Blueprint Drop Rates (Community Sample Size)

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Master Builder 007
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Blueprint Drop Rates (Community Sample Size)

Postby Master Builder 007 » Sat Apr 29, 2017 9:03 am

As we do not have the blueprint drop rates from the various chests, we have to conduct statistical tests. Obviously, obtaining a meaningful sample size is difficult for any one player, especially for the higher quality chests. That's why I'm here. I need your help for this experiment. If we have enough players contributing their blueprint drop rates, we can aggregate the results into statistically meaningful blueprint drop rates. I've seen a few numbers thrown about (around 15%, 20%), but I want more exact numbers and I want to see if it is consistent across the different chests, particularly between magic and dwarvish chests.

So, if you want the best data possible, please join in. Comment your results below and I will add it to the overall tally. Thanks!
(P.S. As we get more participants, the numbers will become better. Early on, they will not be accurate.)

Blueprint Drop Rates:

Wooden: 11/100 (11.0%)
Leather: 26/216 (12.0%)
Iron: 27/198 (13.6%)
Golden: 32/364 (8.8%)
Magic: 99/472 (21.0%)
Dwarvish: 15/87 (17.2%)
Primal: 22/113 (19.5%)

------------------------------------------------------------------------------------------------------------------------------------------------------------------------

UPDATE: Deadeye has posted a reasonably definitive BP Drop Rate. Here's his response (page 2 of this thread)

With data from Lionstar, acespokket, Abqu's stream, and my own chests, I have done some analysis.

Here is a Dropbox link to an OpenOffice/LibreOffice (.ODS) spreadsheet. (That link will pull up a flat view in a browser, change the dl=0 to dl=1 to download the ODS without displaying it).

In it is a summary of all sample proportions ("p hat" or p^ in the sheet) by player and chest type. There is *clearly* enough data in all 15 categories to calculate valid statistics. That p^ value is the portion of the chests opened that contain a blueprint (I showed it in % in the summary table). SE is standard error, which is like standard deviation for a sample. The 95% CI lower/upper columns are P^ +/- 1.96*SE. We would say "we are 95% confident that the population proportion is in this range." Given that there are 15 categories, we should also not be surprised if one or two of the population proportions (true chance of getting a chest) are outside of this range.

Looking at the summary, one thing jumped out immediately: Lionstar's gold blueprint sample proportion (again, "p hat") is a single digit percent chance, and his magic chest is over 20%--even higher for his dwarvish. The confidence interval for the gold chest does not overlap the magic one. Sorted by p^, there is a clear distinction in grouping gold & lower and magic & higher.

When grouped like that, the confidence intervals tighten up with SE in the 1% and 1.5% ranges (for 95% windows about 0.035 and 0.055 wide--from 9.3% to 12.9% for low chests and 19.5% to 25.1% for high chests).

Directly comparing these two samples (gold- and magic+), we can make a null hypothesis (H0) that they are from the same population. (The alternative hypothesis (Ha) is that they are from different populations). This hypothesis has a Z-score of 6.65, pretty much ruling out that both samples came from the same population. (That's the second line in that section; the first line does it by showing the confidence interval of the difference between p1 and p2. p1 and p2 are the population proportions that provided sample proportions p^1 and P^2).

If I stopped there, I would say "I guess gold and lower contain like 10% blueprints, and magic and higher contain like 20% blueprints."

But...

Lionstar and I are the only two who provided gold chest counts, and they don't look very similar. So I ran another comparison. Inconclusive. It's right on the edge. I can't say that they are from different populations, but the Z-score is 1.86 (remember, we're looking for 1.96 for 95% confidence--this is like 90% confidence, but for a hypothesis test, decide the confidence before the test).

Okay, so if we just compare everything every which way, that's called "p-hacking" (which is not the same p as proportion, this one is a probability score related to the Z-score, which I haven't mentioned until now). There are enough ways to compare things that we WILL find results by randomness if we look at enough of them. I'm trying to avoid that, but I test another hypothesis: That gold chests changed at some point. So I slice up my personal data. I don't record the dates, but I'm pretty sure they are roughly in order. So I cut my 130 gold chests into the first 65 and the last 65. The null hypothesis fails: This looks like two different populations. But it's a Z-score of 1.97. Right on the line!

If I slice it into thirds (45/40/45) and test the first against the last, the Z-score softens to 1.78. This is in the "needs more testing" range, but further away from conclusive than the difference between Lionstar and DE golds. If I look for an exact point in my data where the blueprint chance might change, it's at 75 at the lower chance follwed by 55 at the higher chance. This really stands out, which a Z-score of 2.87. However, I'm very concerned about that being a p-hack since I can't pinpoint that to a date linking it to an update of some sort.

TL;DR:

So, three possibilities stand out in my mind:

Lower chests have a lower chance (10%) of blueprints compared to higher chests (20%).
All chests changed blueprint rates at some point in the past, and the sampled players (entirely Lionstar and myself, as the only two giving gold- data) transitioned at about that time (with my gold strongly split).
Lower chests have a lower chance, and gold at some point moved from being a lower chest to a higher chest.

