Drop Rate fallacies

[ailor]

Many of us have several times spent a lot of time farming rare items in wow.
Either it’s a Zul Gurub tiger or Baron’s mount and even for some hardcore grinders Hyacinth Macaw parrot (1/10000 drop rate).
The question is how many of you are actually aware the chances that you have to get your desired loot.
There are 2 parameters to approach the drop rate. The first is the chance and the second it the probability.

In the case of Baron’s mount the chance is 1% and no matter how many times you have killed him the chance of the next kill will still be 1%. Theoretically you can keep killing him forever without getting his mount ever.

On the other hand though we have the probability approach which measures the propability to get the desired loot after X tries.
The equation of the propability is: F(x) = 1 – (1 – a%)^x
Where X is the times you kill the Baron and a% is the drop rate (1% for this case).
In other words for the Baron the formula is: F(x) = 1 – (1 – 0.01)^x = 1-(0.99)^x

Here is a graph for this formula:


Uploaded with ImageShack.us


As you can see less times you have killed him the higher is the probability rate. After the 180 kills the probability rate drops significally.

Here is a table with some sample values:

10 9.56%
20 18.21%
30 26.03%
40 33.10%
50 39.50%
60 45.28%
70 50.52%
80 55.25%
90 59.53%
100 63.40%
110 66.90%
120 70.06%
130 72.92%
140 75.51%
150 77.85%
160 79.97%
170 81.89%
180 83.62%
190 85.19%
200 86.60%
210 87.88%
220 89.04%
230 90.09%

Conclusions:

Before starting farming a 1% drop rate loot note that there is a 10% probability to kill it 280 times without seeing the loot.


Sources: Gambler's fallacy - Wikipedia, the free encyclopedia

[kickassxd]

Thats wrong.

You saying that the 1% drop mount is like when there are 100 balls (99 red and 1 blue) in a bag and you stick your hand into the bag without looking hoping to randomly choose the blue ball. And each time you retrieve a red one you throw it away, raising the probability of randomly retrieving a blue ball because there are less balls in the bag. THIS IS NOT THE SITUATION!

Each time you kill Baron you get a NEW different bag of 100 balls. The probablilty of getting a blue ball is 1% all the time. You can be lucky and get it first time or never ever get it at all. That equation cant be used in this situation because drop rate DOES NOT change after X tries.

The probability each time you kill him of getting the mount is 1% ALWAYS for every single try. IN THEORY AND PRACTICE!!

[ailor]

Thats wrong.

You saying that the 1% drop mount is like when there are 100 balls (99 red and 1 blue) in a bag and you stick your hand into the bag without looking hoping to randomly choose the blue ball. And each time you retrieve a red one you throw it away, raising the probability of randomly retrieving a blue ball because there are less balls in the bag. THIS IS NOT THE SITUATION!

Each time you kill Baron you get a NEW different bag of 100 balls. The probablilty of getting a blue ball is 1% all the time. You can be lucky and get it first time or never ever get it at all. That equation cant be used in this situation because drop rate DOES NOT change after X tries.

The probability each time you kill him of getting the mount is 1% ALWAYS for every single try. IN THEORY AND PRACTICE!!

I think you got it all wrong. You are mixing up chance and probability. I agree that every kill has 1% chance BUT ... the probability for not getting it after x tries is derived from the formula I presented.

Have a look also here, It might help you: Law of large numbers - Wikipedia, the free encyclopedia

[Yamakid]

The thing is, math doesnt have ANY use on this.. not at all..
This is all about luck..

Someone might get it on the first try, someone might not get it after he tryed it a million of times.. so imo Math doesnt apply here..
Tho, thanks for the effort, don't see this as a flaming post

[Parrky]

Math does have use on this you've just bastardized it to the point of no return, nice one!

[ohmaigawd]

Thats wrong.

You saying that the 1% drop mount is like when there are 100 balls (99 red and 1 blue) in a bag and you stick your hand into the bag without looking hoping to randomly choose the blue ball. And each time you retrieve a red one you throw it away, raising the probability of randomly retrieving a blue ball because there are less balls in the bag. THIS IS NOT THE SITUATION!

Each time you kill Baron you get a NEW different bag of 100 balls. The probablilty of getting a blue ball is 1% all the time. You can be lucky and get it first time or never ever get it at all. That equation cant be used in this situation because drop rate DOES NOT change after X tries.

The probability each time you kill him of getting the mount is 1% ALWAYS for every single try. IN THEORY AND PRACTICE!!

He didnt say that after 230 kills the Baron will have 90% drop rate for the mount. He said that 90% of the people that killed him 230 times will have the mount, and only 10% of people that killed him 10 times will have the mount. The drop rate always remains the same.

[bluesius]

Thats wrong.

You saying that the 1% drop mount is like when there are 100 balls (99 red and 1 blue) in a bag and you stick your hand into the bag without looking hoping to randomly choose the blue ball. And each time you retrieve a red one you throw it away, raising the probability of randomly retrieving a blue ball because there are less balls in the bag. THIS IS NOT THE SITUATION!

Each time you kill Baron you get a NEW different bag of 100 balls. The probablilty of getting a blue ball is 1% all the time. You can be lucky and get it first time or never ever get it at all. That equation cant be used in this situation because drop rate DOES NOT change after X tries.

The probability each time you kill him of getting the mount is 1% ALWAYS for every single try. IN THEORY AND PRACTICE!!

Well, now if that was what hes saying, the OP Would not have stated 230 runs yield 90% chance for mount now would it?

Im guessing hes well aware of the thing you are trying to state, but in applied maths, we can close up to certain limits.
If there is a 25% chance for me having item 'x' dropp from creature 'y', and i kill&loot 10 000 creature 'y', im pretty god damn close to 100% chance of actually having acquired item 'x'.

You really need to wake the **** up, and read the shit your commenting on.

Two different things:

• Chance of a item dropping ( This value DOES NOT CHANGE )

• Probability of obtaining a item through rare drop. (This value WILL INCREASE when killing increased amount of mobs )

This is hard to even start to explain if you have no prior knowledge of the Monte Carlo fallacy, and i'm not even going to try, seeing as op has added a link to the wikipage you are better off reading here. If i want to bring anything to this table then it will be the 2 points above, which i hope everyone realizes, but few people know how to actually apply in the maths they use.

[Vixxi]

Copy paste more from wowhead comments lol.

[ailor]

Copy paste more from wowhead comments lol.

The guide was written from scratch. If you have any link from wowhead that shows it is a copy paste please do it and stop throwing accusations without proof.


Note that the reason that I am making guides is to help people playing wow to do it even better and also to understand game mechanics.