I have a common hit error of about -10ms~10ms (something around 140 unstable rate). I don't play HR very much so I was wondering; am I accurate enough for OD10? I always feared HR for the OD, constant 100s would lead to death by drain (maybe I'm more afraid of the drain) so I never really play it. I was just curious as to how accurate you actually have to be in order to hit proper 300s instead of getting constant 100s when dealing with OD10 or Hard Rock. Also is it true that Double Time decreases the hit window for accuracy?
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Accuracy when dealing with HR/OD10/DT
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X means no-mod
Topic Starter
Oh wow, so I should pretty much be able to clear anything (within my speed range)
Well the 18ms is plus or minus 9ms from the beat. So you're slightly not accurate enough to consistently hit 300s on od10.
That thing doesn't show your max error made on a map. I just checked it on a map that has OD9.8 (20ms)
I got 3 100s here, but hit error info showed +6ms ~ -6ms with unstable rate 76
So, it's kinda not useful or I am misunderstanding something
I got 3 100s here, but hit error info showed +6ms ~ -6ms with unstable rate 76
So, it's kinda not useful or I am misunderstanding something
Actually OD10 is plus or minus 18ms (so the time window is 36ms).TRIYP wrote:
Well the 18ms is plus or minus 9ms from the beat. So you're slightly not accurate enough to consistently hit 300s on od10.
With Unstable Rate of 140 you should expect around 86.5% circle accuracy in OD10 though (song length doesn't affect accuracy much in low stability).
Unstable Rate 76 is enough to get about 99.7%acc in OD9.8 (in a short song). 99.27%acc in a long song.Kert wrote:
That thing doesn't show your max error made on a map. I just checked it on a map that has OD9.8 (20ms)
I got 3 100s here, but hit error info showed +6ms ~ -6ms with unstable rate 76
So, it's kinda not useful or I am misunderstanding something
How do you count that % ?
Assuming hit errors follow a Normal Distribution, then you math from there.Kert wrote:
How do you count that % ?
Does it count slider heads? (I have 120 unstable rate on OD10 900+ combo map with 99+ accuracy)
Because I don't have any other idea of why is this happening
Because I don't have any other idea of why is this happening
I think for something like accuracy in osu!, it won't really follow a normal distribution because making a mistake leads to an outlier. Even assuming perfect reading, humans will still screw up, whether that's due to nervousness, strain on fingers, or whatever else. Perhaps outliers are already accounted for, but I would guess that it will follow a roughly normal distribution centered closer to perfect timing with a fair amount of points that are severely mistimed. This is mostly coming from my experience, because my unstable rates on HDHR are usually around 85-90 (when I'm really comfortable with the map), and most of my 100s come from when I can feel myself making a mistake.
The calculations only considers accuracy for circles.Kert wrote:
Does it count slider heads? (I have 120 unstable rate on OD10 900+ combo map with 99+ accuracy)
Because I don't have any other idea of why is this happening
Sliders can screw the approximation. Because maps with a lot of sliders give you high accuracy even with high unstable rate (they are easier to time), and you can play the sliders with a more relaxed timing (increasing the Unstable Rate).
Unstable rate can certainly help to determine how accurate you are, but it's not an absolute number.Kert wrote:
Does it count slider heads? (I have 120 unstable rate on OD10 900+ combo map with 99+ accuracy)
Because I don't have any other idea of why is this happening
Honestly I have no idea how it works, but really accurate players like Cookiezi, thelewa and mugio3 tend to always be under 100 unstable rate.
OP: I think unstable rate 140 should give at least 93% though, as opposed to FullTablet's calculation of 86.5%. This is based off my own experience as a HR player but I realize it can differ from person to person.
I'm curious, have you tested in maps without sliders/spinners?koromo wrote:
OP: I think unstable rate 140 should give at least 93% though, as opposed to FullTablet's calculation of 86.5%. This is based off my own experience as a HR player but I realize it can differ from person to person.
According to the calculations 48.15% of the objects in the map have to be sliders/spinners to achieve an expected accuracy like that.
I can't really even think of any map without sliders tbh, so pretty sure I haven't.Full Tablet wrote:
I'm curious, have you tested in maps without sliders/spinners?
