Drop chance probability
Probability is a greatly misunderstood area of math that impacts most areas of WoW gameplay, but none so intensely debated as drop chances. You don't have to be a math expert to want to know how many times you need to kill a boss to have even odds of seeing that drop you're seeking. Unfortunately everyone seems to be saying something different about how probability works.
If you hope to get the rare Deathcharger's Reins mount from Baron Rivendare for example, we know that it has a 1% drop chance. That means that every time you kill the Black Baron you have a 1% chance of getting the mount. 1% on the first kill, and 1% on the 100th kill. However, over the course of 100 kills, you have a much higher probability of getting the mount. But not 100%. Never 100%.
Join me after the cut where we take a friendly and gentle look at understanding probability, and give you a cool tool to automatically calculate drop probabilities for you!
Your Chance on Each Attempt is the Same
If your mount has a 1% chance of dropping, it will always be 1% on every single attempt. The Gambler's Fallacy trap that many fall into is assuming that previous results will change future results -- or put in WoW terms, "I've run this 50 times, so it must be really likely to drop now!" And it really feels like it should be that way. But it's not any more likely on the 50th kill or the 500th kill, it's still 1%. Every. Single. Time.
As an example, let's say you're flipping a coin. There's a 50% chance that it lands heads. You flip and get tails. Next time the chance is still 50%. Tails again. The next chance is still 50%. The past results don't affect the chance of the next result. That's randomness for you.
Your Chance Over Multiple Attempts Increases
Even though your chance on each single attempt always remains the same, the probability of getting your drop over the course of multiple attempts increases. I know at first this sounds like crazy talk that contradicts what we just discussed, so another example is in order:
We're flipping our coin again. We know that we have a 50% chance of getting heads on any given toss, and it doesn't matter at all what results we got before. But I think we can all agree that if we flip a coin 100 times it's very, very likely that we'll get heads at least one of those times. The chance on the first toss is 50%, and on the 42nd toss it's 50%, and on the 100th toss it's 50%. But over the course of 100 tosses, the probability of getting heads is way more than 50%. (In fact, the chance is 99.999999999999999999999999999921% that we'll get heads at least once.)
So the more often we down a boss, the more likely we are to see the loot that we want. Instinctively we all know this, that's why we keep going back and keep going back, and eventually our persistence is rewarded. Sometimes you'll get lucky, and sometimes you'll get unlucky, and the more you try the better your odds are overall. But the chance will never be 100%. It's never guaranteed.
How to Calculate it for Yourself
The formula to calculate your drop chance ( x ) over any given number of runs ( y ) is this:
1 - ( ( 1 - x ) ^ y )
Thus we can learn that if we kill Baron Rivendare 100 times, we have a 63.4% chance of getting the mount drop at least once.
Drop Chance Probability Calculator
But why do math yourself when the internet can do it for you! Just plug your drop chance and number of attempts into this tool to figure out the probability of seeing your drop. You can find estimates of the drop chances of most items on Wowhead, and be sure to check the comments to see if better drop chance info has been found than the estimates.
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*Disclaimer: this script uses some rounding after lots of decimal places, so when very large numbers are input it can give you a 100% probability due to rounding errors. Your chance is never 100% unless the drop chance is 100%, and if you get that result, you can assume it's very, very, very close to 100%, but never quite there! Obviously entering negative numbers will get you silly results.
