# Drop rate

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**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.

For example, if dust devils are expected to drop a Dragon chainbody once out of 15000 kills, then the probability that a player will get at least one Dragon chainbody after 15000 kills is

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:

### Confidence IntervalsEdit

It is given to us that the confidence interval for the success probability of a model may be expressed as the formula^{[1]}:

*Where:*

- - 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:

Confidence level | ||
---|---|---|

0.2 | 80% | 1.28 |

0.1 | 90% | 1.64 |

0.05 | 95% | 1.96 |

0.01 | 99% | 2.57 |

- 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:

And...

What this means is that we can be about 95% sure that the drop rate of Draconic Visages (from Black Dragons) is somewhere between 1 in 31 and 1 in 129.

- 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 .
^{[2]}

## Trivia Edit

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 .

## Notes Edit

**^**Mayfield, Philip.*Understanding Binomial Confidence Intervals***^**Wikipedia -*Binomial proportion confidence interval*.