for unconventional playstyles (e.g. 2 fingers for one key in 2K, hello taiko) and as a result the realistic endgoal is to make a difficulty scale for the most common/conventional playstyle.

Hope this helps somewhat.

Shoegazer wrote:

.

Yeap. There's also hand positioning that adds to the difficulty with higher keymodes, since your hand would have to move around and not stay in a fixed position. Reading at higher keymodes is pretty different too.

I would argue that at skill level 0 reading difficulty is still proportional to the number of columns, since at skill level 0 ma player has not internalized the proper finger to key automatic response and must consciously read rater than automatically read.

That said I feel this effect is horribly overblown by people who try a higher keymode once (or several times), fail, and denounce it as impossible to learn and return to 4k because it's "easier".

Other than that, yeah you pretty much said everything Shoegazer.

So let me try to tl;dr Shoegazer's post to see how well I understand:

Comparing overall difficulty of keymodes is futile since they have varying degrees of demand depending on what you are looking at. There is the following relationship:

• physical demand ∝ skill level
  physical demand ∝ 1/keys
  reading demand ∝ keys
  accuracy demand ∝ keys

Did I miss something or get something wrong?

Shoegazer wrote:

In addition to this, the average strength and flexibility of a finger in a higher key mode (e.g. 9K) is much lower than say, 4K. This also creates a higher chance for more timing errors. In addition to this, the average strength and flexibility of a finger in a higher key mode (e.g. 9K) is much lower than say, 4K.

This made me realize how bad of a system difficulty rating is. If the player learned to play 4k with just index and pinky finger so that the average strength and flexibility of the fingers evens out, I think the accuracy would have a higher starting point. While I don't think anyone does that, it does seem that some edge cases would make the idea of determining the difficulty for accuracy on a certain keymode based on a player's prominent fingers wrong. Instead about talking in terms of difficulty, we need to talk in terms of skill requirement. Instead of saying, "this pattern is hard" or "this pattern is easy" we need to say, "the player must have this skill value to be able to do this pattern at a % success rate". Maps's skill requirement for tapping a certain finger, skill for reading at a certain rate, skill for endurance, etc. are the things the player should be looking at instead of how difficult the map itself is because it's not possible to know how the player's setup affects the perceived difficulty of the map.

Shoegazer wrote:

It is not possible to create a perfect difficulty system, the best thing you can create is a difficulty scale that exceeds human perception bias (i.e. 10/12 people will say something like "this chart is definitely overrated") and for one particular playstyle.

I'm trying to avoid basing it on human perception and as such that will be the last resort, because as you said, we can't say the absolute skill and we can only say relative skill based on other players. The calculation would be based on theory and the theory would be tested by seeing how much of it correlates with the statistical data on results and replays. Yes. there are A LOT of factors to take account to, but I'm sure it will be easier than what I'm working on with the reading skill for the standard gamemode right now.

Evening wrote:

if you're going to link them somehow using stamina/flexibility relationship good luck lol,

The goal is to separate independent variables. There is no significant relationship between able to jack 1/8th and able to do heavy 02jam style noodle maps. In this case, stamina would have its own difficulty rating, flexibility would have its own, and so on.

abraker wrote:

So let me try to tl;dr Shoegazer's post to see how well I understand:

Comparing overall difficulty of keymodes is futile since they have varying degrees of demand depending on what you are looking at. There is the following relationship:

• physical demand ∝ skill level
  physical demand ∝ 1/keys
  reading demand ∝ keys
  accuracy demand ∝ keys

Did I miss something or get something wrong?

Evening wrote:

if you're going to link them somehow using stamina/flexibility relationship good luck lol,

The goal is to separate independent variables. There is no significant relationship between able to jack 1/8th and able to do heavy 02jam style noodle maps. In this case, stamina would have its own difficulty rating, flexibility would have its own, and so on.

