Drop rate

"Rng or RNG" redirects here. For the Combat skill, see Ranged.

The 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 monster 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, for example, with a drop rate of "1 in 5" does not equate to: "This item will be dropped after five 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 monster $n$ number of times, where ${\frac {1}{n}}$ is the drop rate, or that the likelihood increases with every kill (also known as gambler's fallacy). You are never guaranteed anything, no matter how many of that monster you kill. The chance of receiving a specific item on any given kill remains constant. This means that a player who has killed a monster a thousand times without receiving a drop, has the same chance of receiving that drop within the next hundred (or any other arbitrary number of) kills, as somebody who has not killed that monster once. Calculating the chance of receiving a drop within a number of kills only works for future kills. Probability functions never take the past into account. The only conclusion one can make, when he has not received a drop after killing a monster many more times than the drop rate appears to require, is that what has just happened should have been very unlikely. Unfortunately, unlikely things happen, and give no guarantee for any luck in the future. Chances are also not additive. If the chance of receiving an item is 10% in a 100 kills, it is not 20% in 200 kills.

Some players claim they have 'good' or 'bad luck', because they are often lucky or unlucky, but this is merely a psychological sentiment, and is not based on any real properties of the player's account. All players have the same chance to get the same luck at any given point in time. The formulas in this article can be used to calculate the chance of receiving a drop in the next $n$amount of kills, which will only tell you something about the likelihood of receiving this drop. Do not take anything for granted.

If the King Black Dragon is expected to drop a draconic visage once out of 5,000 kills, then the probability of getting a drop from one kill is as follows:

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

That is 0.02%. To find the drop chance in 5,000 kills, we can raise the equation inside the parenthesis to the 5,000th power, which yields a meagre 63.2% chance of getting a draconic visage, i.e. $1-\left({\frac {4999}{5000}}\right)^{5000}\approx 0.632$.

Similarly, we can solve for the number of king black dragons you need to kill to have a 90% probability of getting one when you kill them:

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

This yields the answer 11,512 meaning that you need to kill 11,512 for a 90% chance of getting a draconic visage.

Extra information

Again, using the King Black Dragon expected to drop a draconic visage once out of 5,000 kills, the probability of getting said drop twice from two kills or back-to-back is as follows:

${\begin{aligned}&1-\left[1-\left({\frac {1}{5000}}\right)^{2}\right]\\=&\ 1-\left({\frac {24999999}{25000000}}\right)\\=&\ 1-0.99999996\\=&\ 0.00000004=0.000004\%\\\end{aligned}}$

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 binomial distribution.

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 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 draconic visage in a task of 234 Skeletal Wyverns, we would plug into the equation:

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

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

See also

• Drops
• Rare drop table
• Items
• Kill count
• Bestiary
• Player identification number