Chaosing Value and Pricing of ATT Capes and Shoes (SCRL 217)

Zenoooo · Oct 6, 2024

Hi, I am wondering if there is a guide about chaosing cost and pricing of unfinished CGS. If there is not, I may write a guide (and possibly a spreadsheet of unfinished CGS value based on finished CGS market price). Also want to see if people would like to have a guide about this.

Previously, I wrote Techniques of Scrolling Cost Calculation and Market Price Estimation

(Sep 4, 2024)

I will try to update the price of 0 slot capes and WS/CS (if become 400m or 600m, for example), and the guide. All market price updates are welcome, including forum page, trading SS, etc. Feel free to reply with latest sale record, which would serve as a BUMP too.

If you want a fast value check, press CTRL + F (or command + F on a Mac). Search for "1st set", and you will see lists of the price or chaosing value of capes and shoes with 0 - 7 slot(s).

(Sep 25, 2024)

Quick price/value check, and x slot to 0 slot equivalence check.

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(version 0.1, 9/11/2024: building blocks)
(version 0.2, 9/17/2024: capes)
(version 0.3, 9/18/2024: shoes)
(version 0.3.1, 9/25/2024: minor update)
(version 0.3.2, 10/4/2024: minor update)

To-do List:

optimize adjustment of shoes with slots

migrate the spreadsheet to google Docs with formula and figures

(maybe) explain n value mathematically

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0. Importance and Making Profit

1. Building Blocks
a. Chaos Scroll 60% and White Scroll
b. Cost of landing a CS with WS
c. Calculating the Value of Capes with 1 Slot

2. Capes with Slot(s)
a. Market Price List (2020 - 2024)
b. Adjusted Price (0 slot)
c. Calculating the Value of Capes with Slots

3. Shoes with Slot(s)
a. Market Price List (2018, 2020 - 2024)
b. Adjusted Price (0 slot)
c. Calculating the Value of Shoes with Slots

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0. Why does it matter, and how to make profit from it
For a long time people have the "consensus" that 1 slot = 1 ATT.
For example, 7/2 cape. "1 slot = 1 ATT" People believe it has the value of a 9/0 cape, and might wanna offer 1.8b for it.
But if you are the person who is actually chaosing the 7/2 cape, the (chaosing) value of the cape is merely 726m if not less. You, the person who actually chaos'es the cape, is losing 1b.

Here is the chaosing value of the 7/2 cape. Math shows that 7/2 < the market price of 7/0, which means that this cape is NOT worth chaos'ing. (As of the market price of capes, WS and CS, 09/17/2024.)

How to profit from it?
Sell your 7/2 cape to someone who assumes "1 slot = 1 ATT". Or trade for 9/0 cape. This may sound mean, but it's how the market works.

For higher att capes, for example the 28/1 cape. Math shows that 1 slot = 1.5 ATT (1.5 times the value difference between 29 and 28 capes).
I believe people will still assume 1 slot = 1 ATT, because it's the majority of the lucky player's total asset, and there may only be single digit number of players who can afford to buy it with 29/0 cape and/or meso/ws/cs.
If you can afford to get -5, -4, etc., you should chaos the cape whose n > 1 (n: 1 slot = n ATT). If not, you still will have to lose value because of "1 slot = 1 ATT".

一直以来很多人都认为1 slot = 1攻击。
例如一个7/2披风，有的人认为它有9/0披风的价值，从而可能为它支付1.8b。
但如果你是那个实际上要在7/2砸混沌卷的人，它的实际价值只有726m或更低。如果你砸它而不是卖给认为它值9/0的人，这实际上失去了1b的价值。

这是7/2的砸cs价值。数学上显示7/2砸cs的价值低于7/0的市场价，意味着这个7/2不值得砸cs。（9/17/2024披风、CS、WS价格。）

如何盈利？
将7/2披风卖给认为1 slot = 1攻击的人（交易meso或者9/0披风）。很残酷但很现实。

更高攻击的披风，例如28/1披风，虽然数学显示1 slot = 1.5攻击（1.5倍29/0和28/0披风的差价）。但我认为最后还是会以1 slot = 1攻击的价格成交。因为没多少人能承担砸28/1的风险。
如果你能承担-5，-4等的风险，你应该自己砸n>1的披风(n: 1 slot = n ATT)，而不是以“1 slot = 1攻击”的价格卖掉或交换。如果你不能承担此风险，而是卖掉或者交换，很可能你还是会因“1 slot = 1攻击”而失去部分价值。

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1. Building Blocks:
a.
Chaos Scroll 60%:
40% fail;
60% succeed, each existing stat individually change by -5, -4, ..., +0, +1, ..., +5 with equal probability 1/11.
White Scroll:
if the scrolling fails, the equipment will NOT lose a slot, and the WS will be consumed;
if the scrolling succeeds or booms (with dark scroll), the WS will be consumed.
Whether or not to use a WS is solely determined by the cost of losing a slot on the equipment.
When chaosing an equipment, if the equipment lose more than WS/40% value when it loses a slot, a WS should be used.

