45 Lich's to get 1 Ephemera = 2.2% Drop rate

[Ikserdok]

Im at my 28th lich, still no empherma but ofc still getting tons of low lvl bonus weapons, under 30% for sure...hard to get anything above with it...

[(XBOX)Erudite Prime]

My first Lich had the Trickster Ephemera, woohoo, 100% drop rate!

[Aceh0li0]

update  --  60th Lich and 1 ephemera .....  1.6% drop rate 

 

[Leyers_of_facade]

Drop chance of ephemera prior to November 14 is 5%, 10% afterwards according to DE. We will use these rates as the null hypothesis

U26 is dropped on October 31, and your post is on november 26. So a total of 27 days.

We will assume uniform progress during these 27 days for your first 45 liches, so 25 liches with old chance (5%), and 20 at new chance (10%).

The probability of having only 1 ephemera among this is therefore the sum of 

i) you get 1 ephemera before nov 14, 0 between nov 14 and nov 26

ii) you get 0 ephemera before nov 14, and 1 after.

 

probability of first scenario is 25*(0.95^24)*0.05*(0.9^20) = 0.044373811

probability of second scenario is (0.95^25)*20*(0.9^19)*0.1 = 0.074942436

sum = 0.119316247

 

Under our assumption of uniform progress, the probability that under the given drop chances, the chance of you only having 1 ephemera after the first 45 liches is 0.119316247

That is actually not that low. Slightly larger than 1 in 9 (11.11%) and slightly smaller than 1 in 8 (12.5%)

 

we do not reject the null hypothesis.

Edited December 11, 2019 by Leyers_of_facade

[schilds]

Here's the binomial distribution for getting any Ephemera (may be duplicates) over 50 Liches:

First 10 values (rounded) are: 0.005, 0.029, 0.078, 0.139, 0.181, 0.185, 0.154, 0.108, 0.064, 0.033, 0.015.

What this tells us is that given 1000 people we can expect that, roughly:

• 5 people will get 0 ephemera
• 29 people will get 1 ephemera 
• 78 people will get 2 ephemera
• 139 people will get 3 ephemera
• 181 people will get 4 ephemera
• 185 people will get 5 ephemera
• and so on (just multiply the 10 numbers above by 1000)

If those 1000 people naively calculate the drop chance (as has been done in this thread) after 50 runs, then:

• 5 people will calculate a drop chance of 0%
• 29 people will calculate a drop chance of 2%
• 78 people will calculate a drop chance of 4%
• 139 people will calculate a drop chance of 6%
• 181 people will calculate a drop chance of 8%
• 185 people will calculate a drop chance of 10%
• and so on

That means we can expect that:

• 185 naive mathematicians out of every 1000 will think DE is telling the truth about the drop chance.
• 432 naive mathematicians out of every 1000 will think DE is overestimating the drop chance.
• 383 naive mathematicians out of every 1000 will think DE is underestimating the drop chance.

Basically, a large majority (~81%) of naive mathematicians will think DE can't math. Out of those, about half will be happy that DE can't math, and the other half will be unhappy (more or less) that DE is trying to cheat them :-P.

Edited December 11, 2019 by schilds