Drop Rate is the probability that a monster is expected to yield a certain item when killed once by a player. When calculating a drop rate, divide the number of times you have received the certain item, by the total number of that NPC that you have killed. For example:
A common misconception is that you are guaranteed that item when you kill the NPC number of times, where is the drop rate. You are never guaranteed anything, no matter how many times you kill that monster. The drop rate is simply the probability of getting a certain drop in one kill. The probability that a monster will drop the item at least once in kills is 1 minus the probability that it will not drop that item in kills, or , where x= number of kills, and y= drop rate.
Which is approximately 63.21%. Similarly, we can solve for the number of Dust Devils you need to kill to have a 90% probability of getting one when you kill them:
Which yields the answer . There is also an equation for computing the probability of a certain amount r of a particular drop after n amount of kills:
And if you take the sum of this equation from when r=1 until r=n you get the probability of at least 1 drop of a particular item after n kills:
It is given to us that the confidence interval for the success probability of a model may be expressed as the formula:
- - the assumed probability of success given by the ratio of successes to sample size. To clarify: if one were to gain 2 Divine Sigils after 2000 Corp kills, the assumed probability of success would be
- - this is the critical standard score such that for . This z-value may be found by checking with this table. Information on how to read this table may be found here.
- - the confidence error you wish your interval to represent. An example value may be 0.05 (this represents 95% confidence).
- - the amount of trials you've conducted. In the example used in the definition of 'p', this value would be 2000.
To save the reader time, a list of possible z-values is supplied:
- Example of usage
Consider the following case: we have killed a combined total of 500 Black Dragons and have gained 10 Draconic Visages between us. This suggests that we take and . Now let us say that we wish to create a 95% confidence interval for our p-value (this is to say that and ). Our confidence interval is constructed as follows:
- Notes on usage
- This method of calculating confidence intervals relies on being able to approximate our binomial model as a normal distribution -- as such, most statisticians will not use this method unless and .
If we let x be an arbitrary number and be the drop rate for a particular drop, the larger x gets (in other words, the rarer the drop is), the closer the probability of obtaining that item in x kills approaches , or approximately , where e is the exponential constant . We can express this limit as follows:
This follows from the definition of :
This leads to the conclusion that, given a drop rate of , the approximate chance of not receiving a drop after kills is . Note that this is only accurate for large values .