According to the calculations 48.15% of the objects in the map have to be sliders/spinners to achieve an expected accuracy like that.
edit:
I'm pretty sure your unstable rate would be lower when playing AR10 since you have a reduced window of visibility of the circle so the OP's unstable rate might be in the range of 110-120 (just estimating) but there are also factors like playing the map based more on reaction time then with the music if AR10 is fast for you which might even out the unstable rate.Full Tablet wrote:
I'm curious, have you tested in maps without sliders/spinners?koromo wrote:
OP: I think unstable rate 140 should give at least 93% though, as opposed to FullTablet's calculation of 86.5%. This is based off my own experience as a HR player but I realize it can differ from person to person.
According to the calculations 48.15% of the objects in the map have to be sliders/spinners to achieve an expected accuracy like that.
For that specific map and unstable rate, according to the model you would have got 91.23%acc. (But that without considering if your sliders are less precise than your circles).koromo wrote:
I can't really even think of any map without sliders tbh, so pretty sure I haven't.Full Tablet wrote:
I'm curious, have you tested in maps without sliders/spinners?
According to the calculations 48.15% of the objects in the map have to be sliders/spinners to achieve an expected accuracy like that.
edit:
If Unstable Rate was separated between Circle Unstable rate and Slider Unstable rate it would be easier to check if the model is right (for example, checking if normal distribution is good or if it is better to use another kind of distribution).
If you want the best advice in this situation. Just play it and find out. I usually get a lot higher unstable rate when playing NOMOD but have gotten as low at 65 unstable rate playing Hard Rock. Don't try to base your skill off of a silly number in game just try it and find out.
Listening to all these people tell you what unstable rate you should play HR at or whether or not you can do it or not yet and what you can expect is just plain dumb.
Listening to all these people tell you what unstable rate you should play HR at or whether or not you can do it or not yet and what you can expect is just plain dumb.
^^^^^^^^JAKACHAN wrote:
If you want the best advice in this situation. Just play it and find out. I usually get a lot higher unstable rate when playing NOMOD but have gotten as low at 65 unstable rate playing Hard Rock. Don't try to base your skill off of a silly number in game just try it and find out.
Listening to all these people tell you what unstable rate you should play HR at or whether or not you can do it or not yet and what you can expect is just plain dumb.
everything that JAKA said is true, seconded by yours truly
unstable rate and hit error don't say jackshit about the accuracy you will get. you can have a super good unstable rate below 100 or even 80 and still get 100s on OD 8. vice versa, you can get really good accuracies upt to almost SS or SS on OD 10 with unstable rates just at 100 or slightly above it, if you hit many circles just at the border to a 100.
also you could theoretically get a SS on OD 9.8 but only 33.33% on OD 10 if you hit all the notes in the thin timing window inbetween those 2. and all that doesn't even include things like slidermisses or actual misses (fun fact: clearing a map with no fail and just hitting one circle will result in unstable rate 0,00).
in the end, you should not worry about unstable rate and hit error and such things all too much. what matters in the end is the actual accuracy, and if you get a SS, it will be a SS no matter what unstable rate you have or what others say which unstable rate results in which accuracy.
also you could theoretically get a SS on OD 9.8 but only 33.33% on OD 10 if you hit all the notes in the thin timing window inbetween those 2. and all that doesn't even include things like slidermisses or actual misses (fun fact: clearing a map with no fail and just hitting one circle will result in unstable rate 0,00).
in the end, you should not worry about unstable rate and hit error and such things all too much. what matters in the end is the actual accuracy, and if you get a SS, it will be a SS no matter what unstable rate you have or what others say which unstable rate results in which accuracy.
Theoretically, yes. In practice, no.Tanzklaue wrote:
unstable rate and hit error don't say jackshit about the accuracy you will get. you can have a super good unstable rate below 100 or even 80 and still get 100s on OD 8. vice versa, you can get really good accuracies upt to almost SS or SS on OD 10 with unstable rates just at 100 or slightly above it, if you hit many circles just at the border to a 100.
also you could theoretically get a SS on OD 9.8 but only 33.33% on OD 10 if you hit all the notes in the thin timing window inbetween those 2. and all that doesn't even include things like slidermisses or actual misses (fun fact: clearing a map with no fail and just hitting one circle will result in unstable rate 0,00).
in the end, you should not worry about unstable rate and hit error and such things all too much. what matters in the end is the actual accuracy, and if you get a SS, it will be a SS no matter what unstable rate you have or what others say which unstable rate results in which accuracy.
