Checking Drop Rates
Loot tables, drop rates, etc. are really tedious to check. The reason these things are so tedious is if you have no vendor or alternative to get the drops you need to farm. This means repeating the same content over and over again to check every single instance of the drop.
Calculating the chance of something to happen works via stochastic. We divide the number of instances or cases through the number of all possibilities. So if we say our item dropped three times and we ran the content 25 times we have a chance of 3 / 25 = 0.12, 12% to get that item.
However, what we want is the rate of procs. For this, we're going to assume a few rules that may or may not be given.
- The proc chance will always be the same
- Items can proc several times
- There's a limit to the procs
The limit is determined by the base item level. Each proc increases the item level by five. The maximum item level is 170. So that means a prime level 0 item, which has an item level of 65 can proc (170 - 65) / 5 = 21 times.
To get the proc chance we're gonna ignore any multi procs for now and just look at any item that procs at least once. We divide this number through the number of items we've gotten in total. The counter chance is the chance to get an item that has no proc, as in an item that has the base item level.
To correct errors and check the values, a double proc must have the chance of the single proc chance multiplied by itself. Vice versa, the double proc divided by the single proc chance must result in the single proc chance.
Gathering Samples
To gather the samples we need to run easy and fast content. It would be even better if we do the same content with the same circumstances to prevent from getting unwanted values in. The fastest prime content is prime level 0. One of my favorite instances to get through fast is the expedition infestation. My runs were around five to six minutes. So I've been running through this expedition in the past days and trying to get a small number of samples:
- 44 items in total
- 35 without a proc
- 5 with only one proc
- 4 with double proc
Knowing this we also know the number of items that have at least one proc is 5 + 4 = 9. We can already calculate the chance of getting an item that has no proc. To do this we divide the number of items without proc through the total amount of items.
P("no proc") = 35 / 44 = 0.7954, 79.54%
We can easily calculate the other ones as well:
P("only one proc") = 5 / 44 = 0.1136, 11.36%
P("only double proc") = 4 / 44 = 0.0909, 9.09%
Though these are only nice to know.
The actual chance that would be relevant is how often we get a proc. There are three ways to calculate this.
P("at least one proc") = 1 - P("no proc") = 1 - 0.7954 = 0.2046, 20.46%
P("at least one proc") = P("only one proc") + P("only double proc") = 0.1136 + 0.0909 = 0.2045, 20.45%
P("at least one proc") = (5 + 4) / 44 = 9 / 44 = 0.2045, 20.45%
Running our checks.
Applying our rules:
P("at least one proc") * P("at least one proc") = P("at least two procs")
Since we had no proc above two we can take P("only double proc") which is 0.0909. Filling everything in we get 0.2045 * 0.2045 = 0.0909, 9.09%. Calculating it gives us 0.2045 * 0.2045 = 0.0418, 4.18%. If we're assuming the rules we've created apply, these numbers will draw nearer.
If we reverse calculate from the double proc to the single proc we divide the double proc through the single proc. Keep in mind:
P("at least two procs") / P("at least one proc") = P("at least one proc")
The actual P("at least two procs") we have is 0.0909. So if we calculate 0.0909 / 0.2045 = 0.4445 we'll get 44.45%. Again the numbers 0.2045 or 20.45% and 0.4445 or 44.45% will draw closer to each other. So we could assume the drop chance may be between 20.45% and 44.45% at this point.
The Myth
I heard the drop chance was 25%. If we assume 20.45% and 44.45% draw closer equally we can find the middle by taking the difference and subtracting half of the difference form the higher value.
44.45% - 20.45% = 24%
24% / 2 = 12%
44.45% - 12% = 32.45%
This is just an estimate that might not be accurate at all.
On-Going
The sample size we have consists of 44 items which means there are going to be huge fluctuations in percentages for each new item we get. To be certain we need to keep on collecting data until we have enough so that the fluctuations are low enough and the difference in our checks is small enough. Most optimal would be a fluctuation lower than 0.0001 since we've rounded up to 0.01%.
Bottom Line
I'm gonna continue my research and make a new post on this next week since I had this topic planned twice accidentally. Whelp :P If you have the information somewhere I'd be glad if it's shared. Well... I'm off to get more samples now evening or night. :P
