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Updated Ultra Rare Drop Rate Data | All sample size goals reached | Will still do occasional updates | Links fixed 2015 April 8


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#1
ComradeShepard7

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Math-Lite Summary

  • As far as we can tell, all packs have the same per slot drop rate.
  • This leads to SPs having a higher average cost per UR drop than PSPs, APs and RPs since a potential UR drop from a SP costs 60k credits while a potential drop from a PSP, AP or RP costs 49.5k credits (due to them having two slots that can drop UR cards).
  • For the packs that can drop multiple UR cards (PSPs, APs, and RPs), each slot is calculated independently.
  • UR character drops and UR weapon drops are handled independently so if you get an UR character drop you are not being "cheated" out of an UR weapon drop.
  • The current drop rate estimates and all the other details involving this project can be found here (last updated September 30, 2014)

About
I've resumed the effort to determine the UR drop rate that was started way back when for PSPs but was never thoroughly extended to the other pack types (at least that I have seen). While going through the old PSP data I did find that the script that was used to determine the drop rate was counting some non UR cards as URs leading to the drop rate that was found being a bit higher than it actually is. I've corrected that with this new effort.

At this point we have more than 10,000 samples per pack type which was my goal. The details of the project can be found here (last updated April 24, 2014). In addition to looking at drop rates and long term costs per UR it also includes info about UR drop streaks as well as information about the independence of the two slots that can drop URs in PSPs, APs and RPs, and UR characters vs UR weapons.

While the sample size goals have been reached I will still be doing occasional updates. If you have data you would like to share please email me at comradeshepard7@gmail.com or contact me on here. When you are sharing data please do it in batches of at least 50 purchases and provide it in the following format as it will make data entry easier for me:

 

         Pack Type, Number of Packs Purchased, number of UR weapon cards dropped, number of packs with more than one drop

Current Progress
The goal for data collection for each pack is to get 10000 samples, and this has been reached. The sample size for each pack type is listed below:

  • PSPs: 19834
  • SPs: 10554
  • APs: 12614
  • RPs: 11606

Stuff that has changed since the topic was originally made:

  • Linked document is now a pdf rather than a google doc as LaTeX gives a lot better formatting for figures and tables than a published google doc.
  • The document now provides a lot more detail, including explanations of the math behind the project, which will hopefully help people understand the results a bit better.
  • wngmv, DocDAM and I have now reached a consensus that the slots are independent. If you read anything about slot independence that was posted here before I suggest you forget it and take a look at the new stuff as there were errors in the previous versions.
  • It has been determined that UR characters are handled independently from UR weapons.
  • If you would like to see the data spreadsheet or the MATLAB scripts they can be found in a zip file here (last updated September 30, 2014). If you want to run the MATLAB script, UR_Drop_Analysis_Script.m is the main file, and you need to make sure all the MATLAB files and the spreadsheet are all in the same folder.
  • Some discussion of the ammo and equipment dropped in SPs vs the 99k packs was added by Qui-Gon Glenn's suggestion to the parts where the packs are being compared. This information has been revised for accuracy.

  • Viper371, regack, Bhaal and 12 others like this

#2
David Diablo

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It's too early in the morning/late at night for me to study your findings. But I can corroborate the fact the fact that APs seem to be the way to go for URs, though I have no data to show for it. Keep up the good work.

#3
mybudgee

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GOod work

#4
stinekandts

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Impressive effort....do you have any regression formulas for the different packs? Sample Size...or did I overlook that?

#5
solidprice

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Posted Image
.......so what dose this mean for derps like myself?
Psp's are still king?

#6
Tupari

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Good work. I was interested when I found that APs yielded a higher UR drop rate just based on the limited data I gathered, I wonder if that will hold true once more data is gathered.

#7
ComradeShepard7

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stinekandts wrote...

Impressive effort....do you have any regression formulas for the different packs? Sample Size...or did I overlook that?


I considered each potential UR card to be one sample when generating the confidence intervals so each SP gives one sample and each of the other packs gives two. The sample sizes so far are
  • PSP: 6832 (3416 packs)
  • SP: 142
  • AP: 400 (200 packs)
  • RP: 400 (200 packs)
I considered this "experiment" to be a case of determining a population proportion as getting or not getting an UR drop is essentially a success/failure type situation. I am going to look around a bit more and see if there might be a better way of analyzing this since statistics isn't really an area I am all that knowledgable in or maybe a BSNer will point out a better way to do it.

#8
ComradeShepard7

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Tupari wrote...

Good work. I was interested when I found that APs yielded a higher UR drop rate just based on the limited data I gathered, I wonder if that will hold true once more data is gathered.


