If you wanted to be within +/- 10% accuracy of the true drop-rate:
Calculated Sample Size:
Where do these numbers come from? Just from looking at the samples in this thread, you can see they don’t work.
Just some examples:
sample of 100:
sample of 100:
sample of 300:
You can clearly see how the numbers for a sample size of at least 100 have a higher margin of error than you claimed to have at a sample of 41! The runic value actually doubles between samples.
The numbers come from established mathematicians & statisticians. Blaise Pascal was one of the first trail-blazers in probability theory.
Archenassa’s data would result in a 95% confidence that majors drop-rate is 19% +/- 10% (i.e. 9 - 29%)
Archenassa’s data would result in a 95% confidence that runics drop-rate is 12% +/- 10% (i.e. 2 - 22%)
xSidarothx’s data would result in a 95% confidence that majors drop-rate is 24% +/- 10% (i.e. 14 - 34%)
xSidarothx’s data would result in a 95% confidence that runics drop-rate is 6% +/- 10% (i.e. 1 - 16%)
CSZ’s data (because 300 sample size) would result in a 95% confidence that majors drop-rate is 30% +/- 5% (i.e. 25 - 35%)
CSZ’s data (because 300 sample size) would result in a 95% confidence that runics drop-rate is 8.5% +/- 5% (i.e. 3.5 - 13.5%)
There is a clear overlap with each of these individual confidence intervals, which suggest the nobel prize winning mathematicians & statisticians most likely got it correct.
In fact many of the much smaller samples of just 20 battles align with these results. A couple, like the one I raised with 18 minors & 2 majors, do not, but this can be explained by hypothesising that it fell outside the confidence interval (i.e. it was a non-representative sample).
You could start adding everything up to get a much closer result (which was the aim of this thread), but a few of the people have not declared the difficulty, and as the developers have indicated, there is a sliding-scale of chance (0-20%) of getting no traitstone as you decrease difficulty from Warlord IV to Normal.
Yes, the chance of getting no traitstone decreases, but the chance for the rarities remain unchanged. My data excludes now the “No Traitstone” from the Rarity and lists them seperately.
All 300 Matches were played on Normal difficulty, and I will make an Update when I get to 500 Traitstones.
Which just shows how worthless those number are. We are not interested in raising the confidence, but with decreasing the margin of error. For that matter, I could say with 100% confidence that the numbers are between 0% and 100%. Does it help me? NO!
So even saying you’re 100% confident that major are set somewhere between 9 - 29%, and runics between 2 - 22%, this level of accuracy will not please anyone. Also when someone did 100 battles yesterday and got 5 runics, and 100 battles today and got 15 runics, both are inside your margin of error (considering both samples of 100 above), yet that person is sure the rate of runic was tripled between yesterday and today - which is just the point I was trying to make, and your “nobel prize mathematics” don’t change that - rather, they actually prove my point.
margin of error and confidence really do mean the same thing… you want the +/- to go down… so raise the confidence means lowering the error… toma-toe toma-ta.
No, they don’t. Confidence would mean how sure you are that a specific margin of error is correct. Sure, you can get a better value on both if you raise the sample size, but that doesn’t mean they’re the same thing. Rather, for a given sample size, better (higher) confidence value means worse (higher) margin of error.
I agree with @yonizaf, that’s actually why I didn’t post anything until I had at least 100 samples. Too small is irrelevant, the margin of error is huge. My first 20 battles gave me a 100% drop rate AND were mainly majors. After 100 fights, the results were more telling. Posting every 10 or 20 fights does not really have much signification.
Archenassa - no one was arguing that more data is less accurate. The point was that one can discern good information from much fewer samples than many people intuitively think.
The aim of this thread was for many people to put in their smaller pieces of data so that we may more quickly discern the drop-rates rather than people processing hundreds of battles themselves.
Here’s my donation to the thread:
100 battles on normal
nothing 14
minor 53
major 22
runic 10
arcane 0
celestial 1
Using the absolute data provided above, we have 566 samples.
(CSZ - I didn’t use your second set of data, as I wasn’t sure if it included your first subset of 167)
With a sample size of 566 and a 95% confidence interval (i.e. we are 95% sure that our sample of 566 is consistent with the total population), then we can say that the derived numbers are correct within +/- 4%.
In summary, once a traitstone has dropped (i.e. excludes when a traitstone does not drop), then:
Minor = 62 %
Major = 27 %
Runic = 9 %
Arcane = 1.8 %
Celestial = 0.7 %
Another ~500 samples is required before we could get +/- 3% accuracy on the derived numbers.
It did, although without any exact numbers. I can give you an update of my data, if you insist. Includes all previous dropped traitstones. When sharing data with the community I don’t start a new count, but rather continue the old one.
That is near exact to the drop rate of the old iron keys.
Okay chaps I have mine from my spreadsheet in the last few weeks to add in, having just hit 200 with it:
Nothing 40
Minor 87
Major 45
Runic 19
Arcane 5
Celestial 4
Total 200
Your total is only 160. You can’t count nothing. Every difficulty gives a different percent of nothing, but does not effect the actual drop rate of rarity. The only important data is everything aside from the “nothing”.
The drop rate of nothing changes based on difficulty. Recording the results of nothing would be inaccurate due to everyone having data on different difficulties.
Just a bit of frustration to share. I have done at least 200 of the “The Grudge” challenge in Khaziel hoping for an Arcane Deep traitstone. I just did one of the challenges in Maugrim Woods and got the Arcane Swamp stones. Wasn’t looking for it but crap - on the first go?! Very random indeed!
Got Arcane death stone and a Celestial right after each other in Karakoths after two quests.
Thanks for your input @Jainus - will add to the table when the new inputs increase the total sample to ~1,015 (which is needed for the 3% accuracy level).
@Tacet - don’t worry, I’m excluding Nil results following @CSZ’s excellent idea to do so. But still happy for people to share this info for completeness.