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What is the forumla used to determine level?

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34
SapphireGhost
osu! Alumni
2,618 posts
Joined June 2010
Topic Starter
SapphireGhost
FIRST OF ALL: I put this in the Gameplay & Rankings forum because
a) It has to do with gameplay and rankings
b) "Anything about playing osu!"
c) I have a question, not a problem, and Help & Support is where "you go when you have a problem"

So yes, topic title. I tried searching but I couldn't find, feel free to link any topic with the answer so I can facepalm. What is that formula?
Hanyuu
2,223 posts
Joined February 2009
Hanyuu
hmm 1 score = 1 experience :P i think
SapphireGhost
osu! Alumni
2,618 posts
Joined June 2010
Topic Starter
SapphireGhost
Aaah
You know what I mean...
Like Level = 2(2*lv)
Or something like that
Claudia_old
571 posts
Joined July 2010
Claudia_old
Good question. I think level gain is relevant to the rate at which your ranked score increases per play...but I don't care about level, especially because I don't play standard osu!.
SapphireGhost
osu! Alumni
2,618 posts
Joined June 2010
Topic Starter
SapphireGhost
Thank you for the kind words. I was planning to use the formula in a game for personal use. peppy's brainpower will not be taken and sold.
Echo
osu! Alumni
3,008 posts
Here since the beginning
Echo
From the games I've seen, level is usually some cubic function of experience.
Claudia_old
571 posts
Joined July 2010
Claudia_old
Well, I had been thinking that because I noticed the better I did as far as improving my ranked score [in other words, the more it rose per song], my level increased faster.

edit: sniped by Echo
Hiyorin
186 posts
Joined September 2010
Hiyorin
I'm guessing the level gain is exponential because from 100-101, and 101-102 the exp gap is insane.
Also, I don't think its relevant to your ranked score, your assumption is ok but whatever ranked score you gain, you gain equal amounts in exp. So, if you gain more ranked score, your level will also increase by more.
storm704
78 posts
Joined October 2009
storm704
Your level exp. also goes up even if you fail a ranked song, not sure about this in multi though. Also if you fail a ranked song in multi your play count also doesn't increase.
Hiyorin
186 posts
Joined September 2010
Hiyorin

storm704 wrote:

Your level exp. also goes up even if you fail a ranked song, not sure about this in multi though. Also if you fail a ranked song in multi your play count also doesn't increase.
Your play count gets clocked the moment you start a song, so I would assume that regardless of failing or passing you would still get a play count.
Azure_Kite
osu! Alumni
3,217 posts
Joined February 2009
Azure_Kite
Beep, wrong. Playcount isn't counted until like 30 seconds into a song.
Drafura
osu! Alumni
2,621 posts
Joined April 2010
Drafura

Azure_Kyte wrote:

Beep, wrong. Playcount isn't counted until like 30 seconds into a song.
So in MPAA - Piracy - It's a Crime (23'' playing) the game will not count your plays ?
Azure_Kite
osu! Alumni
3,217 posts
Joined February 2009
Azure_Kite

Drafura wrote:

Azure_Kyte wrote:

Beep, wrong. Playcount isn't counted until like 30 seconds into a song.
So in MPAA - Piracy - It's a Crime (23'' playing) the game will not count your plays ?

Well played. 8-)


I mean- That's probably it.
Drafura
osu! Alumni
2,621 posts
Joined April 2010
Drafura

Azure_Kyte wrote:

Well played. 8-)


I mean- That's probably it.
That's interresting me (cause I have a big playcount for my rank and my skill) i'll try the mechanism when I go back from work, if nobody does.

However the mechanism of ranked / total score is described on the faq but no info about the formula, but you can use the data of the global ranking and see if you can find a formula wich fit with the results if nobody wants to tell you the exact formula.
Lybydose
osu! Alumni
2,024 posts
Joined January 2009
Lybydose

Drafura wrote:

Azure_Kyte wrote:

Beep, wrong. Playcount isn't counted until like 30 seconds into a song.
So in MPAA - Piracy - It's a Crime (23'' playing) the game will not count your plays ?
Playcount is counted at 30 combo. (or rather, if you miss, it's counted when you reach the point that you WOULD have 30 combo if you didn't miss)

I think there's it also counts if enough time passes (for really easy maps, or maps without 30 notes for a while), but I don't know how long it is.
Drafura
osu! Alumni
2,621 posts
Joined April 2010
Drafura

Lybydose wrote:

Playcount is counted at 30 combo. (or rather, if you miss, it's counted when you reach the point that you WOULD have 30 combo if you didn't miss)

