Drop rate

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 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 a 75% drop rate from Chickens

A common misconception is that you are guaranteed that item when you kill the NPC $$x$$ number of times, where $$\frac{1}{x}$$ 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 yield the item in $$x$$ kills is 1 minus the probability that it will not drop that item in $$x$$ kills, or $$1 - \left(1 - \frac{1}{x}\right)^x$$.

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

$$1-\left(\frac{14999}{15000}\right)^{15000}$$

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 34538.

Estimation
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 Wikia 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 six different groups displayed below.

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

Trivia
The rarer a drop is (or the smaller $$\frac 1x$$ becomes), the closer the probability of obtaining that item in $$x$$ kills approaches $$1 - \frac 1e$$, or approximately $$0.63212$$. 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 $$e$$:

$$e = \lim_{n \to \infty} \left(1 + \frac 1n\right)^n$$