You do have a point though. Stop caring about them statistics and start playing.
I use unstable rate just to scope which way I should adjust a local offset that comfortable to me for each song
other than that is just being cool when it's under 100 at least
other than that is just being cool when it's under 100 at least
i don't even look at unstable rate. when i see that my accuracy sucks i just rage and leave nonetheless
I have to look at it every time for my egowinber1 wrote:
i don't even look at unstable rate. when i see that my accuracy sucks i just rage and leave nonetheless
Outliers are accounted for in normal distributions as long as they occur both above and below the mean at reasonable (AKA low) rates, which is how it works for most people in osu!.pooptartsonas wrote:
I think for something like accuracy in osu!, it won't really follow a normal distribution because making a mistake leads to an outlier. Even assuming perfect reading, humans will still screw up, whether that's due to nervousness, strain on fingers, or whatever else. Perhaps outliers are already accounted for, but I would guess that it will follow a roughly normal distribution centered closer to perfect timing with a fair amount of points that are severely mistimed. This is mostly coming from my experience, because my unstable rates on HDHR are usually around 85-90 (when I'm really comfortable with the map), and most of my 100s come from when I can feel myself making a mistake.
Topic Starter
I didn't care for the unstable rate and numbers anyways, I was just curious as to how accurate you have to really be in order to hit stuff. I played and hard rock isn't nearly as hard as I thought it was. Playing a lot of DT helps and also having a correct UO helps in massive amounts. The test build has a great hit error rate bar that helped me adjust my UO to be perfect. I just hope it gets implemented soon.
Thanks guys for the information. This is all very helpful.
Thanks guys for the information. This is all very helpful.
Need to note that HalfTime and DoubleTime/Nightcore mods may decrease and increase your Unstable Rate along with improves and worsen your Hit Error respectively, because those speed-adjusting mods aren't considered toward the Hit Error and Unstable Rate.
Hit Error is showing average of early hit timings and late hit timings separately. The minus value averages your early hits, while the plus value averages your late hits. This doesn't show your peak hit error, and since it averages your timing instead, the more circles and sliders are involved, the approximation is less accurate. Take an extreme case example: there's a map with 2,000 circles, and you hit -101ms on just one circle while the remaining 1,999 circles are magically hit at -1ms all the time, and there's no late timings at all (HAAAAX! xD). The result of this Hit Error is -1.05ms ~ +0.00ms, yet you can still see that the 300/100/50 result is 1999/1/0.
Unstable Rate also averages your timing as well, but rather than based on the 0ms point, it's based on your overall hit window. Taking the same extreme case example again, you get -100ms all the time on the same map above. The result of 300/100/50 is 0/2000/0 with Unstable Rate of 0.00!
Of course those extreme cases are very far away from being likely to happen anyway, but this also proves that Hit Error and Unstable Rate should be taken as statistical purposes and not as an accurate measurement of skill.
Hit Error is showing average of early hit timings and late hit timings separately. The minus value averages your early hits, while the plus value averages your late hits. This doesn't show your peak hit error, and since it averages your timing instead, the more circles and sliders are involved, the approximation is less accurate. Take an extreme case example: there's a map with 2,000 circles, and you hit -101ms on just one circle while the remaining 1,999 circles are magically hit at -1ms all the time, and there's no late timings at all (HAAAAX! xD). The result of this Hit Error is -1.05ms ~ +0.00ms, yet you can still see that the 300/100/50 result is 1999/1/0.
Unstable Rate also averages your timing as well, but rather than based on the 0ms point, it's based on your overall hit window. Taking the same extreme case example again, you get -100ms all the time on the same map above. The result of 300/100/50 is 0/2000/0 with Unstable Rate of 0.00!
Of course those extreme cases are very far away from being likely to happen anyway, but this also proves that Hit Error and Unstable Rate should be taken as statistical purposes and not as an accurate measurement of skill.
JAKACHAN wrote:
Just play it and find out.
