imported>Surafbrov at 16:32, 20 July 2023

2023-07-20T16:32:58Z

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Syntax: {{t|CumulativeDropProbability|p{{=}}0.001}}
: |p= is the probability of the item drop rate as a decimal number. This defaults to 0.001 = 0.1% = 1 / 1000.

<onlyinclude>{| class="darktable" style="text-align: center;"
|+ Probability of at least one {{#if:{{{1|}}}|{{{1|}}} dropping|drop}} in X kills
|-
! style="text-align: right" | Number of Kills
! 100 || {{#expr: ceil(ln(1 - 0.25)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.33)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.50)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.75)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.90)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.95)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.99)/ln(1 - {{{p|0.001}}}))}} || {{#expr: ceil(ln(1 - 0.9999)/ln(1 - {{{p|0.001}}}))}}
|-
! style="text-align: right" | Cumulative Probability
| {{#expr: floor(1000 * (1 - (1 - {{{p|0.001}}})^100))/10}}% || 25% || 33% || 50% || 75% || 90% || 95% || 99% || 99.99%
|-
| colspan="10" | <small>Neither the drop rate nor cumulative probability increases based on the number of monsters [[Template:CumulativeDropProbability#Computing the probabilities|you have already killed]].</small>
|}</onlyinclude>

== Computing the probabilities ==
The table shows the cumulative probability of getting at least one desired item while killing a particular number of monsters that drop the desired item with a constant probability ''p''.

Mathematically, the probability of ''not'' getting the desired drop as a direct consequence of any particular kill is (1-p). We assume that each mob drops the item independently of any previous mobs killed, so the probability of ''not'' getting a drop as a direct consequence of ''any'' of N kills is (1-p)^N. The opposite of this -- the probability of getting at least one drop as a consequence of all of N kills -- is 1 - (1-p)^N. This probability converges to 1 as N goes to infinity; one is '''not''' guaranteed to get a drop in a finite number of kills.

Note that as the mobs drop items independently of each other, the process is essentially memoryless: having killed (N-1) mobs without getting a drop, the probability of the item dropping on N'th kill is still p, as opposed to the cumulative probability for N kills.

The above describes cumulative probability P as a function of number of kills N; we can also describe N as a function of P:
: P = 1 - (1 - p)<sup>N</sup>
: N = log(1 - P)/log(1 - p)
: N should be rounded up to an integer: can't loot half a monster.

[[Category:WoW table templates]]

Template:CumulativeDropProbability - Revision history

imported>Surafbrov at 16:32, 20 July 2023