Possiblities 2 and 3 are interesting but don't have much strategic implications. They are what they are and the best plays don't change much. It would help give a timeline goal for people, but the randomness doesn't help much with that. Possibility 1 has a large strategic implication, IMO. If gold chests have half the blueprint chance of magic chests, then gold blueprints require the same investment as magic blueprints (250/0.1 = 500/0.2 = 2500 gems spent on keys, not counting chest cost).

In addition to the inherit desirability of gold blueprints, possibility 1 means fragments spent on gold prints would be way more cost effective than saving them for magic prints.

So..., Lionstar, do you have any information on when any of your chests were opened. Does anyone else have wood/leather/iron data from after the December 19th update?

D


If you can give wood, leather, and iron data after the December 19th update, please do so as that would help ensure that those results remain accurate. Thanks!
Last edited by Master Builder 007 on Mon Jun 05, 2017 6:57 am, edited 7 times in total.

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aks47u
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Re: Blueprint Drop Rates (Community Sample Size)

Postby aks47u » Sat Apr 29, 2017 9:07 am

Since a recent change to key exchange rules I've seen here someone dealing with support to find out how many chests (by type) they had opened.
Mail support to get these figures, divide by the amount of BPs you have, adjust for any bought with BP-frags.
Probably best done by those with all chest BPs unlocked.

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Shiroe
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Shiroe » Sat Apr 29, 2017 9:36 am

There's been a bunch of these topics and also about keys vs gems and the general conclusion is that it's near impossible to get a meaningful sample size.
Everyone seems to have 1 or more different chests that feel like their nemesis; for me it was leather, dropping below 3% (I think that was mostly 50-gem openings in 2015 before raid keys...) while my authorized alt actually breezed through leather with keys and has been struggling on iron chests a bit... Higher chests might have somewhat higher percentages, but that might again differ from person to person. (Abqu and Bloops both blitzed the 25 new primal blueprints of the december 2016 patch in a 20-25% drop rate range).

Some previous topics:
viewtopic.php?f=4&t=3492
viewtopic.php?f=4&t=7496&p=32631#p32631
viewtopic.php?f=4&t=7450
as of 2016-09-11: Player level: 44, City: Eolythes, Blueprints: 517, Mastered: 419, Crafted: 78.61K
(except for tier 1 and some tier 2 artifacts mostly running my shop/gearing self sufficient)

VeNoM0619
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Re: Blueprint Drop Rates (Community Sample Size)

Postby VeNoM0619 » Sat Apr 29, 2017 12:55 pm

Despite the new patch adjusting these rates soon anyways (which will throw your figures back out). We don't know if the pool of bps remaining also changes odds, and since the devs don't want to tell us the figures on gambling premium currency, its one of those things we will never truly quite know "exact figures". The figure can very well be 5-20% depending on plenty of factors.

But of course that's statistics... not much accuracy regardless right? :P

I suppose I should also talk very briefly about RNG here... RNG despite what you think, is not at all "random" in the sense you believe. The distribution of numbers in modern RNG is widely unbalanced.

MT was created back in 1997, and has been the de facto standard for modern RNG. It has many flaws, most importantly are the numbers generated. They have ebbs and flows, which in general means you will have lucky periods and unlucky periods. Which can also be used to your advantage, sure its not perfect manipulation, but changing your 5% into 20% is still better, right?

In the end, your chances are based solely on your "gut feeling" (which of course, I could write another few paragraphs about how gut feeling gives wrongs statistics too). However, the easiest solution I provide to all "unlucky" people out there? Open 12 hours later than normal, or run a few tests on other lesser things to determine where the RNG pointer is at in its period.

For those wishing to read more on RNG:
https://en.wikipedia.org/wiki/Mersenne_Twister
http://www.pcg-random.org/ Details flaws, and lack of features in modern RNG, I wish this thing was the new standard...but MT is "good enough" and people don't care

Master Builder 007
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Master Builder 007 » Sat Apr 29, 2017 1:10 pm

Shiroe, thanks for those links! No one has any definite answers because all the sample sizes is far too small. I hope was to build up a sample size of several thousand over time. One of the staff mentioned in one of the posts that the rates are set so there's nothing you can do to improve it.

However, I still have one question that will impact my direction forward. Perhaps you have some insight. If keys for magic and dwarvish cost the same, is it better to start with dwarvish for higher level BPs? (especially if the higher chests seem to have a higher drop rate)

VeNoM619, that's a good point about the rate adjustment so there is no point in conducting a test right now anyway. Did they indicate in any way how they were adjusting the rates - nerf or buff?

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aks47u
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Re: Blueprint Drop Rates (Community Sample Size)

Postby aks47u » Sat Apr 29, 2017 1:39 pm

Master Builder 007 wrote:However, I still have one question that will impact my direction forward. Perhaps you have some insight. If keys for magic and dwarvish cost the same, is it better to start with dwarvish for higher level BPs? (especially if the higher chests seem to have a higher drop rate)

That all depends really on what you're after from those chests;
If you want a moneymaker then you want the Goddess' Tear from Magic,
Or if you want Revive then you want the Keeper Of Souls from Dwarven.
Personally I've finished Dwarven, but not Magic (and am still even missing 1 Golden) but I don't know if that's down to luck or the smaller total BPs available from Dwarven compared to Magic.

