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Drop rate

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This is an old revision of this page, as edited by (Talk) at 19:02, April 28, 2012. It may differ significantly from the current revision.

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 x number of times, where \frac{1}{y} 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 x kills is 1 minus the probability that it will not drop that item in x kills, or 1 - \left(1 - \frac{1}{y}\right)^x, 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:

1-\left(\frac{14999}{15000}\right)^{x} > 0.9

\left(\frac{14999}{15000}\right)^{x} < 0.1

Which yields the answer x>34538. There is also an equation for computing the probability of a certain amount r of a particular drop after n amount of kills:

P(r,n)={}^{n}\textrm{C}_{r} p^{r}q^{n-r}
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:
\sum_{r=1}^{n}{}^{n}\textrm{C}_{r} p^{r}q^{n-r}=1-\left (1-\frac{1}{n} \right )^{n}


Drop rates are often quite difficult to obtain, as an accurate estimation of one requires thousands of kills. Because of this, some players who wish to calculate drop rates keep a list of items that a monster drops after each kill, sometimes called a "drop log." Then they calculate the percentage by dividing the number of desired drops by the total number of kills. All monsters found on this Wiki contain a list of the items they drop. Behind those items you will often find between brackets a drop rate indication for that item. The drop rate of items has been divided into five different groups displayed below.

Rarity Drop rate^(-1) Example*
Always 1 Bones
Common 2-50


Uncommon 51-100 Rune armour
Rare 101-512 Abyssal whip
Very rare 513+ Draconic visage

* Examples are only given as indication because they depend on the monster that drops it. An item dropped by a boss monster could be a common item while it would be very rare for normal monsters.


If we let x be an arbitrary number and 1/x 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 1 - \frac{1}{e}, or approximately 0.63212, where e is the exponential constant \approx{2.718281828459045}. We can express this limit as follows:

\lim_{x \to \infty} 1 - \left(1 - \frac 1x\right)^x = 1 - \frac 1e

This follows from the definition of e:

e = \lim_{n \to \infty} \left(1 + \frac 1n\right)^n<br>
 =\sum_{i=0}^{\infty} \frac{1}{i!}

This leads to the conclusion that, given a drop rate of \frac{1}{r}, the approximate chance of not receiving a drop after n kills is \left(\frac{1}{e}\right)^\frac{n}{r}. Note that this is only accurate for large values r.

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