Drop rate

Drop Rate is the frequency at which a monster is expected to yield a certain item when killed by players. When calculating a drop rate, divide the number of times you have gotten the certain item, by the total number of that NPC that you have killed. For example:


 * Bones have a 100% drop rate from chickens.
 * Feathers have approximately a 75% drop rate from chickens.

Drop rate
All items have a chance of being dropped that is expressible as a number, their drop rate. Drop rates are not necessarily a guarantee; an item with a drop rate of "1 in 5" does not equate to "This item will be dropped after 5 kills." While each kill does nothing to increase the drop rate itself, it is trivial to state that more kills gives rise to more chance overall.

A popular misconception is that you are guaranteed that item when you kill the NPC n number of times, where $$\frac{1}{n}$$ is the drop rate. You are never guaranteed anything, no matter how many of that monster you kill. For example:

If the King Black Dragon is expected to drop a Draconic visage once out of 5,000 kills, then the probability that you will get at least one drop in 5,000 kills is:



\begin{align} & 1-\left(1-\frac{1}{5000}\right)^{1} \\ = & \ 1-\left(\frac{4999}{5000}\right)^{1}\\ = & \ 1 - 0.9998 \\ = & \ 0.0002 \\ \end{align} $$

Which is approximately 0.02%. Similarly, we can solve for the number of KBDs you need to kill to have a 90% probability of getting one when you kill them:



\begin{align} & \ 1-\left(\frac{4999}{5000}\right)^{x} \approx 0.90 \\ & x = \frac{ln(1-0.9)}{ln(\frac{4999}{5000})} \\ & x \approx 11511.774 \approx 11512 \\ \end{align} $$

Which yields the answer 11,512. Thus, we have shown that, while being counterintuitive, drop rates are not what they seem to be.

Binomial model
Given a known value of $$\frac{1}{x}$$, the chance of receiving such an item $$k$$ times in $$n$$ kills can be calculated using.

The probability of receiving an item $$k$$ times in $$n$$ kills with a drop rate of $$\frac{1}{x} = p$$ follows:
 * $$ \binom n k p^k(1-p)^{n-k}$$ where $$\binom n k =\frac{n!}{k!(n-k)!}$$

For finding the probability of a obtaining an item at least once, rather than a specified number of times, we can drop the binomial coefficient and simply the equation to:
 * $$1 - (1 - p)^x$$

Where $$(1-p)^x$$ is calculating the probability of not receiving the item, and we use that to calculate the inverse.

For example, it is known that the drop rate of the Draconic visage is $$\frac{1}{10000} = 0.0001$$. If we want to know the probability of receiving one visage in a task of 234 Skeletal Wyverns, we would plug into the equation:

\begin{align} & 1 - (1 - 0.0001)^{234} \\ = & \ 1 - 0.9999^{234} \\ \approx & \ 1 - 0.97687 \\ \approx & \ 0.023129 \end{align} $$

Giving us the answer, we have approximately a 2.3% chance of receiving a visage during this task.

Elusive drops
Below is a table of the rarest and most sought-after drops in Old School RuneScape. Also, the kill count or number of kills required is based on a 90% probability of getting the drop.