Yeah but in osu!, pretty much all the outliers will lead to 100s on a high OD because outliers will often be the result of nervousness where the player completely mistimes a note in the heat of the moment. I just don't think unstable rate can properly predict accuracy because someone who has perfect accuracy under normal conditions could still mistime notes due to stress.Ekaru wrote:
Outliers are accounted for in normal distributions as long as they occur both above and below the mean at reasonable (AKA low) rates, which is how it works for most people in osu!.pooptartsonas wrote:
I think for something like accuracy in osu!, it won't really follow a normal distribution because making a mistake leads to an outlier. Even assuming perfect reading, humans will still screw up, whether that's due to nervousness, strain on fingers, or whatever else. Perhaps outliers are already accounted for, but I would guess that it will follow a roughly normal distribution centered closer to perfect timing with a fair amount of points that are severely mistimed. This is mostly coming from my experience, because my unstable rates on HDHR are usually around 85-90 (when I'm really comfortable with the map), and most of my 100s come from when I can feel myself making a mistake.
Mistimed notes due to stress increase the Unstable Rate too.pooptartsonas wrote:
Yeah but in osu!, pretty much all the outliers will lead to 100s on a high OD because outliers will often be the result of nervousness where the player completely mistimes a note in the heat of the moment. I just don't think unstable rate can properly predict accuracy because someone who has perfect accuracy under normal conditions could still mistime notes due to stress.Ekaru wrote:
Outliers are accounted for in normal distributions as long as they occur both above and below the mean at reasonable (AKA low) rates, which is how it works for most people in osu!.
Unstable rate only tell how unstable you are. You can, for example, constantly drift from -17 to +17, thus SSing OD10 but also having ridiculously high unstable rate
You can't say which accuracy you should get with xxx.xx unstable rate
You can't say which accuracy you should get with xxx.xx unstable rate
Unstable Rate can help to tell what accuracy you should expect, with a certain probability.GoldenWolf wrote:
Unstable rate only tell how unstable you are. You can, for example, constantly drift from -17 to +17, thus SSing OD10 but also having ridiculously high unstable rate
You can't say which accuracy you should get with xxx.xx unstable rate
It's analogous to something like this: You have a die with 10 sides (each side marked A,B,C,etc...), so with 1000 throws, the expected number of times you get an A is 100 times (but of course there will be some variation, and the probability of getting EXACTLY 100 times an A is very low).
There are some things you can know for sure, though. For example, if your average hit error is exactly 0 (this isn't shown in the results screen), you pressed each object (managed to at least click each object while on the MISS time frame), and your Unstable Rate is 100, then the worst possible accuracy you can get in OD11 (in the worst case scenario) is 30.55%; and if the Unstable Rate is 60 then the worst possible accuracy you can get is 75% (knowing this doesn't actually help in anything though).
Similarly, if your average hit error is 0, and your unstable rate is below 12.0605, you will always get a SS in any map under 100 circles/sliders (if you also complete the slider paths correctly, and the spinners). With unstable rate under 1.69723, you will always get a SS in maps with up to 5000 circles/sliders (if you also complete the sliders paths and spinners correctly).
I've SS'd with 140 unstable rate I've SS'd with 65 unstable rate.Full Tablet wrote:
GoldenWolf wrote:
Unstable Rate can help to tell what accuracy you should expect, with a certain probability.
Once again do not judge what you should have through numbers. Just play and find out yourself.
Trying to put numbers on everything starts to complicates things and just adds more stress to something that should be a fun game to begin with people.
Well, some people like numbers.JAKACHAN wrote:
Trying to put numbers on everything starts to complicates things and just adds more stress to something that should be a fun game to begin with people.
You quoted me wrong JAKACHAN ;_;
so basically, adding hr would be the same between 8~10? it doesn't seem at all. ex in Gensou no satellite (od9) is way harder keeping a good acc rate rather than airman (od8).Kert wrote:
X means no-mod
HR increases OD and AR by 40% and it caps at 10. So both OD8 and OD9 become OD10 after adding HR, OD7 becomes OD9.8.Genshin wrote:
so basically, adding hr would be the same between 8~10? it doesn't seem at all. ex in Gensou no satellite (od9) is way harder keeping a good acc rate rather than airman (od8).
let's see how many people freak about the necrobump instead of realizing what I'm trying to say
Is that OD10 or OD9?thelewa wrote:
let's see how many people freak about the necrobump instead of realizing what I'm trying to say
If that is OD9 it seems that the offset is wrong.
or he's having trouble keeping up with the map
thelewa needs to teach me the art of accuracy
so i can be #1
so i can be #1
OD10Full Tablet wrote:
Is that OD10 or OD9?thelewa wrote:
let's see how many people freak about the necrobump instead of realizing what I'm trying to say
If that is OD9 it seems that the offset is wrong.
