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osu! math

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Topic Starter
[Vriska Serket]
There are probably other threads about this, but I am trying to figure out some math for osu! standard scoring. I'm pretty bad at math, which is why I'm coming here for help.

What I want to do is create a graph of how many points you will have after x notes hit, assuming you hit 300 each time. According to the wiki, the scoring is worked out in this way:
Score = Hit Value + Hit Value * (Combo multiplier * Difficulty multiplier * Mod multiplier) / 25
Hit Value The hit circle judgement (50, 100 or 300), any slider ticks and spinner's Bonus.
Combo multiplier (Combo before this hit - 1) or 0, whichever is higher.
Difficulty multiplier The difficulty setting for the beatmap.
Mod multiplier The multiplier of the selected mods.
I wasn't sure what difficulty multiplier is, but this thread had some useful things to say.

Using all this information, I was able to get that your score = 300 + 300(5x)/25 (Assuming the difficulty multiplier is 5x). This tells you how many points you will get for hitting a 300 note with a combo of x.

What I can't figure out though is, how would you make a function to know how many points you would have with a combo of x? All I can think of is something like this:
g(y)=300 + 300(5y)/25
f(x)=g(x-0) + g(x-1) + g(x-2) + . . . g(x-x)

This doesn't seem right :? , and I just can't figure anything out. Plus, you would have to write out a long thing each time, which becomes increasing difficult with larger numbers.

Again, I am no good at math, so sorry if I said something dumb. >:(
Corin
ur mum
Bweh
There's a difficulty multiplier? I honestly had no idea.

Godspeed, OP.
AutoMedic
Math is hard


mang
UnderminE
Where is mathexpert when i need him
ColdTooth
The answer is 69 42
Granger
Too bad that Full Tablet doesnt visit offtopic.
Chamelo

Brian OA wrote:

There's a difficulty multiplier? I honestly had no idea.

Godspeed, OP.
I'll leave this here.

MillhioreF wrote:

Circle Size, HP Drain and Overall Difficulty (not Approach Rate) each give one "difficulty point" for every tick of difficulty you give each of them; e.g. a map with CS6, OD4 and HP5 would have 15 difficulty points. Remember that CS cannot normally go below 2 or above 7, so you'll always have at least 2 difficulty points and at most 27.

These "difficulty points" affect the multiplier as so:
0-5: 2x multiplier
6-12: 3x multiplier
13-17: 4x multiplier
18-24: 5x multiplier
25-30: 6x multiplier

Note that Hard Rock does not increase this multiplier, even if it pushes the map up into the next difficulty bracket, and Easy likewise retains the original multiplier.
Maybe like this?
(Given difficulty multiplier = 5 and no mod)



So that means when you hit the 15th combo you'll get 1,200 points.
I hope I did it right. :roll:
Topic Starter
[Vriska Serket]
@Chamelo

That is kinda where I got stuck. I was able to find the graph of how many points you get per hit at a certain combo, but what I am looking for mainly is a graph of how many points you will have cumulatively after a certain combo.

The function would have to take the points of every single hit before combo x and add them together.
Chamelo
I see.

Then the score will also depends on these conditions:
- The slider head / reverse arrows only give us 30 points instead of 300.
- Each spin of the spinner gives us 100 points and a bonus of 1,000 points after the spin meter is full.

But if you want to do the function that calculate only a beatmap of plain notes then it's fine. But it's still a hard thing.
(I shouldn't skip calculus classes. >.>)
Topic Starter
[Vriska Serket]
@Chamelo

For simplicity's sake I am trying to exclude spinners and sliders, just straight up 300s. I've been thinking about this for a while and I just cant figure anything out. If I knew how to code I could probably make a program that just runs the function 300+300(5x)/25 for every number before combo x and adds them together. But I'm looking to make a graph
Chamelo

[Vriska Serket] wrote:

If I knew how to code I could probably make a program that just runs the function 300+300(5x)/25 for every number before combo x and adds them together. But I'm looking to make a graph
Coding for this case is real easy. But putting it into one equation is challenging.

I'll just leave this here
1st hit = 300
2nd hit = 360 (300 + 60)
3rd hit = 420 (300 + 60 + 60)
4th hit = 480 (300 + 60 + 60 + 60)
5th hit = 540 (300 + 60 + 60 + 60 + 60)
and so on...
Topic Starter
[Vriska Serket]
Do you think somehow sigma could be used? This is where things start to get confusing for me, I have never learned about summation before.
AutoMedic
osu meth
Chamelo

[Vriska Serket] wrote:

Do you think somehow sigma could be used?
Yes, and it's the best way.

Score = (300 * x) + Sigma(0 -> x-1 ) 60 * x
Topic Starter
[Vriska Serket]

Chamelo_Th wrote:

Score = (300 * x) + Sigma(0 -> x-1 ) 60 * x
Perfect!

Now, how do you think I could graph summation? I've been looking around for like 30 minutes and I can't find much
Chamelo
This is what I can't do. :o
loldcraft
I hope I understood the question correctly (my math is horrible, and this looks too simple to be correct, but it's what I got)

C is combo
M is diff mod * mods

Score=(c*c+c)6m+300c

Tell me if it's right though.
mathexpert
yay, meth my favorite drug~~~

[Vriska Serket] wrote:

Chamelo_Th wrote:

Score = (300 * x) + Sigma(0 -> x-1 ) 60 * x
Perfect!

Now, how do you think I could graph summation? I've been looking around for like 30 minutes and I can't find much
You really shouldn't be surprised that you can't find a way to graph a summation... you can't get smooth nice graphs with them since they aren't "dense" enough. Because you're graphing points, you will need to find a way to write the summation as a recursive sequence.
I think it's:


You can then easily graph this using any decent graphing calculator (It works fine on my TI-89, I've done it many times in the past). Just remember to set the nmin to 0 though, in the windows menu. It should look like a generic exponential graph.

You could also graph, as a regular function:


You can do this on most graphing calculators as well, but it'll look really ugly and won't be really accurate either. That's why I think the recursive sequence is better than the function.

(Hope I helped. Hopefully you know how graph w/ a graphing calculator...?)
Yoeri
The scoring system is shit that's all you need to know
UnderminE
yay it's methexpert
Friendan

Corin wrote:

ur mum

Thanks for giving out my location.
winber1
e=mc^2

pls, you guys all useless
Chamelo

winber1 wrote:

e=mc^2

pls, you guys all useless
Well, considering c = 3*10^8 none of the variables can contain this number, even double!

imma reshape the formula I've posted before.

                             x-1
Score = 300x + Sigma[60i]
                             i=0
                x-1
because Sigma[300] = 300, ne, mathexpert?
                i=0
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