#### Taboo

##### Admin's slave

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- Taboo

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 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

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 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.

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.

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

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

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.

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.

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.

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.

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.

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

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

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!

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__
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

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)__
Code:

`[0, 184], [1, 334], [2, 239], [3, 133], [4, 42], [5, 69]`

__Miraculous Chaos Scroll (Mchaos)__
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]`

__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

__for each node:__*my guesses*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!