I also had runs where I had 1x100 with the same unstable rate
unstable rate is a poor measurement for accuracy if used alone, since it only measures how constant your clicks are. You could get all 100's and still have like, 59 unstable rate.
Well, the expected unstable rate for that accuracy in that map (with OD10) is 88.0688, not very far from the unstable rate you really got. The expected unstable rate for getting 1x100 is 62.3514 (that means, if the errors follow a normal distribution, with that unstable rate, there is 50% chance you get at least 99.85%acc, with a slight probable deviation from 99.85%).thelewa wrote:
OD10
I also had runs where I had 1x100 with the same unstable rate
unstable rate is a poor measurement for accuracy if used alone, since it only measures how constant your clicks are. You could get all 100's and still have like, 59 unstable rate.
The thing is, the calculation is a ESTIMATION that helps linking unstable rate to accuracy (the calculation assumes the average timing error is 0, assumes normal distribution of hit errors). It's possible to get all 100's with 59 unstable rate, but it is very improbable (it would only likely happen in situations where you intentionally set your offset to a very wrong value).
Even if the calculation assumptions are right, there is an expected deviation from the mean for the results. For example: You can play that song 1000 times, every time with a unstable rate of 90, with different results each time (50% of the time it will be below 97.067%, 50% of the time above 97.067%, the median accuracy in those plays would be 97.067%) (this is not considering deviation in the unstable rate itself, of course).
Where do you people even get these numbers? "Expected unstable rate?" you just made that up lol...
People are taking this game way to serious nowadays.
People are taking this game way to serious nowadays.
Where are you pulling this from
edit: LOL JAKA NICE NINJA
edit: LOL JAKA NICE NINJA
He's likely applying statistical analysis to the mathematical formulas (not sure if he has the exact formula for the unstable rate or if he's estimating it, though). For example, the timings of a player's hits will usually resemble a normal distribution (excluding misses). There's an astounding amount of shit you can do with such normal distributions. And yes, there are ways to account for that one hit that was waaaaaaay off.JAKACHAN wrote:
Where do you people even get these numbers? "Expected unstable rate?" you just made that up lol...
People are taking this game way to serious nowadays.
EDIT: And and and and and yes, you could use the formulas to create an "Expected unstable rate" if you were some sort of mathematical genius and had plenty of time on your hands. I'm not, though.
And neither is he. If you are going to provide evidence about any of this you shouldn't use a your own calculation or treat it like you know what you are doing.Ekaru wrote:
EDIT: And and and and and yes, you could use the formulas to create an "Expected unstable rate" if you were some sort of mathematical genius and had plenty of time on your hands. I'm not, though.
Unstable rate is most likely just standard deviation, which has a known formula and is easily analysed by maths software.
Of course this is just an assumption, but it would make sense.
Of course this is just an assumption, but it would make sense.
Why do math when u can play OSU! -_-
What is OSU! ?ScarletFrost wrote:
Why do math when u can play OSU! -_-
I only know osu!
And osu! is serious business.
When I asked woc2006 how was Unstable Rate calculated, he said it was Standard Deviation. By looking at the numbers it usually gives, I think he meant standard deviation of the hit errors measured in tenths of a millisecond (so 100 Unstable Rate means 10ms of standard deviation).
Now, assuming that the hit errors follow a Normal Distribution, and the average errors are zero, for a certain standard deviation there is a probability for each hit to have an error with a magnitude less than A (where A is the time leniency for getting a 300, it depends on OD, it is 18ms for OD10).
Now, estimating the amounts of 300s and 100s in circles given a certain accuracy and number of circles:
Number of 100s: C = Circles*(3/2)*(1-Acc)
Number of 300s: T = Circles - C
(Note that this estimation only considers 300s and 100s; plays with 50s and Misses would be calculated as having a non-integer amount of 300s and 100s, which should be fine as an approximation in plays where most hits are 300s and 100s).
