About spell casting times with the Envoy Staff

Praise · February 18, 2020 at 12:54 AM

I've been doing some research on how spell casting times are calculated by the game. I've gathered quite a lot of data, which I'm dumping here regardless of whether it is interesting to anyone. To some, all of the below will be stating the obvious. If you've never really thought about how spell casting times are modified by different effects, there might be one or two interesting pieces of information here.

The original goal was to observe an Envoy Staff hitting all three possible "halves casting time of spells" (HCT) effects at the same time. Envoy Staffs (the gold versions only) are unique post-nerf staffs because they give an inherent 10% HCT rather than 20% HSR:

Agent Chevy · February 19, 2020 at 1:54 PM

Great Job, Praise!

This was a very intriguing project as you conducted your experiments. This was certainly an eye opener for me as someone who has always used melee style professions versus casters.

The results highlight the ever game/life challenge that perception is not always reality, perfect example is that 40/40 is really 36/36, mind blowing!

Thank you for sharing the final verdict!

Chevy

Speed Clear Ele · February 21, 2020 at 11:29 AM

"I am not a statistician, but a quick google search showed that for comparing dice rolls to expected values, a chi-squared test is appropriate. So, the below table contains the observed and expected results, and the outcome of the comparison indicating how well the results match the expectations. If I understood correctly, the P value is the probability of getting the observed result if the expectations were correct."

Well, no a chi Squarred Distribution is used in a chi Squarred Test to make sure(with a certain confidence threhshold) that the data collected(statistics) follow or not a certain distribution. The random function in Computer Science isn't really random, so I don't think that khi squared is the way to go here but anyway ~~.

In order to do that you'll have to fix a threshold that will condition wether or not you accept the null hypothesis .

The method below comes from a statistical textbook, I haven't worked with Chi Testing before, only studied a bit about Chi Distribution, so perhaps it has flaws which I'm keen to correct if pointed out:

Let's call this threshold α = 0.05 ( ie : we'll build a 95 tolerance interval )

Then you proceed onto the sample collection which you did.

You collected 2859 sample.

Now let's start resuming stuff in an array.

10/10/10	0	2	4	8	Total
Theorical(%)	72.9%	24.3%	2.7%	0.1%	100%
Data Count	2016	767	? c_4+c_8=76	? c_4+c_8=76	2859
Theorical From Data	2192.853	694.737	problem	problem v2

You already have a problem here because you joined the 4 & 8 events together.

PRovide me with the complete dataset and I could help you continuing

Also where does that 9.95 comes from ?

I can't read it anywhere in any cell of the chi squarred table for any degree of freedom.

Considering you have 4 different types of data the degree of freedom is generally r=k-1 where k denotes the number of types of data you're collecting(columns in your array), we can try with r=4 but since all events aren't independent(ie : if you have the amount of sample for 0 2 4 & total, you can deduce the amount of sample for 8), we should go down to a degree of freedom r=3.

And since we fixed α = 0.05 , then your Chi value should be 7.815 ( \mathbb{P}(X \leq 0.95)_{ r=3} = 7.815)

https://online.stat.psu.edu/stat414/node/147/

Also if theres any statistician here I'd happily take lessons from you if anything I said above is incorrect to some extends.

Praise · February 21, 2020 at 12:43 PM

The threshold I set before starting the experiments was 0.01. It's quite arbitrary, but I always feel that the standard 0.05 is a bit too loose. The null hypothesis was 'the Envoy Staff will give the expected probabilities'.

Let's work out the 10/10/10 case. Those experiments were done with only Nature's Renewal up, so observation of 0, 2, 4x HCT is possible but the case of 8x, even though it is calculated in the background, gets capped to 4x. So I assumed that it was allowed to group them together: total expected probability of 4+8x = 2.7 + 0.1 = 2.8%. The 76 observations will include both 4x and 8x since they are indistinguishable.

The chi-squared value was calculated by putting the counts for each column separately into: [(observed-expected)^2] / expected and then summing. This value was then used to calculate the right-tailed P with the excel formula =CHISQ.DIST.RT().

There are 3 different types of data effectively (since 4 and 8x are indistinguishable in the observations), so 2 degrees of freedom.

Quote from Speed Clear Ele

The random function in Computer Science isn't really random, so I don't think that khi squared is the way to go here but anyway ~~

That's a very good point I hadn't thought about. Do you know if there are any standard tests or corrections we can use instead?

Many thanks for your help.

Speed Clear Ele · February 21, 2020 at 2:45 PM

Quote from Praise

The threshold I set before starting the experiments was 0.01. It's quite arbitrary, but I always feel that the standard 0.05 is a bit too loose. The null hypothesis was 'the Envoy Staff will give the expected probabilities'.
Let's work out the 10/10/10 case. Those experiments were done with only Nature's Renewal up, so observation of 0, 2, 4x HCT is possible but the case of 8x, even though it is calculated in the background, gets capped to 4x. So I assumed that it was allowed to group them together: total expected probability of 4+8x = 2.7 + 0.1 = 2.8%. The 76 observations will include both 4x and 8x since they are indistinguishable.
The chi-squared value was calculated by putting the counts for each column separately into: [(observed-expected)^2] / expected and then summing. This value was then used to calculate the right-tailed P with the excel formula =CHISQ.DIST.RT().
There are 3 different types of data effectively (since 4 and 8x are indistinguishable in the observations), so 2 degrees of freedom.
And in fact I see now that I made a typo in the formula for P in the 10/10/10 set! With 2 degrees of freedom, it should have been P = 0.007. (I will correct the original post after feedback on whether this is actually the way to go)

That's a very good point I hadn't thought about. Do you know if there are any standard tests or corrections we can use instead?
Many thanks for your help.

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No, I despise statistics so I can't help you on that. I'll try to look over in the books I have but there's nothing that comes to my mind atm

Speed Clear Ele · February 21, 2020 at 2:58 PM

Nevermind, we can generate truly random numbers using entropy, I completely forgot about that but I don't think that gw1 is using that kind of technique.

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