I think there's it also counts if enough time passes (for really easy maps, or maps without 30 notes for a while), but I don't know how long it is.
Okay that's good to know. The map tries count works with the same system ?
Zekira
9,233 posts
Joined September 2008
Zekira
Lol I think no one has actually answered the OP's question yet

Closest would be Echo's answer, but I think even he forgot the formula?
SapphireGhost
osu! Alumni
2,618 posts
Joined June 2010
Topic Starter
SapphireGhost
Thanks for derailing the thread guys <3 I asked peppy, and his answer is "it's magic" so I guess that's the "official" answer. I will try to figure out a close estimation of the formula with these four phases:
Phase A will be trying to find a ballpark formula we can use. Then...
Phase B will be testing it to see if it works many, many times. If it doesn't work, we refine the formula in...
Phase C will be refining the formula. Once it works, we go back to Phase B. If it works many, many times in Phase B, we skip to...
Phase D will be the final phase, and hopefully a phase with a close estimation of the level formula.

Phase A
At this point in time, we have no formula we can use whatsoever. Let's begin by looking at some existing levels and matching Total Scores.
5,459,746,297 = Level 92
5,912,104,970 = Level 93
6,348,067,476 = Level 94
Clearly, at higher levels there is a large gap between levels which means these are likely going to be very unhelpful at Phase A. Let's take a look at the following information.
6,700,261,682 = Also Level 94
This, as we all already know, leads us to the conclusion that each Level is from x total score to y total score. I now had the idea to open the osu! program and sort by level. Let's look at the player rinrinn000, who has a level of 1.
Level 1 = 26,118
Let's now consider the player Kioko-chan, who has a level of 2.
Level 2 = 85,398
Finally, SeakoNat, with a level of 3.
Level 3 = 272,604
These gaps make it quite clear we are dealing with exponential growth, whether this is simple exponential growth or whether it has extra applied formulas will make it difficult without even a basic idea of the type of formula we are looking for. One of the first things we can do is attempt to search for the gap between Level 1 and 2.
The highest score I found for Level 1 is: 26,118
The lowest score I found for Level 2 is: 41,230
So the magical number must be somewhere in there. As a bonus fact...
The highest score I found for Level 2 is: 113,996
This is getting frustrating. Anyone who would care to help out is greatly appreciated. We can figure this out.
Arcorann
6 posts
Joined May 2009
Arcorann
It's easier to sort the official rankings and go from there:

127,600,619,879 (101)
126,019,219,471 (100)

26,947,605,501 (100)
26,909,616,331 (99)

17,715,539,256 (99)
17,686,182,293 (98)

12,513,236,472 (98)
12,470,856,367 (97)

etc.

Also, my own statistics:
40,863,849: Lv18, 49%
41,980,055: Lv18, 64%

Also:
165,706,749,049: Lv101, 4%, which suggests that Lv102 will be well over 1 trillion...
thelewa
3,537 posts
Joined August 2010
thelewa
I think we could figure out the exact amounts required to level up simply by looking at the percentages that represent the exp required to level up, for example if player A has 1000 points and it counts as let's say 10% of the exp required for lvl 1 we can just multiply that 1000 points with 10 to get the point number required for lvl 2, now getting the required point number for lvl 2 is a bit more complex because we have just deduced that we need 10000 points for lvl 2, so if player A has 11000 points and it counts as 3% of the exp required for level 2 we simply have to remove the 10000 from the points, and do this magic trick here: 1000/3x100+10000 and we have the exact number of points required for level 2.

It's a bit messy I'll explain it better in a while.

Fuck it, the percentages are messing with me. Seems like the scaling of the percentages is exponential too or the numbers i'm using are just bad. Example: I compared 3 lvl 1 profiles and got these numbers: 25,824 = 26%, 20,140 = 20%, 18,320 = 18%. This would suggest that the magic number between lvl1 and lvl2 is 100000, but then the scores just piss me in the eyesocket. Suddenly 56,376 = 13% of LVL2, and 45,236 = 7% of LVL2. What is this. I think the percentage for level progress is bugging out or something. The percentages for the low level players must be inaccurate for the purpose of making the figuring out of this magic formula harder. Or just buggy because almost nobody looks at the level percentage of lvl 1 players.
Attertwo
8 posts
Joined November 2010
Attertwo
there's also the fact that you only get a number with 2 decimals accuracy out of looking at the percentage there, and you don't even know exactly how it's rounded. You will want better numbers than that to figure the formula out.
XPJ38
osu! Alumni
3,570 posts
Joined February 2010
XPJ38
I don't know what is the score to obtain to gain one level, but I have the feeling that stars difficulties are playing a role somewhere. I noticed that when playing hard/insane maps, my percentage goes up quickly.

For example, when I began to play hard/insane songs (I was at level 80-85 approximately), the level increased with the same speed as when I was 10 or 15 levels down (approximately).

