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[Guides] The statistical test of the shard drop in skilled dungeons

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Posted on 12/13/13 3:26:34 PM | Show thread starter's posts only

This is stolen from android forum, I couldn't find a post about it here.

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[backcolor=rgba(255, 255, 255, 0)]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-
[backcolor=rgba(255, 255, 255, 0)]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".