Statisticians, pencils up!
I want to maximize my chances to loot an item with 0.5% drop chance. I know farming the drop on multiple characters helps, obviously, but even if I farmed it on 200 characters the chance would still not be at 100%. It would also not be at 0.5% anymore. So out of curiosity, what would be the drop chance with 15 characters, for example?
What’s the equation for this?
.5%
The chance for the item to drop does not change.
The odds for you to see the item change depending on the number of runs, but odds and chance are two very very different things in math.
Each attempt is still .5%.
Which means that odds are that in 200 attempts you will see it once. That is not a guarantee, though. That just gives you the likely outcome.
You could go 200 attempts and never see it. You could go 5 million attempts and never see it. You could go once and see it.
Probability is funny that way.
If you want the mathematical formula edit, derped and pushed the button before I finished I believe the math formula is Odds of event multiplied by number of attempted events. Since the chance doesn’t change from event to event, there’s nothing to subtract or modify, so it should be a fairly linear number.
Google may have a more accurate formula, but:
Odds: .05(Attempts) = Odds of seeing item within that number of events.
Awesome post, thank you for taking the time to write this. I was not aware of the odds factor. I always thought there was no place for stuff like floating variables in mathematics. It was all set in stone, like a natural law. But I guess statistics aren’t 100% pure mathematics. And frankly, I was kinda hoping for a better outcome for me.
i have my own formula. it’s a conditional formula.
it starts with a simple mathematical proposition that can be expressed in basic English: do i want it?
yes: it will not drop until a few years after i forget it exists.
no: it will drop within the first 10 rolls.
want it? i didn’t even know it was a thing: it will drop on the first roll.
yes, but i PRETEND not to want it by whistling casually 
: it will drop sooner, rather than later.
does someone else in the group want it? and if it drops for me will it be trade-able? if yes, but no: then it will drop on the first roll. and they’ll be SOOOOO TICKED. if yes, and yes, then it won’t drop. if no, and no… i’ll get disconnected.
this all may sound unscientific, but i can show you proofs. 
of course i’m being silly, but it sure feels like it sometimes 
Statistics is 100% Mathematics.
edit: i guess there is a difference between pure and applied math. let me go read more.
edit: 2…Statistics is applied mathematics.
It’s still pure math; it just doesn’t necessarily work out how you’d necessarily expect if you just look at it at face value. Basically, if the chance of a particular outcome is neither one (always happens) or zero (never happens), the chances of it happening every time will go down with every iteration because it’s less than 0 and multiplies by itself (assuming each chance doesn’t impact the next; I’m sticking with simple probability for now).
For a simple example, think of a coin flip.
One flip is .5^1 chance of getting a heads every time, or 50%.
Two flips is .5^2 chance of getting a heads every time, or 25%
Three flips is a .5^3 chance of getting heads every time, or 12.5%
And so on. The chances of it happening every time get lower quickly but they never hit zero. The formula in your case for not getting it is .995^X where X is the number of runs.
Wowhead might say 0.5% chance but the true rng mechanics for drop rates are a secret blizzard said they will never reveal.
In the case of mount drops from rares, we can use something called the geometric distribution to calculate the probability of getting a success after a certain number of trials. In this case a success is the mount dropping and a trial is looting the rare.
the requirements for using the geometric distribution are
One rare kill does not affect the drop chance of another so we meet this condition
Here there are only two outcomes the mount drops or it doesn’t
The drop chance is always 0.5%
The mean value of a geometric distribution is 1/p (where p is the drop chance as a decimal) which gives a good estimate for the MINIMUM amount of kills you can expect it to take. For a 0.5% drop chance that would be 200 kills, meaning for 15 characters each killing the rare daily the minimum amount of days would be 14 (13.33 rounded up).
However there is no strict maximum number of attempts, it could be infinite. But for a 90% chance of getting the mount to drop you would need to loot the rare 460 times(31 days) and for a 99% chance you would need to loot the rare 918 times(62 days).
One thing that makes this more complicated is that when you do 200 trials, it could drop 0 times total, 1 time total, 2 times total, 3 times total, etc. Of course, you just want to know the odds that it will drop at least once, but not necessarily just once. Best way to figure that is to figure the chance it will drop ZERO times, and then from that tidbit you know the chance it will drop AT LEAST ONCE. The chance it will not drop is 99.5% or .995 The chance it will not drop in 200 tries is then .995 to the 200th power (.995 x .995 x .995 …) Let say it turns out the odds of it not dropping at all is 84%, then the odds of it dropping at least once is 100% minus that, or 16%
Yes this is another way to calculate it. Doing that method is the same as using another distribution called the binomial distribution which can tell you the probability of getting X success in N trials. If you solve for 0 success in 200 trials and do 1 - P(X=0,N=200) you would get the probability of getting at least one success.
As it turns out both methods give very close answers, using the geometric distribution you get p=63.48% and with the binomial distribution you get 63.30%
90% chance for one month with 15 characters. That’s doable. But there’s a possibility that I deleted it once or twice, when I didn’t care at all about it. And I read that Blizz has some algorithm that could punish me for that. It’s still very encouraging what you guys wrote. Thank you.