So my idea is that when playing a 1-star diff song, you gain "1 level point" (necessary for gaining levels), a 2-stars diff song "2 level points", ..., and a 5-stars diff song "5 points".

This theory could be proven with two freshes accounts: what is the new level of a lvl 1 player if he plays an easy diff, and what is the new level of another lvl 1 player if he plays an insane diff?

Could be interesting.
aevv_old
aevv_old

XPJ38 wrote:

So my idea is that when playing a 1-star diff song, you gain "1 level point" (necessary for gaining levels), a 2-stars diff song "2 level points", ..., and a 5-stars diff song "5 points".
sorry but no, its just that insanes are likely to grant far more total score. You can sort the ranks by score and check levels, its 100% total score based
XPJ38
osu! Alumni
3,570 posts
Joined February 2010
XPJ38
Oh ok then.
Waryas
Waryas
165,706,749,049: Lv101, 4%, which suggests that Lv102 will be well over 1 trillion...
No one will go that far unless you drill marathons and FC them each time for 1 year, 24/7.
h3k1ru
osu! Alumni
1,910 posts
Joined March 2010
h3k1ru

Arcorann wrote:

It's easier to sort the official rankings and go from there:
Also:
165,706,749,049: Lv101, 4%, which suggests that Lv102 will be well over 1 trillion...
% currently works wrong

for example i have 100 lvl and 50kk points atm, i need 127kk points for 101 lvl, but it shows i have only 23% - its wrong, coz i have about 40% to 101 lvl
Hiyorin
186 posts
Joined September 2010
Hiyorin
I've noticed that the exp needed between levels about doubles+some everytime
Kitsunemimi
2,188 posts
Joined April 2009
Kitsunemimi

SapphireGhost wrote:

Let's look at the player rinrinn000, who has a level of 1.
Level 1 = 26,118
Let's now consider the player Kioko-chan, who has a level of 2.
Level 2 = 85,398
Finally, SeakoNat, with a level of 3.
Level 3 = 272,604
These gaps make it quite clear we are dealing with exponential growth, whether this is simple exponential growth or whether it has extra applied formulas will make it difficult without even a basic idea of the type of formula we are looking for. One of the first things we can do is attempt to search for the gap between Level 1 and 2.
The highest score I found for Level 1 is: 26,118
The lowest score I found for Level 2 is: 41,230
So the magical number must be somewhere in there. As a bonus fact...
The highest score I found for Level 2 is: 113,996
This is getting frustrating. Anyone who would care to help out is greatly appreciated. We can figure this out.
Alright, the problem with the numbers that you (and thelewa) got is that they're WAY too inaccurate. Actually, thelewa's percentages are probably accurate enough, but I figured it would be easier if we got the exact numbers of certain levels. So for this, I sorted out the online rankings and went all the way down to page 200 (the last page). By the looks of it, there were at least 500 people with the same level (before the last page, and probably more after that), so we can say that the number will be accurate.
In order to get to level 65, one must have what appears to be exactly 1,810,000,000 points.
Level 66 is at 1,895,000,000 points.
And level 67 is at 1,982,500,000. That's a 4.617% increase.
Level 68 is 2,073,000,000. That's a 4.565% increase
Going even further, level 69 appears to be 2,166,000,000.
The differences are 85 million 87.5 million, 90.5 million, and 93 million. So they appear to be fairly consistent.
However, we may be able to get different numbers at level 80/81.
To be level 81, you'll need 3,510,000,000, and level 82 is 3,643,000,000, and the difference is 133 million.
That's a 3.789% increase.
....
Damn.
Well, I'll leave the numbers here in case someone can figure it out.





Kioko-chan is my new bestest nub buddy
100kV
33 posts
Joined February 2011
100kV
Why doesn't the developer just tell us?
Arcorann
6 posts
Joined May 2009
Arcorann

h3k1ru wrote:

% currently works wrong

for example i have 100 lvl and 50kk points atm, i need 127kk points for 101 lvl, but it shows i have only 23% - its wrong, coz i have about 40% to 101 lvl
You're working out the percentage wrong. The percentage displayed is the percentage of the way from Lv100 to Lv101, not the percentage from 0 to Lv101. In this case it equals roughly (50B-26.9B)/(127B-26.9B) ~ 23%, which is what it displays.

pickashoe wrote:

Why doesn't the developer just tell us?
Because he doesn't want to.