Now, calculate the "probability of getting a 300" that each hit has to have to have a median amount of 300s equal to the amount of 300s in the play. The amount of 300s in this case would follow a binomial distribution, and using the inverse regularized beta function to get the probability: (Mathematica Syntax)
Probability:
Now that we have the probability of getting a 300 each hit, using the inverse error function would allow to calculate the expected standard deviation of the hits in the normal distribution:
Where A is measured in tenths of milliseconds if the standard deviation calculated corresponds to Unstable Rate.
Also, for plays that have sliders and spinners, assuming that all sliders and spinners are 300s, calculate the "Circle Accuracy" of the play:
Circle Accuracy gives a better estimation than shown accuracy for the previous formulas (still not as good as the estimations obtained in a map with only circles though)
Now, assuming that the hit errors follow a Normal Distribution, and the average errors are zero, for a certain standard deviation there is a probability for each hit to have an error with a magnitude less than A (where A is the time leniency for getting a 300, it depends on OD, it is 18ms for OD10).
Now, estimating the amounts of 300s and 100s in circles given a certain accuracy and number of circles:
Number of 100s: C = Circles*(3/2)*(1-Acc)
Number of 300s: T = Circles - C
(Note that this estimation only considers 300s and 100s; plays with 50s and Misses would be calculated as having a non-integer amount of 300s and 100s, which should be fine as an approximation in plays where most hits are 300s and 100s).
Now, calculate the "probability of getting a 300" that each hit has to have to have a median amount of 300s equal to the amount of 300s in the play. The amount of 300s in this case would follow a binomial distribution, and using the inverse regularized beta function to get the probability: (Mathematica Syntax)
Probability:
Now that we have the probability of getting a 300 each hit, using the inverse error function would allow to calculate the expected standard deviation of the hits in the normal distribution:
Where A is measured in tenths of milliseconds if the standard deviation calculated corresponds to Unstable Rate.
Also, for plays that have sliders and spinners, assuming that all sliders and spinners are 300s, calculate the "Circle Accuracy" of the play:
Circle Accuracy gives a better estimation than shown accuracy for the previous formulas (still not as good as the estimations obtained in a map with only circles though)
I demand a gorgeous excel table for this.
http://www.mediafire.com/download/k1zw8 ... _Rate.xlsxAqo wrote:
I demand a gorgeous excel table for this.
that was not gorgeous at all
I kinda like it, it's nice. gj
osu! standard science/ math never ceases to amaze me.
To reflect the variability that is to be expected according to the previous model, I updated the tables so they reflect the expected unstable rate with different levels of confidence.
For example, in the table with 70% of confidence, for an entry with (90%acc - 150Unstable Rate): According to the model, if you play a certain map several times all of them with 150 Unstable Rate (or close to it), it is expected that you get AT LEAST 90%acc 70% of the times you played that map. This can be useful if you want a estimation of how many times you have to retry a map to get certain accuracy if your unstable rate is almost constant each try.
(yes, I have nothing else to do)
http://www.mediafire.com/download/pgb55 ... te_v2.xlsx
For example, in the table with 70% of confidence, for an entry with (90%acc - 150Unstable Rate): According to the model, if you play a certain map several times all of them with 150 Unstable Rate (or close to it), it is expected that you get AT LEAST 90%acc 70% of the times you played that map. This can be useful if you want a estimation of how many times you have to retry a map to get certain accuracy if your unstable rate is almost constant each try.
(yes, I have nothing else to do)
http://www.mediafire.com/download/pgb55 ... te_v2.xlsx
To test if the Normal Distribution model is appropriate, you can analyze the distribution of this variable in several plays.
A: Leniency of getting a 300 measured in tenths of milliseconds. It is 180 (18ms) for OD10.
Acc: Accuracy on the circles of the map.
Circles: Number of circles in the map.
For that calculated variable,
Values near 1 mean that the play got bad accuracy for that Unstable Rate, according to the normal distribution model.
Values near 0 mean that the play got good accuracy for that Unstable Rate, according to the normal distribution model.
The variable itself should follow a Continuous Uniform Distribution, with values in the [0,1] range (so the mean should be 0.5, and the Standard Deviation 0.288675). This is the same distribution as a "Perfect die with an infinite amount of sides, with values in the sides that go from 0 to 1".
