## 04 February 2018

### WildStar: Proc Chance of Prime Drops Result Update

This was a bad idea and I'm kinda running out of time to write this post so here we go in three, two, one...

### Recap

So you might or might not remember that I was wondering about the proc rate of items in prime expeditions, or any prime content for that matter, in WildStar. So to check whether or not the myth of it being 25% is correct I started my drop research. Of course, starting off the sample size is small so the values are anything but accurate. I've now continued for another week to get more samples and that's why I'm here now.

### Research State

So the current state is almost as I planned it. My goal was to reach a total of 100 samples. I've... reached 96 samples. I know, I know, 100 samples are still like nothing. However, it's at least a number I have proof of and that's something that matters to me. Well without further ado let's look up my old research and start the comparison! That's something I haven't done yet on my blog.

So back in my first research, I had
• 44 samples
• 35 without a proc
• 5 with only one proc
• 4 with a double proc
The current state is
• 96 samples
• 68 without a proc
• 19 with only one proc
• 8 with double proc

### Calculating the Chances

It's nice looking at those numbers but we want to see chances so let's go calculate the chances. The only interesting values are how many items of these samples had at least one proc and how many didn't.

In our first example it were 4 + 5 = 9 items so 9 / 44 = 0.204545 or 20.45%.
Currently we've got 19 + 8 + 1 = 28 items with at least one proc from 96 samples so 28 / 96 = 0.2917 or 29.17%.

As you can see our proc rate jumped by about 8.7% and is now far above the 25% people believe it to be. Well with only 96 samples the number still fluctuates a lot.

### Concept of Checking

We use math to check if everything went as it's supposed to be and whether or not we've made mistakes. We can use this checking to see if our number is accurate and how far it might be off.

If we assume to have a 25% chance to proc an item and the chance does not change, additionally we can proc an item multiple times, it's safe to say that our chance to get two procs is the chance for the proc to occur and then the same chance again. This means our chances in this scenario are the following:

The chance for no proc: 75%
Chance to proc: 25%
Chance for two procs: 25% * 25% = 6.25%
Chance for three procs: 25% * 25% * 25% = 1.5625%
Chance for four procs: 25% * 25% * 25% * 25% = 0.390625%

and so on. This means if we calculate the chance on how many items at least proc'd twice the chance we get here must equal the chance for one proc multiplied by itself. We can continue this throughout all our occasions. You can call this forward checking.

In our example:
25% * 25% should equal 6.25%. If not our check fails. If it does, perfect.

Well obviously if I'm naming this "forward checking" there must be another type of checking. Not hard to guess, the opposite I'll call it backward checking. Backward checking works by doing what we just did backward. We take the chance of for example two procs and divide it through the chance to proc at least once. The result should be the lower value.

In our example:
6.25% / 25% should equal 25%. If not our check fails. If it does, perfect.

### Forward Check

So let's apply this forward check to our newest numbers.
Our chance for one proc is 29.17%. So the chance for two procs should be 29.17% * 29.17% = 8.51%. So let's check out what the chance actually is. We got nine items that have at least a double procs from 96 samples, that's a chance of 9 / 96 = 0.09375 or 9.375%. So as you can see our chance for double procs isn't too far off from the chance for only one proc. Of course with our sample size, this could just be a coincidence.

We can do the same with the quadruple proc. The chance for this one should be our chance for at least one proc multiplied by itself four times.

29.17% * 29.17% * 29.17% * 29.17% = 0.7240%

With us having only one such proc from 96 samples that's a chance of 1 / 96 = 0.0104 or 1.04%. This one is a bit too high. Now let's do the other check.

### Backward Check

Without chance being 9.375% for at least a double proc if we divide this through our chance of at least getting one proc the result should be the same chance we divide through. If not our numbers are still off of what they should be. It's important for them to match up but more to this later.

9.375% / 29.17% = 32.14%

Now that's off by about 3%.

### Conclusion

So as you can see all our checks failed forward and backward. This was to be expected though. A sample size of 96 is still not enough. So what do these checks tell us? If the numbers don't match up we can assume one of two things.
• The system does not work as we assumed (the chances change)
• Our chances are off, wrong or incorrect
So what went wrong? In our first forward check, the chance we've calculated was 8.51% but we got 9.375%. This means we've gotten more at least two times procs than we were supposed to if we assume the at least one proc chance of 29.17% to be correct. Same with our second forward check. We've got more quadruple procs than our proc chance of 29.17% for at least one proc allowed. So we can say 29.17% is wrong. So what must change for our number to get accurate? We need to get either
• less at least double procs
• more at least one procs and more without any proc
Our backward check more or less tells the same. The resulting chance from our calculation is slightly higher. This is the result of our at least double proc being too high or our at least one proc being too low.

So what can we take from this? The research kicks us in the face with a "keep on researching".
and with this, I'll leave for now. If I make another post on this it's most likely going to be a test of significance.

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