Right now your records are my only solid source for AP and RP drops but as I get more data the confidence interval will deffinately shrink but I don't think it will shift too much. I am going to see if I can use any more of Artificial-Ignorance's records but since they alternated pack type constantly I would rather just get more, newer data sources.

#9
ComradeShepard7

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solidprice wrote...

.......so what dose this mean for derps like myself?
Psp's are still king?


It is still too early to say anything definative but it is looking like APs will give at least a slightly better cost/UR ratio than PSPs, and RPs are looking like they will have either the same or slightly better cost/UR than PSPs. Can't say anything about SPs yet though.

#10
chcknwng

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Op send your data this way. I might be able to help you more.

#11
ndw542

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So the bottom line is that URs, true to their name, are ultra-rare, and to continue to obtain them I must buy packs, yes? Got it.

#12
chcknwng

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Also lower bound is supposed to be the smaller number, and upper bounds is supposed to be the larger number.

In terms of sampling process, # of packs between UR drops are essentially the same as getting URs. The only difference is what you care. This is called a negative binomial distribution.

Edit: Getting UR or not is a classical binomial situation. I'm 99.5% sure this is how bioware's RNG works. The only thing I'm not sure of is whether those 2 slots are independent of each other.

Edited by wngmv, 20 September 2013 - 05:21 AM.


#13
ComradeShepard7

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wngmv wrote...

Also lower bound is supposed to be the smaller number, and upper bounds is supposed to be the larger number.

In terms of sampling process, # of packs between UR drops are essentially the same as getting URs. The only difference is what you care. This is called a negative binomial distribution.

Edit: Getting UR or not is a classical binomial situation. I'm 99.5% sure this is how bioware's RNG works. The only thing I'm not sure of is whether those 2 slots are independent of each other.


Ya, I wasn't paying attention when I labled the bounds on the CIs.

I didn't use the packs between UR drops to get the CIs. I just made those histograms for a visual to see how often packs are dropping and I couldn't remember what the distribution was called. Calculating the CIs was just based on the total samples and total UR drops. In the stats book I have from back when I took a stats course it is refered to as a "large-sample confidence interval for pi (population proportion with a certain trait)".

I sent you a friend request so we can work out how to exchange data in PMs.

Edited by ComradeShepard7, 20 September 2013 - 05:32 AM.


#14
Titus Thongger

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ermagherd econometrics and data analysis!?!!? I thought I left that unholy stuff behind at university D:

#15
i hate you all

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I'm about to spend two million+ creds in a few hours. Let me know if I can be of any help.

#16
chcknwng

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i hate you all wrote...

I'm about to spend two million+ creds in a few hours. Let me know if I can be of any help.


Please take note of which pack you have bought and how many URs you get from each kind of pack. Also note if you got double UR.

Thanks.

#17
yamada1979

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I've been keeping notes on each pack I've bought for the past 5 months (since I maxed everything except UR weapons). I'll send you an email with the info.

#18
Ganius

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I can help with sample data as well. I will buy 20 APs tonight.
My current inventory

#19
TheTechnoTurian

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In this thread: math
Me: derp

I can send in some of my data though, with about 130 URs to go I'll be gathering it for a while... :/ It sounds like you have enough on PSPs, I think I'll be buying mostly APs and SPs to fill up my level III equips

#20
Alfonsedode

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Don't u think the drop rate depends on the number of UR left to receive ?

Anyway, I will keep track of the AP I am buying :police:

Edited by alfonsedode, 20 September 2013 - 08:21 AM.


#21
Pearl (rip bioware)

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alfonsedode wrote...

Don't u think the drop rate depends on the number of UR left to receive ?

No. The drop rate does not change, but since it's all random, it may seem that way.

#22
i hate you all

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ok i bought 25 AP's and only got one UR...  yeah thats what im working with...  makes me rage. 

something has changed.  when i was a complete nublet, i got more UR's with less money.  its been this bad since the beginning of summer or more specifically when i got my last UR.  after that,  the drop frequency plummeted.  getting nothing from millions.

i maxed out my gels, etc. before hand so i dont know if that affects the drop rate or not.  not really sure who to send the data to so i'll just leave it here.

#23
DesioPL

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If i good understand... Better buy Spectre Pack instead of Premium Spectre Pack for UR's?

#24
ndw542

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Might be helpful to mention that anyone providing data should differentiate between UR character cards and UR weapons. I think most people around here know the two have different drop rates, but some might not.

#25
SwoopIM

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When you max out all your normal and rare weapons at level X, will that increase your drop rate odds of getting or upgrading a UR? Think I have bought about 10 PSPs and 10 APs recently with no URs--getting mostly useless character cards it seems.