I tested this playing this map https://osu.ppy.sh/b/207567&m=0 (edited to have OD10) 26 times. Got a mean of 0.519718 and a standard deviation of 0.27152, which is close to the expected values.
A: Leniency of getting a 300 measured in tenths of milliseconds. It is 180 (18ms) for OD10.
Acc: Accuracy on the circles of the map.
Circles: Number of circles in the map.
For that calculated variable,
Values near 1 mean that the play got bad accuracy for that Unstable Rate, according to the normal distribution model.
Values near 0 mean that the play got good accuracy for that Unstable Rate, according to the normal distribution model.
The variable itself should follow a Continuous Uniform Distribution, with values in the [0,1] range (so the mean should be 0.5, and the Standard Deviation 0.288675). This is the same distribution as a "Perfect die with an infinite amount of sides, with values in the sides that go from 0 to 1".
I tested this playing this map https://osu.ppy.sh/b/207567&m=0 (edited to have OD10) 26 times. Got a mean of 0.519718 and a standard deviation of 0.27152, which is close to the expected values.
I made a new version of the table (with a new formula that is more accurate for lower accuracy percentages, since it considers the probability of getting 50s and misses too).
https://www.dropbox.com/s/6ravpyq7zssfy ... %20v3.xlsx
Also I made a table for osu!mania based on the timing windows indicated in this table http://i.imgur.com/V7EbLVZ.png
From what I tested, it seems to be accurate with plays where I don't mess up too badly with hold notes.
It is based on base score (without mods) of plays https://osu.ppy.sh/wiki/Osu!mania#Score. That value is a better indicator than the accuracy percentage (a rainbow 300 is worth the same as a regular 300 for the accuracy percentage).
https://www.dropbox.com/s/c07paqv9hull2 ... mania.xlsx
Note that the model considers getting a miss as pressing way too early/late (and in that case the game might not register the key press at all, so in-game would be impossible to achieve Unstable Rates so high). Also, it doesn't consider the case where the player doesn't hit the object.
https://www.dropbox.com/s/6ravpyq7zssfy ... %20v3.xlsx
Also I made a table for osu!mania based on the timing windows indicated in this table http://i.imgur.com/V7EbLVZ.png
From what I tested, it seems to be accurate with plays where I don't mess up too badly with hold notes.
It is based on base score (without mods) of plays https://osu.ppy.sh/wiki/Osu!mania#Score. That value is a better indicator than the accuracy percentage (a rainbow 300 is worth the same as a regular 300 for the accuracy percentage).
https://www.dropbox.com/s/c07paqv9hull2 ... mania.xlsx
Note that the model considers getting a miss as pressing way too early/late (and in that case the game might not register the key press at all, so in-game would be impossible to achieve Unstable Rates so high). Also, it doesn't consider the case where the player doesn't hit the object.
I made a table based on the Taiko OD table in this thread: t/146678
osu! Standard Table: https://db.tt/WDQRi0MM
o!mania Table: https://db.tt/a10M2n1T
Taiko Table: https://db.tt/hSeemliT
The formula used in more detail (using Taiko as an example, since it is the simplest case):
osu! Standard Table: https://db.tt/WDQRi0MM
o!mania Table: https://db.tt/a10M2n1T
Taiko Table: https://db.tt/hSeemliT
The formula used in more detail (using Taiko as an example, since it is the simplest case):
- For a given OD, take the timing windows of the judgment. In taiko, for OD10, the timing windows are:
GREAT (300 base value): 18ms
GOOD (150 base value): 48ms - For a given accuracy percentage, calculate the percentage of GREATs a play would have in average if the hit errors of each hit followed a Normal Distribution (with mean error in the hit errors equal to 0, and a standard deviation set so the mean accuracy the plays would have is equal to the given accuracy).
The probability each hit has to be a GREAT is:
(Erf is the error function http://en.wikipedia.org/wiki/Error_Function).
The probability of getting GOODs is:
So the mean accuracy given a Standard Deviation is:
So, to calculate the percentage of GREATs (equal to it's probability) given a accuracy percentage, one has to find the standard deviation that makes the mean accuracy equal to the value given (the properties of the error function makes it easy to calculate the value numerically).