Meant exactly that, and also:

Suggesting some changes/additions if you manage to finish the wireframe for this project on osu!mania

• physical demand ∝ skill level
  physical demand ∝ 1/keys
  reading demand ∝ keys
  accuracy demand ∝ keys

physical demand ∝ skill level
The issue mainly here is that you have defined 2 subjective/unknown variables for "physical demand ∝ skill level" which may be not that accurate but not bad of an approximation
Physical demand varies from chart to chart, some charts are more physically demanding and hence some players may find it harder/easier, there are other charts in which demands other skillsets which some players may find it harder/easier. The main thing I'm trying to get here is that it's hard to gauge a skill level using just physical demand, you will have to take in consideration how technical/bursty/rolly/noodly/jacky a chart is and how well a player can handle that.
TL;DR : Other factors being included into physical demand ∝ skill level would be much more accurate, it's more of a
f(physical demand,reading,control,etc.) ∝ skill level (within 1 specific key)

physical demand ∝ 1/keys
This might be generally true but sometimes you have to take note that skill level/physical demand may go undefined in 1k vibro charts, some people just can't vibro , making it slightly inaccurate at 1k charts up from 180BPM 1/4 streams
Also there is also another factor that edisk mentioned that anything >10k would require constant movement of hands, this might be horribly tiring depending on what setup they use, personally haven't tried anything horribly hard on >10k yet but this might be something to take note of

reading demand ∝ keys
lol i'm not too sure about this, sounds theoratically correct but i have trouble reading 1k, maybe that's just me xd

accuracy demand ∝ keys
uhhh yeaaa you might want to take note that any pattern for 1k is going to be jacks and jacks are horribly hard to time, most people would have trouble at getting an S on a 4* 1k already if they don't have control, and again, these equations might be too simplified to guage how you're going to link everything together

You're probably right if you clump all these variables together like:

f(physical demand,reading demand,accuracy demand) ∝ skill level but you really can't simplify everything to keys itself as there are a ton of anomalies. Though it would be fine if you get create a rough gauge that works with all keys in general, it wouldn't be that much accurate when it comes to specific charts that would break difficulty judgement programs, but there would probably never be a very accurate difficulty calculator anyways.

Evening wrote:

...

Physical demand is a generalization. I do like f(physical demand,reading,control,etc.) ∝ skill level (within 1 specific key) better. The current skills I plan on applying to mania so far are Speed, Stamina, Reading, and Flexibility, where accuracy is used to measure how well the player did in those skills. Rhythm is another skill I am considering which would take care of technical maps and repetitive notes/patterns. Each of those fall into either one of the two categories mentioned.

Evening wrote:

you have to take note that skill level/physical demand may go undefined in 1k vibro charts, some people just can't vibro , making it slightly inaccurate at 1k charts up from 180BPM 1/4 streams

A demand is a demand, it can't go undefined. What can go undefined (or rather go to 0) are the odds of a human meeting that demand.

Also,

Evening wrote:

lol i'm not too sure about this, sounds theoratically correct but i have trouble reading 1k, maybe that's just me xd

I think that has to do with the screen's refresh rate and lack of reference points. In higher keys, there are surrounding notes which allow you to keep track where each note is in relation to other notes, but in 1k there is just one note after another. When using a high scroll speed and trying to hit notes close together, there are tearing effects which make the notes double or just end up in a location similar to a frame before, causing something close to a Wagon-wheel effect.

abraker wrote:

Evening wrote:

you have to take note that skill level/physical demand may go undefined in 1k vibro charts, some people just can't vibro , making it slightly inaccurate at 1k charts up from 180BPM 1/4 streams

A demand is a demand, it can't go undefined. What can go undefined (or rather go to 0) are the odds of a human meeting that demand.

Talking about a yes or no situation here, some people can hit up to 220 bpm streams and some cannot do that even if they try for 10 years, it is more of a "trait" that people can/can't vibro, there's no scaling on this is after a certain point is what i'm saying

you can either look at the exponential curve of wrist jacking which scales up really high after 180bpm or you can look at vibro in which some people are just born with the ability to hit >200bpm streams with 1 finger in which i don't even know how it scales

So what you are getting at is that there is no point in measuring how fast a person can vibro after a cetain point, even if some people are capable of going faster? Even if it's ludicrous, it's a statistic I would not want to go without.

abraker wrote:

So what you are getting at is that there is no point in measuring how fast a person can vibro after a cetain point, even if some people are capable of going faster? Even if it's ludicrous, it's a statistic I would not want to go without.

uhh I think i'll break it up into small points:

Scenario 1

- Person A cannot vibro while Person B can vibro (this is a trait thing):

- Person A takes 3-4 years to get to 180BPM wrist jacking, this is a gradual jack skill level scaling thing, so you can improve your wrist jack speed after practice

- Person B takes literally 1 week to be able to vibro 180 bpm, this is not a gradual scale, it's more of like a set value for a person, of course he can't really control 180 BPM jacks well in terms of accuracy and consistency but naturally he will perform better than Person A when they are faced with 1K jacks if they are tested within 3 months on how well they can play a 180bpm constant 1/4 1k chart

