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Drop rate

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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:

Drop rateEdit

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 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 monster 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; the probability will infinitely approach 1 (100%) with each roll on the drop table. For example:

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:

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

Which is approximately 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 visage.

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:

& \ 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 \\

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

Binomial modelEdit

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 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:

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

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

Elusive dropsEdit

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.

Icon Item Dropping monster(s) Drop rate Kills
Dragon full helm
Dragon full helm Mithril dragon, Brutal black dragon Very rare (1/32,768)[1] 75,450[1]
Dragon chainbody
Dragon chainbody Dust devil, (Thermonuclear) Smoke devil, Kalphite Queen Very rare (1/32,768)[2][3] 75,450[2][3]
Draconic visage
Draconic visage (Brutal) Black, Iron, Steel, Lava, Mithril dragons, Skeletal Wyvern, King Black Dragon, Brutal blue dragon, Brutal red dragon Very rare (1/10,000)[4] 23,025[4]
Dragon warhammer
Dragon warhammer Lizardman shaman Very rare (1/5,000) 11,512
Elysian sigil
Elysian sigil Corporeal Beast Very rare (1/4,095) 9,428
Arcane sigil
Arcane sigil Corporeal Beast Very rare (1/1,365) 3,142
Spectral sigil
Spectral sigil Corporeal Beast Very rare (1/1,365) 3,142
Dragon pickaxe
Dragon pickaxe King Black Dragon, Chaos Elemental, Callisto, Venenatis, Vet'ion Very rare (1/1,500)[5] 3,453[5]
  1. 1.0 1.1 1/250 from chewed bones (and 574 bones for 90% chance)
  2. 2.0 2.1 1/2,000 from Thermonuclear smoke devil (and 4,604 kills for 90% chance)
  3. 3.0 3.1 1/128 from Kalphite Queen (and 294 kills for 90% chance)
  4. 4.0 4.1 1/5,000 from King Black Dragon (and 11,512 kills for 90% chance)
  5. 5.0 5.1 1/1,500 from King Black Dragon only (3,453 kills for 90% chance) and 1/256 from other Wilderness bosses (588 kills for 90% chance)

See alsoEdit

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