Maplestory Chaos Scroll Rates

Taboo

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Hello gamers
I am making this thread for those who play Maplestory in general. If you have followed my comments way back when, I always would bring up the fact that chaos scrolls were weighted in GMS. Anyone who has played on the official Maplestory server is familiar with this. However, anywhere you look, you see different claims on what stats are possible. There is a general acknowledgement among players that Chaos Scroll is +-5, and Chaos Scroll of Goodness is +0-5. These are the only two scrolls people are sure about.

Miraculous Chaos scroll (Mchaos) and Incredible Chaos Scroll of Goodness (ICOG) have always had random claims whether it be a range of up to 6,7,8, or 10 stats. Unfortunately, private servers are to blame somewhat for various reports. There are assumptions that this could be datamined and private servers would be the ones to have the values in their hands. This is a misconception and those private server developers guessed chaos scrolls went up to 10 stat. This could perhaps be a misinterpretation of a +10 HP/MP. HP/MP goes up by 10's so that would in fact be a +1. Who knows...

In another life, I grinded over 100 Incredible Chaos Scroll of Goodness's and I was quite upset with how unrewarded I was. All my attempts seemingly gave me 0-2 stats. Very few times I landed a +4 or +6. I have since decided I would keep track of some scroll stats.

Notice how I wrote +4 or +6. I found this quite interesting. Mchaos and ICOG do NOT have the chance to grant you |5|. With extensive tests ran, the graphs below show the rates. I have done my best to make sense of the actual rates per number. Nothing can be certain because of how probabilities work.

Chaos Scroll

ChaosScrollGraph.png
Code:
[-5, 42], [-4, 19], [-3, 32], [-2, 63], [-1, 105], [0, 141], [1, 160] [2, 108], [3, 76], [4, 10], [5, 4]

Chaos scrolls show a "Bell Curve" standard normal distribution for the most part. This deviation holds true for the first 4 deviations on the left, and the first 3 on the right.
This is my assumption on what happens for -5, -4, 4, and 5:
-5: takes what should have been the next deviation for the right side. This would make it the same probability as -3.
-4: Is the next deviation. My current assumption is that they take both sides for the next deviation and combine them to -4.
+4: It could be that they possibly do the same thing for the next deviation but this time for +4.
+5: Gets the leftovers.
With this, you get a graph that looks like this
ChaosScrollProb.png

Please understand that this is only just a possibility I created to align it with what my data shows. The thing with probabilities is that it hardly ever will come out with the proper rates. What is clear is that Chaos Scroll has a very low chance to give a +4 or +5. This aligns with a test gathered years ago by a user on Southperry / BasilMarket. This user did not have as many data points as I do. Understandably, Chaos Scrolls were far more expensive.



Chaos Scroll of Goodness (CoG)

ChaosOfGoodnessGraph.png
Code:
[0, 184], [1, 334], [2, 239], [3, 133], [4, 42], [5, 69]
Chaos Scroll of Goodness uses the same formula as a regular Chaos Scroll. The only difference is, the stat given is just the absolute value of said stat. This reinforces Chaos Scroll's formula.

ChaosOfGoodnessProb.png


Miraculous Chaos Scroll (Mchaos)

MchaosScrollGraph.png
Code:
[-7, 0], [-6, 45], [-5, 0], [-4, 30], [-3, 25], [-2, 81], [-1, 138], [0, 225], [1, 175], [2, 170], [3, 89], [4, 18], [5, 0], [6, 12], [7, 0]
I am not happy with how this graph came to be. However, it is important to know that data is never 100% accurate. Perhaps I had very bad luck with landing 1's or very good luck with landing 0's. Given that -2 and 3 are nearly the same and the curve is similar, I still believe it is the same formula. Nexon is a creature of habit and it just wouldn't make sense to make a new formula for scrolls that have incRandVol.

MchaosScrollProb.png

Incredible Chaos Scroll of Goodness (ICoG)

I don't have the money nor time to gather data on this. Given it's nodes are randstat, noNegative, and incRandVol, it is safe to say it's exactly like Chaos Scroll of Goodness but all +5's are +6's.

So here are my guesses for each node:
randstat: This item has randomized stats. It will enter the code that determines the stats. The base case is a standard normal distribution.
noNegative: All values calculated by randstat are set to |x|.
incRandVol: This will replace any 5 with a 6. Formula doesn't change.

Possible flaws:
I am iffy on how a few are calculated. Especially when you have a look at the Chaos Scroll of Goodness graph. With the data given, I am certain that this is the correct path for both Chaos and CoG scrolls. However, it is clear that there's a bit of uncertainty with 4 and 5. This leaves be to believe I may be slightly off. We're still dealing with probabilities so this formula still stands a chance to be as accurate as can be.
Mchaos... again... probabilities. I tend to lean towards the fact that they are creatures of habit and wouldn't concoct a whole new formula for an incRandVol node. On top of that, it is possible probability really had it's way with my miraculous scroll data. Regardless, these are all safe ballpark estimates.

In conclusion, Chaos Scrolls are free yes, but Return Scrolls are $5. I understand it is in place because only the very wealthy people will actually bother to spend such money to perfect an item in this way. This also allows for them to introduce more ways to gain range without damage becoming out of control. With that said, you're better off dumping money into the Marvel Machine. I also want to say that I am not the best at explaining math. I'm decent at handling data and making sense of it but I am terrible with math terminology.