Scenario 2

- Person A cannot vibro while Person C can vibro up to 220 bpm:

- Person A probably takes up to ... forever to be able to wrist jack 200 bpm properly while Person C does it within 3 months

- Test results may be off due to that factor if you test them after 3 months

Conclusion

So you will gather results like even if you have all of these 3 people play and start VSRG-ing at the same time

Person A:
Jack Ability: 2/10 (Caps at around 8/10 after 10 years of playing)

Person B:
Jack Ability: 8/10

Person C:
Jack Ability: 9/10

1K (and lower keymodes in general) have a lower skill cap because of human physiology with a conventional setup, yes. I don't think it's necessary to have an undefined function for 1K (and vibro in general) at a certain point, but trying to find out the nuances of the statistical distribution of how hard a person can tense up their forearm muscles is not something that you can easily find out - getting heuristics for such isn't easy either.

In any case, I don't think you should really include straight-up vibration speed to begin with, because it throws off many other variables that pertain to jacking. That is another limitation with difficulty scales like this - the parser/calculator will only give an accurate rating if the chart isn't too much of an anomaly from a conventional chart. Considering that charts that mainly test vibration are gimmicky and the tinkering required for charts like those to ensure that those charts aren't overrated causes too much trouble as a whole - you're better off just not including vibro in your calculations - just deal with regular jacking instead. I guess you can do it for something like 1K? But at high levels the "conventional" setup will be a 2 finger to 1 key setup. It's similar to Taiko in a sense, if you're only given a one-to-one configuration then every high-level Taiko map would be impossible.

abraker wrote:

The current skills I plan on applying to mania so far are Speed, Stamina, Reading, and Flexibility

You are generalising VSRG skills far too much. You're also implying that every single key mode will have the same reading/speed/stamina difficulty and all that, or at least you are trying to scale them. Again, a heuristical approach won't help here - you won't be able to find a good enough variable to scale difficulty/skill accordingly.

The skills that you're better off covering are keymodes. 4K, 6K, 7K and 8K seems ideal. 9K/10K if you're feeling ambitious. From there, you create subskills, consisting chordstream (though this can be divided quite a bit, but we'll go with a general term for now), speed (not just stream charts, but also chordstream charts where the chords are too light to contribute much meaningful difficulty), jacking, technique (basically for charts where if you remove a skill needed for a chart, the chart becomes much much easier) and accuracy. Your "rhythm" attribute will fall under accuracy. Accuracy shouldn't be a multiplier/be influencing every skill given, because you will already have a set accuracy needed (which is quite a good amount, in one of the parsers used for SM it's a AA grade, or about 97-98% on o!m) for a skill rating assigned for a score in a given chart to be meaningful.

I recommend you give this a read if you have the time, by the way. This is from the person who has made a difficulty parser for StepMania charts - I'd say his parser is currently the most accurate out of any other VSRG difficulty system out there. https://docs.google.com/document/d/1Abp ... B3nmQ/edit

Side note:

Evening wrote:

reading demand ∝ keys
lol i'm not too sure about this, sounds theoratically correct but i have trouble reading 1k, maybe that's just me xd

accuracy demand ∝ keys
uhhh yeaaa you might want to take note that any pattern for 1k is going to be jacks and jacks are horribly hard to time, most people would have trouble at getting an S on a 4* 1k already if they don't have control, and again, these equations might be too simplified to guage how you're going to link everything together

Has more to do with the fact that you haven't built muscle memory for that keymode more than anything else. While you can actually hit the 1K pattern in a 4K chart with more notes around it, it's not easy to particularly isolate the column. Try playing the right four columns (left four if you use a left thumb) of a 7K chart that you can barely FC with one hand. Chances are, you'll have significantly more issue hitting patterns in the four columns in isolation. That's how muscle memory works - they don't look at columns; they look at patterns holistically.

This also applies for accuracy. You build muscle memory to hit a certain pattern at a certain level of precision. The reference points are only helpful if you're used to playing another keymode at a much higher level.

Is there any downloadable working binary for that guy's difficulty parser? The google doc you linked doesn't seem to have a DL.
You say it's pretty accurate, I want to try it out.

Evening wrote:

...

