View Full Version : A note on drop rates and probability

09-08-2012, 11:55 AM
Since there seems to be a new post every week asking if drop rates are changing for a specific item, I figured I'd write a little bit about the probability for drops, and when to really concern yourselves that the drop rate has changed.

Note: This assumes drops are truly random, which we don't necessarily know is the case.

As there are only two outcomes for a drop (does drop and does not drop), drops follow a binomial distribution. For this example, we will use the following data (stealing from mxz's great spreadsheet).
Drop rate: 30% (or 0.3)
Energy required per job: 518

First, if we want to calculate the mean number of drops for a given number of jobs completed, the mean is simply: n_jobs * drop_rate.
So for 10 jobs we would expect a mean drop rate of 3 items.

The standard deviation of such a scenario is given by the square root of n_jobs * drop_rate * (1 - drop_rate).

So for 10 jobs we would have a standard deviation of sqrt(10*.3*.7) = 1.44. 0 drops is only two standard deviations away. This result can occur ~5% of the time.

What this tells us: If you do 10 jobs in a row and don't get any drops, this does not mean that the drops have changed. When we think that this occurs, we are most likely subjecting ourselves to confirmation bias, thinking that GREE is f***ing us over (which obviously has happened in the past).

Alternatively, we can calculate the probability of misses in a row at just (1 - drop_rate)^n_jobs. As people are constantly farming, how many jobs until we should be concerned that drop rates may have changed? To do this, you can set an arbitrary threshold (let's say 0.5% occurrence, or 1/200 probability).

For this, you can just then take (1 - drop_rate)^n_jobs and look at when the number of jobs gets below a given threshold. As drop_rate is 0.3, solving for n_jobs, yields 15 jobs or approximately 7500 energy. For a standard refresh of energy, this is 43 hours of constant energy usage. Chances are, that since most of us do sleep, we won't get to use all of this energy. So lets say 2.5 days of no drops before you should really get concerned.

The take away message: There is a very good chance that a lot of the complaints result from too small of sample sizes. Certainly, polling other people can help, but thinking about true data distributions can hopefully reduce the number of threads that pop up...

09-08-2012, 04:00 PM
Didn't check your math but this is a solid post with good advice.

I do believe it is not truly random as a few people have heard me preach. I'm not saying you make your own luck, but minimizing "losses" is a good idea. If you don't get a drop wait a minute or two before trying again.

09-08-2012, 05:00 PM
The phrase "casting pearls before swine" is appropriate here. Thanks for the effort, but it's wasted here.