Spiral Knights - UV and Crafting

UV and Crafting

14 replies [Last post]

Sat, 03/30/2013 - 12:32

Eltia

Summary:
This is a pet project of mine, started back in November, 2012. I have been recording how many UV's I got from Mist crafting. After about four months, I have gathered over 800 data points. So I think maybe this is a good time to present some preliminary results to the rest of the community.

I started this project mostly out of frustration of pricing UV'd items on AH and that Punch has been abused in the past as a money laundry machine. (There was this incident before that people found exploits in the game to obtain a ridiculous amount of CR, then spend them all on Punch and the GMs decide no harm done therefore no action taken.) I want to find out what is the proper pricing for various UV'd items without resorting to using prices suggested by Punch. (If we price UV by Punch, a 1UV item should worth at least 20k. In practice, it is rare that people would offer 20k for an 1UV item.)

Once we get rid of that dirty Gremlin, we also get rid of one money laundry machine in the game and the GM could proceed to prosecute those who abuse the currency system in the game.

Sampling methodology:
Everyday, I'll summon my trusty alts (4 of them) and pick some 2* items to craft. e.g. Brandishes, Calibar, Skelly Shield, Alchemer, mist bombs, wolver / demo gears. Up to 8 crafts would be performed a day. The number of UV's would be recorded, stratified by the three categories: single UV (1UV), double UV (2UV) and triple UV (3UV).

A score is then calculated for each day, based on the result of the crafting. The matrix I used is:

score = 1UV + k * 2UV + k * k * 3UV,

where k = 7. k is estimated based on the ratio of 1UV to 2UV, which is around 7 : 1. i.e. for every seven 1UV you obtain, the next UV you obtain is expected to have at least 2UV. e.g. if the crafting today results in one 1UV, the score will be 1. If the results are one 2UV and three 1UV, the score would be 3 + 7 * 2 = 17.

Assume: each craft is independent of each other and the ratio of UV2 to UV3 is the same as UV1 to UV2.

Preliminary results:
This is a plot of the raw data I collected.

UV data collected from November 11th, 2012 to March 30th, 2013

The X Axis is time (or number of days since November 11th, 2012) and the Y Axis represents scores calculated based on the number of UV's obtained on that day.

There are two periods of idleness in the data. i.e. no crafting were done. First period was from December 3rd to December 10th, 2012, and the second period was from February 14th to March. 1st, 2013.

Here are some statistics:

Total number of crafts = 872
Number of 1UV = 85 (~= 9.8%)
Number of 2UV = 12 (~= 1.4%)
Number of 3UV = 0 (< 1%)
Overall chance of UV = 11%
Ratio of 1UV to 2UV ~= 7.1 : 1

Note: chance of UV (11%) is comparable to previously reported results (10%).

Questions to the readers:
While the study is ongoing, I would like to hear from the rest of you what other things you like this study to look into. The data are available upon request.

Sat, 04/06/2013 - 23:27

Goofio

This seems like a good place to share my results, too. I have been recording crafts since January 16, 2012 (roughly 14.5 months). I record the date and every UV crafted each day in a spreadsheet (type of equipment and specific UVs), and I use some macros to parse the results. General overview:

Crafts = 7028
Items with a UV = 819 (11.65%)

3UVs = 6 (0.09%)
2UVs = 62 (0.88%)
1UVs = 751 (10.69%)
Total UVs [3*(3UVs) + 2*(2UVs) + 1UVs] = 893

Very High/Max = 22 (2.46%)
High = 58 (6.49%)
Medium = 169 (18.92%)
Low = 644 (72.12%)

Sat, 03/30/2013 - 14:08

Eltia

Cooperstown, ND

Thanks for sharing your results. Glad to see the results we got are pretty consistent. (1UV ~= 11%, 2UV ~= 0.8-1%, 3UV < 0.1%.) I'll continue sample more data points and see if the ratios between 1UV to 2UV and 2UV to 3UV would get closer to what you got. Also, would you be interested to produce a plot of your data using the matrix I used?