Note: the standard deviation calculated here doesn't correspond to the expected unstable rate, since the value calculated here uses the mean, instead of the median (or a percentile)(using the median or percentiles has better practical applications in this case: in the case of 100% accuracy, the mean standard deviation is 0, since with any value higher, there is a small probability the accuracy achieved is not 100%. With the median, one would calculate a value where 100% accuracy is achieved half of the time).
In the old formula, there was the assumption that every hit that wasn't a GREAT (or what the best judgment is in the game mode) was a GOOD. Now, this also accounts for the probability of getting MISSES (in other game modes, 50s-MISS in standard, and 200s-100s-50s-MISS in o!m). This is the main difference the new formula has.
Note that using the (mean amount of GREATs a normal distribution with a mean accuracy equal to the accuracy achieved would have) instead of the (real amount of GREATs) makes the results depend on the base values of the judgments (which are very subjective), the dependency is bigger when the real amount of GREATs and GOODs is unlikely to be caused by a process that follows a Normal Distribution (Gaussian process). This calculation weights all the possible judgment distributions that have certain accuracy value, by the probability they occur by a Gaussian process, and gives a result based on the mean case.
Example: OD10, 100 hits.
62 GREATs, 36 GOODs, 2 MISSES (this distribution is likely to be caused by a Gaussian process: the mean distribution with 80% accuracy, with the current judgment values, that represents a Normal Distribution is 61.9385 GREATS, 36.1229 GOODs, 1.93853 MISSES).
If a GREAT is worth 300, and a GOOD is worth 150: The expected unstable rate (median) is: 207.636
If a GREAT is worth 300, and a GOOD is worth 50: The expected unstable rate (median) is: 207.433
62 GREATs, 6 GOODs, 32 MISSES (this distribution is very unlikely to be caused by a Gaussian process).
If a GREAT is worth 300, and a GOOD is worth 150: The expected unstable rate (median) is: 320.89
If a GREAT is worth 300, and a GOOD is worth 50: The expected unstable rate (median) is: 233.923
With this way of calculating the amount of GREATs (based on the accuracy percentage achieved instead of the amount of GREATs, GOODs and MISSES achieved in the plays directly), it is possible to compare different judgment distributions according to the game rules (for example, being able to determine whether 300 GREATS and 200 GOODs is better than 310 GREATs, 180 GOODs and 10 MISSES). - Now, that we have calculated the percentage of GREATs represented by a Normal Distribution, we calculate the (probability of getting a GREAT per hit) so the (probability of getting at least the calculated amount of GREATs) is equal to a certain probability (50% for the median case).
In the simplest case (100% GREATs), the probability needed per hit to get a GREAT so there is a 50% chance of getting 100% GREATs, if there is a total of 1337 hits in the map, is: 0.5^(1/1337) = 99.9482%.
In general, one can use the Inverse Beta Regularized Function (used to calculate the value required in the Binomial Distribution) to calculate this probability. The probability needed per hit to get a GREAT so there is an A chance of getting B GREATs or more, if there is a total of M hits in the map, is (Wolfram Syntax):
(The value of A is the Confidence value in the tables).
One can change the value of A to reflect the expected accuracy obtained with several retries when the Unstable Rate obtained is constant, with the expected deviations encountered in the normal model. For 1 try, A is 50%, with R tries, A is is 1/(1+R). This is equivalent to the expected minimum value obtained when drawing a random real number between 0 and 1 several times (where each number has the same chance of appearing). - With the probability per hit of getting a GREAT calculated, calculate what is the Standard Deviation of the Normal Distribution where the probability of obtaining a value between -18ms and 18ms (the timing window of a GREAT in OD10) is equal to the calculated probability. This is:
Where InverseErf is the Inverse Error Function.
- With the standard deviation calculated, multiply to a value so it corresponds to the Unstable Rate shown in game.
For 10ms standard deviation: 100 Unstable Rate no mod, 150 Unstable Rate with DT, 75 Unstable Rate with HT.
For any mode that is not osu!mania, for a given OD, 150 Unstable Rate in-game in a map would have the same expected accuracy than 150 Unstable Rate in the same map with DT (but 150 Unstable Rate is harder to achieve with DT, since it corresponds to less standard deviation in milliseconds). For osu!mania, DT and HT don't change the timing windows, so 150 Unstable Rate with DT would have better accuracy than 150 Unstable Rate no mod (and would be harder to achieve)