Not sure how to argue this. Yes, a person's skill may cap at a certain point due to physical limits. If a human's max tapping speed is modeled correctly, the graph would show a function f(x) with an asymptotic behavior as x->∞. When calculating skill, this theoretical human peak will be fixed at skill value 1000. Beyond that, it will be obvious that it's not a human playing the game. Not much can be done in regards for people who will never reach close to that limit, but I need the system to have a fixed absolute limit at 1000 so waaaay later when I'm done with osu!skills (and if I'm around), I can start research on how to tell apart whether AI or a human is playing the game. I don't know whether you want to see that 1000 value of have osu!skill have a cutoff point at 950, for example, but I would just adjust so that 950 point so that it becomes 1000 in that case.

Shoegazer wrote:

I recommend you give this a read if you have the time, by the way. This is from the person who has made a difficulty parser for StepMania charts - I'd say his parser is currently the most accurate out of any other VSRG difficulty system out there. https://docs.google.com/document/d/1Abp ... B3nmQ/edit

H O L Y S H I T... an entire "book" on VSRG difficulty theory. I read through the first several pages and skimmed though the rest so far. It looks promising, though skimming, I was didn't see formulas or at least citations, which makes me believe it's more philosophy than science (my first thoughts on it). I'll definitely give it a read and see if that gives me any ideas.

Shoegazer wrote:

but trying to find out the nuances of the statistical distribution of how hard a person can tense up their forearm muscles is not something that you can easily find out - getting heuristics for such isn't easy either.

That's what I plan to do. As mentioned, I am deriving the formulas and those are based on research material I find rather than making them up based on statistical data. Statistical data is just there to check my answer, nothing more.

Shoegazer wrote:

In any case, I don't think you should really include straight-up vibration speed to begin with, because it throws off many other variables that pertain to jacking. That is another limitation with difficulty scales like this - the parser/calculator will only give an accurate rating if the chart isn't too much of an anomaly from a conventional chart. Considering that charts that mainly test vibration are gimmicky and the tinkering required for charts like those to ensure that those charts aren't overrated causes too much trouble as a whole - you're better off just not including vibro in your calculations - just deal with regular jacking instead. I guess you can do it for something like 1K? But at high levels the "conventional" setup will be a 2 finger to 1 key setup. It's similar to Taiko in a sense, if you're only given a one-to-one configuration then every high-level Taiko map would be impossible.

A good formula should be able to take care of any type of pattern. What would be troubling is the unknown. People using 2 fingers to jack one column and other setups are problematic. For these kind of things, I can only come up with a formula which calculates based on a default setup or a setup most players are likely to use to better their play.

You are generalising VSRG skills far too much. You're also implying that every single key mode will have the same reading/speed/stamina difficulty and all that, or at least you are trying to scale them. Again, a heuristical approach won't help here - you won't be able to find a good enough variable to scale difficulty/skill accordingly.

For my version the precision/Aim skill formula I made for standard, the formula doesn't look at one thing. Humans are not perfect and have error or instability within every action. I had to think of all of the possible things preventing the person to aim dead center. There is human error within the path's angle going from one note to the next, error within said angle's range, and error within timing. I expect speed, reading, stamina, etc be depended on more technical factors as well.

Aqo wrote:

Imagine the same 4key chart on a 4K key mode, and on a 7K key mode.
You can bind your keys any way you want to. So in conclusion, the chart has exactly the same difficulty on different key modes.

The reading difficulty would vary though. As for the keys, as I mentioned, I will likely use the setup most players are likely to use to better their play. That means for 7k the index, middle pointer and thumb would be taken into account and pinky setups disregarded (unless you can name someone who can play with pinky better than without pinky).

abraker wrote:

The reading difficulty would vary though.

uhh go try playing a 4k chart on 7k where the notes are on columns 2356. it's literally the exact same both reading and playing -wise.

Aqo wrote:

abraker wrote:

The reading difficulty would vary though.

uhh go try playing a 4k chart on 7k where the notes are on columns 2356. it's literally the exact same both reading and playing -wise.

If a 4k chart is transfered 1:1 and mapped to certain columns and stayed in those columns, then yes, I see the difficulty being approximately same (I say approximately due to possible negligible difference). However, 7k allows more notes and patterns that are not possible in 4k, making it harder to read at times. Even if you have a max of 4 notes at any given time, that would still allow 7k to have pattern that are not possible in 4k. Since any of those 4 notes may end up in any column, the player would need to focus on 7 lanes instead of 4.

This actually gives me a good idea on how to check my work. Patterns from Nk, if mapped 1:1 to another keymode higher than Nk, should result in the same skill requirement. If the values dont match, then I would know I am doing something wrong.