So I was talking to another player about this study. He also mentioned the results I got are consistent with his. However, here is a hypothesis I have after the talk.

I think for the score, it may actually look like this:

score = c(t) + 1UV + k1 * 2UV + k2 * 3UV,

where k(i) are constants estimated from the ratios iUV : (i+1)UV for i = 1 or 2, and c(t) is a function that is inversely proportional to t, the number of days since the last p consecutive idle period on the crafting accounts. e.g. p = 14, then t is the number of days since the last 14 days without any crafting on the accounts.

Sat, 03/30/2013 - 14:18

Goofio

Hmm, I haven't noticed better odds after being idle for X number of days. To me, it really seems like there is some probability P of getting 1UV, and for 2UVs it's P^2, and 3UVs it's P^3. Properly estimating the chance of getting 3UVs is pretty tricky, though, because the odds are so low, and each event is incredibly rare.

Sat, 03/30/2013 - 14:20

Eltia

Cooperstown, ND

I used a linear approximation to model the overall "outcome" of crafting, using the matrix above. It's exactly because it looks to me the chance of 1UV, 2UV and 3UV share some multiples of the same constant factors. In layman's term, the crafting machine rolls the same dice three times to determine the outcome of the UV.

The idle number of days is also tricky to define, because it also need to quantify the length of the idle period to be meaningful. So my current definition on the function c(t) involves one variable (t) and one constant (p). I'm guessing p has a floor value to be effective, something like p >= 14.

Sat, 03/30/2013 - 14:40

Goofio

Hmm, interesting idea. I think it would be quite difficult to prove or disprove the way idleness affects the probability, though. With a flat probability model, you can use hypothesis testing pretty easily. The number of successes (UVs) each day should follow a binomial distribution (assuming the number of trials/crafts each day stays constant). I haven't done this yet myself, but I may give it a try in the future.

Sat, 03/30/2013 - 16:06

Eltia

Cooperstown, ND

Well, assuming an idle period of p = 14 (2 weeks) and r = 5 alts (r = 1 / P / 2 = 1 / 0.1 / 2), the expected number of crafts to score an UV). Suppose we rotate the alts every q days, we need ceiling (p / q) * r crafting alts.

e.g. for a 14 days idle period and 5 days rotation, and the chance of a UV is 10%. we need ceiling (14 / 5) * (1 / 10% / 2) = 3 * 5 = 15 alts.

It's doable, just need enough alts.

Sat, 03/30/2013 - 20:21

Blaknt

what about time

not sure if this is just a coincidence or not but i had crafted my DA and got single UV ctr med and with in the same 5 min my bro crafted his Sudaruska and got the same single uv ctr med, and one time i inspected a person who had the same double uvs on all his weapons (mabye he took his time and lots of money to get them) but do u think the crafting machine could be based on time and day.

did u remember while u were crafting if any of the items received the same uv back to back

Sun, 03/31/2013 - 08:07

Eltia

Cooperstown, ND

I was crafting Prismatech Alchemers earlier this month and I got Mech UV Low 2x back-to-back, followed by Mech UV Med the other day, and then a few days later, another Mech UV Low. I think it's just coincidence. But it certain did happen.

Performing crafting within a short period of time (within 30 sec time lapse) may give people the illusion that UVs chance are "clustered". Looking at the data I gathered so far, there are no evidence to support the improvement from burst crafting is significant enough. What I'm more inclined to believe, is the c(t) function I mentioned above which plays a more major role in crafting.

This kind of make sense from a development perspective. Because when you have returning customers, you want to send them a little "gift" to retain them in the game. So having a slightly higher chance of UV for these customers seem logical and easy to implement.

There is also no evidence to support there is any easy way to gain an advantage in obtaining multiple UVs through crafting.