When 30%'ing an equipment, if the equipment loses more than WS/35% value when it loses a slot, a WS should be used.
This 35% is the probability of failing. The 35% of booming doesn't affect whether or not to use a WS.

b. The cost of successfully landing a CS with WS is:
(CS + WS)/0.6 = 1667m (as of Sep. 2024)

c. Calculating the value of capes or shoes with 1 slot:
EXAMPLE:
Here is a list of market price (Jul. 2024) from @Sylafia 's Price Guide:

Chaos 10/1 slot cape without WS, the (possible) value of the 10/1 cape is:
SUM(*5 att to 15 att capes*)/11 × 60% + [10/0 cape] × 40% - CS = 2682m

Chaos 10/1 slot cape with WS, the (possible) value of the 10/1 cape is:
SUM(*5 att to 15 att capes*)/11 - (CS + WS)/0.6 = 2102m

Thus it is reasonable to chaos the 10/1 slot cape WITHOUT a WS, and the value of the 10/1 slot cape is 2682m.

[11/0 cape] = 3200m
[10/1 cape] = 2682m
11/0 cape is about the value of (10/1 cape + CS).
The 1 slot on the 10/1 cape is worth 65% of 1 ATT.

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So far, we have (almost) everything needed.

With the price list of 3 to 27 att cape, we can figure out the value of 1 slot cape up to 22 att.
By doing this over and over again, value of capes with more slots could be calculated.

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2. Capes: Market Price List (2020 - 2024), Adjusted Price (0 slot), Calculating Value of Capes with Slots

a. Capes: Market Price List (2020 - 2024) and 1 Slot Capes Value
(Taken from some of other price guide, obvious market price of low att capes, and forum price research, and taking the average of the price)
Data available HERE (Google Docs).
Still, the value of cape with 1 slot grows exponentially with ATT.
But I am not happy with the result, as the value of n is all over the place (boxes filled with yellow). (Again, n: the slot equals n ATT ).
In section 2.b, I will adjust the price with the fitting equation, which allows us to extend the price list to 35 ATT cape.

With the techniques in Building Blocks, values of capes with 1 slot are as follows.
n: the slot equals n ATT
Capes:

b. Capes: Adjusted Price (0 slot)

According to the curve of 0 slot capes,
log(value of 0 slot cape) = 0.2916 ATT + 4.8817
So
[value of 0 slot cape] = exp( 0.2916 ATT + 4.8817 ), or equivalently [value of 0 slot cape] = 131.855 × 1.3386^ATT

What's also good about this, is that we can extend it to 35 ATT.

Capes: the adjusted price of capes with 0 slot, and the calculated value of capes with 1 slot:
(blue boxes: actually market price.)

Disclaimer:
Should the market price differ from the adjusted price, the actual market price shall prevail.

Interesting results (capes):
1. 1 slot capes with ATT lower than 13 are NOT worth using a WS.
2. the slot on 15/1 cape is about the same as the value of 1 ATT. Higher ATT ==> higher slot value.
3. n<0: the chaosing value of the cape is lower than the cape with the same ATT but 0 slot, meaning you are actually losing value (of the cape and the CS) if you chaos the cape (8/1, 7/1, 6/1, etc). Again, should the market price differ from the adjusted price, the actual market price shall prevail. Always do your own research about current price when you decide whether to chaos the cape or to sell it (to someone who doesn't read this thread or just wanna YOLO.)
5. @DoubleNine 's 28/1 cape is worth far more than a 29/0 cape (https://royals.ms/forum/threads/p-c-28-1-bfc.237020/)

The market price of the capes varies, but the 1 slot = n ATT relationship holds, because it's from the nature of math and exponential function.

c. Capes: Calculating Value of Capes with Slots

Do this over and over again.
Also make some adjustment based on the assumption that a x ATT/y slot cape is worth less than a x ATT/(y+1) slot cape. In the pink, yellow, green, gray boxes, I adjust the price higher.
On the first set, I use 1.2, 1.25, 1.3, 1.35 of the 0 slot cape's value.
On the second set, I use 1.1, 1.15, 1.2, 1.25 of the 0 slot cape's value.
Both give similar results.

(Capes: )
3rd set:
In this set, adjusted price is modified to better fit the market price of 10 to 15 att capes that most players care about. Also, recent price of 8 and 9 att capes dropped a lot. The price list is adjusted accordingly.

n of 2 slot cape: now, for example, the 1 slot on 10/2 is compared to the value difference between 11/1 and 10/1.

n of 3 slots cape: now, for example, the 1 slot on 10/3 is compared to the value difference between 11/2 and 10/2.
n of 4 slots cape: now, for example, the 1 slot on 10/4 is compared to the value difference between 11/3 and 10/3.

n of 5 slots cape: now, for example, the 1 slot on 10/5 is compared to the value difference between 11/4 and 10/4.

Note:
n: now, for example, the 1 slot on 10/2 is compared to the value difference between 11/1 and 10/1.

Note:
n: now, for example, the 1 slot on 10/3 is compared to the value difference between 11/2 and 10/2.

Note:
n: now, for example, the 1 slot on 10/4 is compared to the value difference between 11/3 and 10/3.