Anyway, I'm posting numbers for levels 64-101 from the current rankings for analysis, this time including ranks for easier searching later (prev means that the number is from my previous post):

SPOILER
#6 129,227,086,970 (101)
(prev) 127,600,619,879 (101)
#7 126,049,065,205 (100)
(prev) 126,019,219,471 (100)

(prev) 26,947,605,501 (100)
#394 26,931,764,147 (100)
#395 26,913,708,920 (99)
(prev) 26,909,616,331 (99)

(prev) 17,715,539,256 (99)
#767 17,711,833,398 (99)
(prev) 17,686,182,293 (98)
#768 17,668,563,602 (98)

(prev) 12,513,236,472 (98)
#1193 12,502,631,691 (98)
#1194 12,491,318,182 (97)
(prev) 12,470,856,367 (97)

#1683 9,521,700,658 (97)
#1684 9,514,830,064 (96)

#2150 7,789,016,740 (96)
#2151 7,785,177,351 (95)

#2546 6,746,827,178 (95)
#2547 6,740,862,474 (94)

#2844 6,094,312,717 (94)
#2845 6,089,257,495 (93)

#3080 5,652,481,508 (93)
#3081 5,650,748,726 (92)

#3283 5,334,404,387 (92)
#3284 5,332,633,347 (91)

#3467 5,084,842,737 (91)
#3468 5,079,823,394 (90)

#3634 4,876,335,010 (90)
#3635 4,875,345,515 (89)

#3781 4,692,276,908 (89)
#3782 4,689,499,281 (88)

#3930 4,525,980,391 (88)
#3931 4,520,974,212 (87)

#4093 4,362,038,224 (87)
#4094 4,361,511,830 (86)

#4226 4,209,451,030 (86)
#4227 4,205,459,472 (85)

#4395 4,061,185,464 (85)
#4396 4,060,525,204 (84)

#4556 3,919,034,598 (84)
#4557 3,916,947,583 (83)

#4748 3,778,791,017 (83)
#4749 3,778,123,997 (82)

#4944 3,642,555,663 (82)
#4945 3,642,517,865 (81)

#5151 3,510,863,181 (81)
#5152 3,509,711,434 (80)

#5358 3,381,482,598 (80)
#5359 3,381,387,264 (0) <-- glitched
#5360 3,380,347,724 (79)

#5594 3,255,999,853 (79)
#5595 3,253,950,552 (78)

#5825 3,133,203,119 (78)
#5826 3,133,082,099 (77)

#6052 3,015,367,487 (77)
#6053 3,011,918,038 (76)

#6273 2,898,433,562 (76)
#6274 2,896,980,015 (75)

#6494 2,784,362,385 (75)
#6495 2,783,845,588 (74)

#6775 2,674,771,039 (74)
#6776 2,673,519,141 (73)

#7059 2,566,854,926 (73)
#7060 2,566,413,380 (72)

#7342 2,462,420,917 (72)
#7343 2,461,840,617 (71)

#7631 2,361,418,553 (71)
#7632 2,360,227,037 (70)

#7955 2,262,125,591 (70)
#7956 2,261,983,627 (69)

#8279 2,166,258,790 (69)
#8280 2,165,596,551 (68)

#8624 2,073,072,395 (68)
#8625 2,072,390,895 (67)

#9020 1,982,644,228 (67)
#9021 1,982,253,250 (66)

#9383 1,895,166,700 (66)
#9384 1,894,271,272 (65)

#9783 1,809,917,485 (65)
#9784 1,809,438,759 (64)
SapphireGhost
osu! Alumni
2,618 posts
Joined June 2010
Topic Starter
SapphireGhost
I understand this is a necropost but I believe I have something meaningful to add to this thread.

Good news everyone, assuming Arcorann's data is accurate we have a PROGRAM now to help us determine level from Total Score or Total score from level. The program can be downloaded here:

Version 1.0 http://puu.sh/1OKN
Version 2.0 http://puu.sh/1Plv

It doesn't look like there is an easy formula but this program is a good substitute.
Arcorann
6 posts
Joined May 2009
Arcorann
Since the thread is temporarily resurrected, my current set of data is attached (last updated Mar 20 - unfortunately one set that I gathered later was lost). Due to the change in rankings to only display 5000 players, it is unlikely I will work on this much further.

Download: osu_level_stats2.xls
helion
53 posts
Joined June 2010
helion
I found this while browsing old announcements a while ago. Might be useful.

viewtopic.php?f=9&t=4362
http://pe.ppy.sh/levelling.htm

Only goes up to Level 99 though.
Arcorann
6 posts
Joined May 2009
Arcorann
Useful? It gives every level cutoff except for two!

Formula derived:

EXP(n) = 5000/3*(4n^3-3n^2-n)+1.25*1.8^(n-60), round to nearest whole number

EDIT: The formula matches my results for n=100 (exp = 26,931,190,829) but not n=101. I think peppy only programmed it properly to level 100, given that the increase to 101 seems to be very close to 100 billion.
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