Sun, 03/31/2013 - 09:38

Lukehandkooler

OMG this thread is hawt <3

Thu, 04/04/2013 - 19:30

#10

Goofio

@ Eltia
I suppose I could add a similar plot with the different scores if you want, but the number of crafts per day varied quite a lot, because sometimes I crafted 1-star equipment, and other times I crafted 2-star equipment.

Fri, 04/05/2013 - 02:41

#11

Wu-Wei

Mist spam crafting is too tedious, resource and time consuming.
Considering the avg. person has one account. A 2 star recipe uses 50 mist. This guy has an elevator pass. So he crafts 2 items per day.
Considering the chance of 1 UV is about 11%. Lets make it 10% for worst case. And within that 10% there is a ~2% (again worst case) chance of that UV being Very High/Max.
So 100 out of every 1000 crafted will have 1UV, and of that 100, 2 items will have a very high/max UV. To craft 1000 items to end up with 2 items with random very high/max UV, will take 500 DAYS with 1 account, 1 char... which boils down to 250 days per very high/max UV.

Considering that low UVs appear 72-75% of the time, and they are quite useless. At worst case, 25 out of 1000 items crafted will not have low 1UV. blah...

So if you are hunting for that very high/max UV, the cost to get 1 item with RANDOM said UV, will be:::
1veryhigh/maxUV = 500crafts x (400cr + cost-of mats).

Without mat costs that is 200k crowns per very high/max UV.

Time is the major factor, hence Punch was created. You will still get low UVs at roughly the same percentage, but you will be guaranteed of a UV.

So with Punch, 2% chance also for 1UV very high/max, but chance of ANY UV is 100%. hence, 50 crafts for 1UV very high/max.
That will be 1million crowns per very high/max UV.
If you make 10k crowns /day runiing clockworks or missions or whatever, it will take you 100 days to get this... faster, but a little more expensive. That is what you pay for, to get it faster.

.. Unless you are saying. 2% of all crafts will have very high/max 1UV. Then the amount of crafts are 50 per very high/max 1UV

Fri, 04/05/2013 - 04:16

#12

Wu-Wei

This whole thread is actually ironic..

Getting rid of the money "laundering machine" Punch.. will result in the next money laundering machine in line being under the microscope, which is...
Multiple alt accounts.. IRONIC

Actually I have played a few MMO games until the game eventually disappeared.. and what I have noticed is:

Amount of total alts currently present in the game is indirectionally proportional to the total life time left of the game. Take that math! :P

Sat, 04/06/2013 - 00:31

#13

Stelli

you should try to summarize

you should try to summarize it so it is more friendly to read for common players who has less patience scanning this whole thread.

From my experience, when crafting, it is roughly 10% give or take a slight % to get 1UV, then at this point, you will get an additional UV (2UV) at 10%, when successful, you will get another UV (3UV) at 10%.

Making 1uv approximately 10% (one in ten) 2uv approx. 1% (1 in a hundred) and 3uv approx 0.1% (1 in a thousand)

well you can argue that the 1% and 0.1% is separate, but yeah its only 1%.. so let's just leave that out of the equation for now.

So let's say you want Fire Maximum on your wolver cap for example, you will need to averagely craft 10 caps to get one with a UV (10%), and to get a Maximum it is (for now, according to goofio's stats) 2.5%, and to land on the right stuff you want and assuming all resistance and defensive options are equally in chance (Fire, Shock, Stun, Freeze, Curse, Poison, Elemental, Normal, Shadow, Piercing) which is 10%.

So taking in all that probability, it is roughly:

UV appearance x Maximum Appearance Chance x Choice of UV

in this case it is:

1/10 x 1/40 x 1/10= 1/4000

so yeah craft 4000 caps, but I normally find it to be easier than this.

What do you guys think?

Sat, 04/06/2013 - 22:08

#14

Goofio

It's a geometric random variable with mean equal to 1/P, so I would say 4000 caps is correct.

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