Blueprint Drop Rates (Community Sample Size)

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Retep
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Retep » Mon May 01, 2017 11:27 am

Abqu wrote: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


Ya, that's what I was saying, though not nearly as clearly, so thanks for sharing this; should clear up any confusion from my poor wording. Also nice to have a visual and audio explanation for those that prefer information in those formats :D

Ronin
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Ronin » Mon May 01, 2017 2:08 pm

This was attempted about a year ago:

viewtopic.php?f=4&t=6157&start=10

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Shiroe
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Shiroe » Tue May 02, 2017 1:55 am

Abqu wrote: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

CC_Darkis wrote:Chests:
Wood/Leather Chests to Have 100% Higher Mythical/Legendary Drop Rates for Items/Rare Items
Iron/Gold Chests to Have 50% Higher Mythical/Legendary Drop Rates for Items/Rare Items
For Magic and Higher Chests Opened, made some adjustments to loot to better reflect the quality of the chest

Based on those 3 lines your statement seems to be true for golden and below, while probably not for magic and above. (based on people mostly complaining about getting artifacts from a 500/750 gem chest and the wording of that line, I kind of expect CC's reaction will be to lower the artifact chance and up the item chance. (Not sure if people will end up being happy with that for primal chests, since that would also mean less of those 2 chest/raid exclusive artifacts. I have opened few primal chests myself, but would probably prefer getting 10 of those artifacts [1] over getting a random flawless item...))


[1] a batch of 10 seemed common in Abqu's "get the 25 new primal blueprints" video.
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)

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Lionstar
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Lionstar » Wed May 03, 2017 10:54 pm

Image

acespokket
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Re: Blueprint Drop Rates (Community Sample Size)

Postby acespokket » Thu May 04, 2017 3:27 am

My contribution:
Dwarven
Keys BP
54 10
18,52%

Magic
Keys BP
143 28
19,58%

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Deadeye
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Deadeye » Thu May 04, 2017 10:01 pm

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:

  1. Lower chests have a lower chance (10%) of blueprints compared to higher chests (20%).
  2. 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).
  3. 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

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

Postby Master Builder 007 » Fri May 05, 2017 9:03 am

That's fantastic work, Deadeye. I'll see if I can link your response in my original post as the answer.

Ronin
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Ronin » Fri May 05, 2017 2:10 pm

Good analysis Deadeye, confirming the general approximations many of us have been relying on to inform our strategies.

At the end of the day, BP drop rates are useful for answering two questions:
1) Is it worth it for me to open chests vs spend gems on other issues?
2) When should I use fragments?

The metrics you've provided help answer both of those questions.

River
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Re: Blueprint Drop Rates (Community Sample Size)

Postby River » Tue May 09, 2017 9:07 am

since the last patch.
10 magic chests (8 with keys; 2 with gems) -> 0 BP :cry:
2 dwarven chests (1 keys; 1 gems) -> 1 BP :) (but the BP requires a magic chest's BP I don't have :( )

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Lionstar
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Re: Blueprint Drop Rates (Community Sample Size)

Postby Lionstar » Tue May 09, 2017 7:14 pm

Hey Deadeye, my gold chests were opened a long time ago. If I were to make a guess I would say at least a year ago. Probably a bit more than that.


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