Kim!
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Kim! » Sat Apr 29, 2017 1:43 pm

However, I still have one question that will impact my direction forward. Perhaps you have some insight. If keys for magic and dwarvish cost the same, is it better to start with dwarvish for higher level BPs? (especially if the higher chests seem to have a higher drop rate)

The advice I was given as a f2p newbie was to start with dwarvish chests to get a moneymaker (specifically KoS or FF harp), and then switch to magic or primal to get a better moneymaker (tears, gaia's, drac tea). Magic contains 58 blueprints, dwarvish has 23, primal has 44. If you assume similar drop rates on each, your odds of getting a specific blueprint are much higher in dwarvish. After you've got that first okay moneymaker (ocarinas, KoS, FF harp, etc) you won't need to worry as much about gold while you're working on finding better BPs. :)

After getting a moneymaker I'd look at which chests has the most useful blueprints to you - either a precraft you need or a skill for your quest teams. That'll change depending on your goals and current BPs so a blanket "magic or dwarvish" answer wouldn't be fitting. ^^;

VeNoM619, that's a good point about the rate adjustment so there is no point in conducting a test right now anyway. Did they indicate in any way how they were adjusting the rates - nerf or buff?

They're increasing the leg/mythic drop rates a tiny bit, they didn't mention any changes to bp drop rates. I would assume that it's a buff and the drop rate of quest mats will go down a smidge, since that's been a huge complaint for a long time.

VeNoM0619
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Re: Blueprint Drop Rates (Community Sample Size)

Postby VeNoM0619 » Sat Apr 29, 2017 2:02 pm

Kim! wrote:
VeNoM619, that's a good point about the rate adjustment so there is no point in conducting a test right now anyway. Did they indicate in any way how they were adjusting the rates - nerf or buff?

They're increasing the leg/mythic drop rates a tiny bit, they didn't mention any changes to bp drop rates. I would assume that it's a buff and the drop rate of quest mats will go down a smidge, since that's been a huge complaint for a long time.

Yea.. exactly, they are changing rates, but we can't assume they won't touch bps (or re-balance it exactly)

Code: Select all

         BP/Item/Artifact
Before:    1   1      1
After:     1  2       1

Increased rates for items right? Decreased bp/artifacts.

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Retep
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Retep » Sat Apr 29, 2017 2:52 pm

VeNoM0619 wrote:
They're increasing the leg/mythic drop rates a tiny bit, they didn't mention any changes to bp drop rates. I would assume that it's a buff and the drop rate of quest mats will go down a smidge, since that's been a huge complaint for a long time.

Yea.. exactly, they are changing rates, but we can't assume they won't touch bps (or re-balance it exactly)

Code: Select all

         BP/Item/Artifact
Before:    1   1      1
After:     1  2       1

Increased rates for items right? Decreased bp/artifacts.


Actually there was a big discussion about this in the Discord channel a little while ago, apparently it first rolls whether you get a blueprint, an item or an artifact. After that it does another roll to determine which blueprint, what item (quality) (There may actually be an additional roll here, one for the quality and one for the actual base item), or which artifact.

This means that increasing the legendary/mythical drop rate would decrease the chance of epic and flawless items and have no effect on bp rate. We still have no idea what's happening for magic+ chests though as the wording is extremely vague.

As for the intent of the OP, I've actually kept track of every single chest I've opened since I started playing (600+). I'm busy atm but I will share the spreadsheet by Monday at the latest. But as others have pointed out, this data may be obsolete in a few days. Also it's not truely random as someone else pointed out, it seems I may have subconsciously picked up on some things that improve odds, as my BP rates have continually increased over time (or it could be a fluke, who knows :P). Also, again I'm not 100% sure, could be a fluke, but it does seem opening chests with gems rather than keys does improve your chances for a BP, at least when it comes to gold and magic chests (I went from about 5% drop rate with keys to 20% with gems).

I also have 2 videos where I opened a couple hundred bags each time that I may eventually get around to uploading if we want to try to figure out bag rates as well lol
Last edited by Retep on Mon May 01, 2017 11:23 am, edited 1 time in total.

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Abqu
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Abqu » Mon May 01, 2017 11:03 am

Retep wrote:Actually there was a big discussion about this in the Discord channel a little while ago, apparently it first rolls whether you get a blueprint, an item or an artifact. After that it does another roll to determine which blueprint, what item (quality) (There may actually be an additional roll here, one for the quality and one for the actual base item), or which artifact.


If you're bored and have five minutes, I went over this in a stream: https://www.twitch.tv/videos/138919243?t=13m0s

too long, didn't watch:

Image

The chance to get a BP stays the same.
The chance to get an item stays the same.
The chance to get artifacts stays the same.

What IS changing, however, is that when you do get an item, the chances of getting myths/legs are better, and the chance for epics/flaws are lower.

Edit: please don't beat me up about the odds listed, i'm sure they're wrong and were used for educational purposes, thx


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