### 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* - 1 with quadruple
*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*.