No adjustment is made. Negative value means the cape is not worth chaosing at all.
If the value here is lower than the price you can sell, you should probably not chaos the cape (for example, 5/5 cape).
Note:
n: now, for example, the 1 slot on 10/5 is compared to the value difference between 11/4 and 10/4.

5 slot: No adjustment is made. Negative value means the cape is not worth chaosing at all.
If the value here is lower than the price you can sell, you should probably not chaos the cape (for example, 5/5 cape).

What ATT (0 slot cape) are the capes with 1, 2, 3, 4, 5 slots equivalent to?

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3. Shoes: Market Price List (2018, 2020 - 2024), Adjusted Price (0 slot), Calculating Value of Shoes with Slots

a. Shoes: Market Price List (2018, 2020 - 2024) and 1 Slot Shoes Value

2 price in 2018 are also taken into the database, because they are good data:
19 sold for 18 FS + 15b
20 sold for 19 FS + 25b coin

Price of Shoes = exp(0.2829 ATT + 5.7835)
or equivalently
Price of Shoes = 324.8943 × 1.32697^ATT

1 slot Shoes Chaosing Value

5/1 chaosing value = 878, which means that 5/1 shoes is not worth chaosing.

b. Shoes: Adjusted Price (0 slot)

Disclaimer:
Should the market price differ from the adjusted price, the actual market price shall prevail.

c. Shoes: Calculating Value of Shoes with Slot(s)

In the pink, yellow, green, gray, and orange boxes, I adjust the price higher. (If you need to know the chaosing value, please refer to the boxes where the numbers are in gray color.)

1st set of data, used 1.2, 1.25, 1.3, 1.35, 1.4 of the 0 slot cape's value (except 2/5 shoes, which I use 700m as clean FS is close to this price, and 3/4 700m).
2nd set of data, used 1.1, 1.15, 1.2, 1.25, 1.3 of the 0 slot cape's value (except 2/5 shoes, which I use 700m as clean FS is close to this price, and 3/4 700m).

It turns out that VL Boots with 3/2/1 att clean is very close to the current price.

(Shoes: )
1st set:

Note:
n: now, for example, the 1 slot on 10/2 is compared to the value difference between 11/1 and 10/1.

Note:
n: now, for example, the 1 slot on 10/3 is compared to the value difference between 11/2 and 10/2.

Note:
n: now, for example, the 1 slot on 10/4 is compared to the value difference between 11/3 and 10/3.

Note:
n: now, for example, the 1 slot on 10/5 is compared to the value difference between 11/4 and 10/4.

Note:
n: now, for example, the 1 slot on 8/6 is compared to the value difference between 9/5 and 8/5.

Disclaimer:
Should the market price differ from the calculated value, the actual market price shall prevail.
But if you buy 10/6 at 7.2b and chaos it (and you can afford to lose the game), you are profiting 190% from it.

Note:
n: now, for example, the 1 slot on 1/7 is compared to the value difference between 1/6 and 2/6.

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I got a list of price of capes. The price grows exponentially as ATT increases.
However, just a slight deviation from the fitting line could be 10 to 20% difference from the actual trade price.
Also by adding different test-sample value of high att cape, the fitting formula changes, and the calculated price of lower att capes changes (for example at att 16 the price could change by 1b.)
What we can confirm here is that price does grow exponentially with att.

Comparing capes and shoes:

Disclaimer:
Should the market price differ from the adjusted price, the actual market price shall prevail.

to be continued

Kheb · Sep 6, 2024

A while ago I have plugged the available data of these items from different price guides in Excel and plotted a trendline.

Iirc I used 3 data sets from 123, Sylavia and one I forgot (maybe very old or someone's private data set)

Each exponential trendline for these data sets resulted in a r^2=0.99

Wich does imply (un)finished cgs very accurate follows an exponential increase in price.

I did start a project where I listed all possible outcomes when cs scrolling for each atk/slots combination.

I do remember that when I tried comparing it to the trendlines from before that it matched my expectations. Tho I never finished it

Nevertheless, I am fairly certain there is no guide available. This is just my two cents ^^

Geto · Sep 6, 2024

I would actually be really happy to see a guide for unfinished common market items (such as FS / SCG / BWG / Mittens / BFC / PGC and the list goes on).

I usually ask this specific person (ahem @Sylafia ) as she is one of the greatest sources of information regarding prices, but if there will be a guide specific for unscrolled items..

It would be great for the whole market.

I don't think there is one, and if there is - it's a non-updated one.

Zenoooo · Sep 11, 2024

just wrote 80% building blocks of the possible guide, but the edit was not auto-saved, and I mistakenly clicked on X.
Now working on it again, will be saving often.

Zenoooo · Sep 17, 2024

update cape (chaosing) value with 1 slot
update cape with slots

Zenoooo · Sep 18, 2024

updated shoes with slots
It turns out that VL Boots with 3/2/1 att clean is very close to the current price.

Zenoooo · Sep 25, 2024

update preface, and shoes with 7 slots (1 att , 2 att and 3 att)
feel free to reply with latest market price of capes and shoes with 0 slot (forum page or SS)

Chaosing Value and Pricing of ATT Capes and Shoes (SCRL 217)

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