Huge thanks to @Nyu for being a second pair of eyes and pointing out that Chaos Scroll of Goodness is |x|! derp

Q&A:
Why should I trust this data?
It's ultimately your choice on whether or not you accept this data to be true. What I can say is that myself, as well as the developers here on Croosade always go above and beyond in the name of accuracy. All formulas on this server are GMS like for the time at which they were coded. And let me tell you, they have some really stupid formulas.

How was this data accumulated?
Through lots of time and grinding. I have avoided any outside stats such as videos or clips showing peoples rolls. This is because there is a large biased in what gets uploaded and passed around. Either "LUL -6 everything check out this loser" or "OMG I got a +6". While yes, those are indeed stats that were rolled, the videos do not show all other failed attempts are rolling something extreme. This would heavily skew results towards the end numbers.
Not to mention that it is sometimes hard to confirm whether or not the video or clip is from a private server.

Can we help update this data set?
Nah, I don't trust anyone to be honest with their data. It's also too much work to confirm and again, there is biased to what people would want to add to the list. You are more likely to impulsively drop an item if you got a bunch of -1's than to go "I should add my data to the pool." You can however add on to this. But if you want to add on your own set and you trust that what I have provided is accurate, I recommend starting here and not on top of someone else's.

What if an item's stats were low and it went to 0? How would you determine what negative number it was?
If the item had a stat that was < 7 I avoided counting that line. I wanted to be sure +-7 wasn't a possibility. So it's as if that line never existed regardless of whether it went positive or negative.

Are all stats weighted equally?
I found this to be the case, yes. STR, ATT, Speed, all appear to be completely random. However, I wouldn't put it past Nexon if it was somehow weighted.

What's the point?
I don't know. Data is fascinating and found the fact that +- 5 does not exist for Miraculous scrolls to be hilarious.

Will this be added on Croosade?
It has nothing to do with Croosade. This is just a little project I wanted to work on and post my findings.

Finally
Please share your thoughts! I am curious if someone can come up with something more accurate. I think the place that has the most potential for improvement are 4's and 5's. If something makes more sense for Mchaos, let me know!
 

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yuvalzr234

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hmm i quite cant understand why would it give a bell curve if it shud be distributed evenly ? or am i just misreading the data?
i mean if its like avg of players then cog looks really ugly there feels like its continuance of the normal chaos scroll just added the other possibilities to the currents in some kind of ways?
 

Meiko

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Are they weighted evenly across all outcomes on croosade?
I knew that chaos were weighted weirdly on gms and always wondered what they were like on croosade
 

Taboo

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hmm i quite cant understand why would it give a bell curve if it shud be distributed evenly ? or am i just misreading the data?
i mean if its like avg of players then cog looks really ugly there feels like its continuance of the normal chaos scroll just added the other possibilities to the currents in some kind of ways?
As stated in the thread, these are GMS rates. There is no data out there currently about rates aside from this and the Southperry thread I linked.
I don't understand the second part of your post. If it's about how CoG gets its rates, please re-read the post.

Are they weighted evenly across all outcomes on croosade?
I knew that chaos were weighted weirdly on gms and always wondered what they were like on croosade
Most, if not all, private servers just do 1/x. I'm pretty sure they also all do +-10 for mchaos and such.
 

Nyu

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This was a fun read!
Glad to help with my procrastination :LOL:
 

yuvalzr234

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I don't understand the second part of your post. If it's about how CoG gets its rates, please re-read the post.

i mean on the cog shudn't it have been a normal distribution as well? or at least something that looks like it? what i see here is something different that isnt natural makes me suspect them thats all xD
o well at least in croosade i can land a +5 mcs *.* thank you guys for not using gms formulas, ours is better :D
 
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nzcorona

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i mean on the cog shudn't it have been a normal distribution as well? or at least something that looks like it? what i see here is something different that isnt natural makes me suspect them thats all xD
o well at least in croosade i can land a +5 mcs *.* thank you guys for not using gms formulas, ours is better :D

Cog is just the reg chaos distribution with the negatives cut off
 

Taboo

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Cog is just the reg chaos distribution with the negatives cut off
"With the negatives cut off" is a bit misleading but I think you understand the premise. I didn't respond because it's pretty straight forward in the original post so I'm not sure how else to explain it.
It uses the same formula, gets the same numbers as a normal chaos scroll, then it gives you the absolute value of that number. |-5| = 5, |-4| = 4, etc.
 
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mitbuiviet

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That's very interesting I have always thought it should be a discrete uniform distribution, just like rolling a dice. But your data shows that it's more like normal distribution. Maybe you could try increase the sample numbers and see if it evens out a bit?
 

Taboo

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Maybe you could try increase the sample numbers and see if it evens out a bit?
As in sample size? I find 760 results sufficient for chaos, 1000 more than enough for CoG and 1000 sufficient for Mchaos. Sure, Mchaos is ugly, but this was already a lot of work so I personally will not continue to gather more data.
It is 100% not uniform given my sample sizes of a total of 2760 entries.
 
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Harvey

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i mean on the cog shudn't it have been a normal distribution as well? or at least something that looks like it? what i see here is something different that isnt natural makes me suspect them thats all xD
o well at least in croosade i can land a +5 mcs *.* thank you guys for not using gms formulas, ours is better :D
The only reason GMS formula isn't used because we had no clue what it is. Their formula makes sense, because in private servers Chaos Scrolls renders most scrolls useless which is absoluty ridiculous.

ps. Let's not start a discussions here about our rates and whether or not we will implement GMS rates. If we will ever do so we will create another thread.
 

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