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[Guides] The Statistical Test of the Shards Drop Rate in Skulled Dungeon [Finalized]

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#1
Posted on 9/1/13 11:13:50 PM | Show thread starter's posts only

Edited by Hero87884419 at 9-12-2013 12:59 AM

[Finalized Sep 11, 2013]

I read in previous discussions that some players argued about their shard drop rates and discussed whether there is a difference if not winning by 100%. Some players suggested that there was no difference as dropping shard is solely dictated by win or fail. So since then, I have been logging my results from raiding skulled dungeons by either  finishing it with 100% or just winning by 50~99%. By doing this, I will be able to answer two questions:
1) What is the shard drop rate?
2) Is there a difference in the shards drop rate if I don't finish by 100%?

I made three assumptions:
1) The drop rates are the same across all skulled dungeons;
2) The drop rate stays constant throughout time and throughout ver1.1.3 to 1.2.1
3) Each trial is independent, ie., whether I get shards this time does not change the probability of the next trial.

So here is my observed result from 430 tests recorded from Aug-18-2013 to Sep-11-2013:
Achieved 100% but no shards: 196
Achieved 100% and got shards: 76
Achieved 50~99% but no shards: 130
Achieved 50~99% and got shards: 28

Here is some statistical analysis:
In general, disregard of whether I have achieved 100% or not, the estimated drop rate is 104/430 = 24%
The 95% confidence interval is 20%~28%, meaning that if I repeat this test 100 times, for at least 95 times, the estimated drop rate will be in this range.

And here is the important message:
If you know how to do a Chi-square test, you will figure out that the p-value is 0.017, indicating that there is a difference  if you finish the dungeon with 100% against not 100%.
The drop rate (100%) is 28% (95% confidence interval 23%~33%)
The drop rate (not 100%) is 18% (95% CI: 12%~24%)

So if you want to farm shards, try to win by 100%. Over the long run, it gives you more shards.

In the future, it'll be interesting to test whether there is a linear relationship between the percentage and drop rate. It may also be worthwhile to find the reason that the drop rate is higher if the raid is won by 100%. One possibility is that killing all the heroes is actually crucial as it's called "hero shards".

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#2
Posted on 9/6/13 6:07:52 PM | Show thread starter's posts only

I hope you keep doing this test and I would be appreciated if you post your new results because I would love to 50% - 99% my dungeons instead of 100%. Just an FYI, I asked the live support about the difference in drop rates and they said there was no difference, but I don;t trust them.

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#3
Posted on 9/9/13 10:50:14 AM | Show thread starter's posts only

Awesome thanks for this info

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#4
Posted on 9/11/13 4:34:12 PM | Show thread starter's posts only

Great work Hero87884419

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#5
Posted on 9/14/13 5:40:34 AM | Show thread starter's posts only

I feel like shard drop rate increased with the new patch. Anybody else notice that?

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#6
Posted on 9/23/13 11:03:43 PM | Show thread starter's posts only

krzikiller replied at 9-14-2013 06:40 AM
I feel like shard drop rate increased with the new patch. Anybody else notice that?

Yes, since ver 1.2.12, the shard drop rate increased to 42% (CI: 33% ~ 51%) in my small trial. This is good. Now I can easily get 40 shards every day.

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#7
Posted on 9/25/13 8:34:49 AM | Show thread starter's posts only

Hero87884419 odpowiada, dnia 9-24-2013 12:03 AM
Yes, since ver 1.2.12, the shard drop rate increased to 42% (CI: 33% ~ 51%) in my small trial. Thi ...

I can't agree with this theory, i was farming shards ( and still doing that ) from month. What can i say is that drop rate in skull dungeon is on level 15-25%. This patch doesn't introduce any changes in drop rating imo.

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#8
Posted on 9/25/13 6:36:56 PM | Show thread starter's posts only

odins91 replied at 9-25-2013 09:34 AM
I can't agree with this theory, i was farming shards ( and still doing that ) from month. What can ...

Okay, let me do a test again and get back to you in a few days.

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#9
Posted on 9/26/13 8:14:25 PM | Show thread starter's posts only

odins91 replied at 9-25-2013 09:34 AM
I can't agree with this theory, i was farming shards ( and still doing that ) from month. What can ...

I managed to run 50 dungeons before upgrading to 1.2.14. I got shards 16 times. So the rate is 32% (19~45%). It is not different from my previous test (23~33%) (p=0.56). So you are right, no change in the new patch.

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#10
Posted on 9/28/13 2:14:05 AM | Show thread starter's posts only

hi..i have been observing lately that when i raid dungeons and get 0 deaths from my troops..its 100% shard drop. as long as NOT ONE of my troops die.hope this helps

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