# Thread: Probability

1. Neganova and Daedelus are correct but they're purposefully avoiding the meaningful and true mathematics provided by voidspark. If someone's goal is to get the mount one time. The number of attempts they make do indeed increase the chance of having that one time occur. The chance for each individual attempt is unchanged unless Blizz is doing something fishy on their end like with the coin rolls. However, the chance that "NONE of 458 attempts will produce a mount drop at a 0.79% drop rate is indeed less than 1%"

What does this mean for the OP (and any other interested parties)? That if 100 people collectively made 458 attempts each. Statistically 99 of them would have found the mount, and 1 would still be looking for it. Each and every one of their 45,800 attempts would have had the same 0.78% chance, and while we're in the realm of mathematics, the mount would have dropped 357 times meaning that a few of those 100 people got it twice (or more!) the lucky dogs.

2. Ah, now I see the difference between voidspark/7seti and Daedelus and what void is getting after...

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Originally Posted by kreationkin
Neganova and Daedelus are correct but they're purposefully avoiding the meaningful and true mathematics provided by voidspark.
Not purposely.

Ignorantly

At least on my end.

3. Originally Posted by kreationkin
If someone's goal is to get the mount one time. The number of attempts they make do indeed increase the chance of having that one time occur. The chance for each individual attempt is unchanged unless Blizz is doing something fishy on their end like with the coin rolls. However, the chance that "NONE of 458 attempts will produce a mount drop at a 0.79% drop rate is indeed less than 1%"
Pretty much, however I used a 1% drop rate for the figure of 458. The 0.79% is itself another estimate by Wowhead, and it seems that the drop rate for most dungeon rare mounts hovers around 1% (some are higher, some are lower). Only Blizzard actually knows the true drop rate!

Also, only runs in the future increase the chance, not runs in the past (but you knew that).

Originally Posted by kreationkin
What does this mean for the OP (and any other interested parties)? That if 100 people collectively made 458 attempts each. Statistically 99 of them would have found the mount, and 1 would still be looking for it. Each and every one of their 45,800 attempts would have had the same 0.78% chance, and while we're in the realm of mathematics, the mount would have dropped 357 times meaning that a few of those 100 people got it twice (or more!) the lucky dogs.
Would be 458 using my data (1% drop rate). It's actually another interesting part of statistics to see what your mount distribution would look like after a lot (and I mean, a lot) of runs. If you did 100,000 runs your expected # of mounts is ~1,000 (of course, the chance you actually get 1,000 is quite small!). You can give a pretty good confidence interval of roughly how many you'd have though... that said I think most of us would stop after the first, and end up not getting near 100,000.

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Originally Posted by Neganova
Ah, now I see the difference between voidspark/7seti and Daedelus and what void is getting after... Not purposely. Ignorantly

At least on my end.
It's cool, it actually is difficult to understand, I wasn't being snide/sarcastic about that. Really interesting though if you get into it more!

4. Originally Posted by Daedelus
THERE IS NOTHING CUMULATIVE ABOUT THIS. Jesus, I give up.
There is. No one is saying that the 500th run will have a 99.3% chance of dropping the mount. They are saying that if you run 500 times, there is a 99.3% chance that you saw the mount on one of those runs.

You fundamentally don't understand what the others are saying and you are shitting up a storm about that.

5. Originally Posted by voidspark
Pretty much, however I used a 1% drop rate for the figure of 458. The 0.79% is indeed an estimate by Wowhead, and it seems that the drop rate for most dungeon rare mounts hovers around 1% (some are higher, some are lower). The 0.79%/1% is itself an estimate (with error), only Blizzard actually knows the true drop rate!
Ah! Teaches me to not pull out the calculator and do it myself first!

6. Originally Posted by kreationkin
Ah! Teaches me to not pull out the calculator and do it myself first!
lol, it probably is lower just because well... I'm not sure what their sample size is. But if the sample size is high it's a pretty good chance the drop rate is in fact less than 1%... sadly.

7. Originally Posted by Daedelus
Wrong, wrong, wrong.
No it's correct. P(X) is an increasing function. As in, the probability of getting at least one mount drop in 20 kills is higher than the probability of getting at least one mount drop in 10 kills.

You're talking about simple Bernoulli trials, I'm talking about binomial distribution.

Though Poisson or Geometric might be more relevant to the OP. They all increase with X though, obviously.

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Originally Posted by voidspark
Pretty much, however I used a 1% drop rate for the figure of 458. The 0.79% is itself another estimate by Wowhead, and it seems that the drop rate for most dungeon rare mounts hovers around 1% (some are higher, some are lower). Only Blizzard actually knows the true drop rate!
Hard to say why Wowhead's data is off in this case, unless a lot of people who kill the boss don't bother to loot it. Might just be an error of some kind. It's usually very close to the 1% mark unless a lot of people can't access the drop due to it being limited by profession or something, or if the drop was added late, after the boss had already been killed a bunch of times.

Ah, now that I think of it - it's possible the mount doesn't show up if you already have it.

8. Originally Posted by Mormolyce
Hard to say why Wowhead's data is off in this case, unless a lot of people who kill the boss don't bother to loot it. Might just be an error of some kind. It's usually very close to the 1% mark unless a lot of people can't access the drop due to it being limited by profession or something, or if the drop was added late, after the boss had already been killed a bunch of times.
Wowhead frequently seems to reset their data (for instance, when drop-rates change) which means their sample sizes are often not as large as people think. Also with such a low drop rate to begin with, I believe the data is far more error prone (for instance, getting 1 drop versus 2 drops out of hundreds of tries will change the rate a lot!). I'm not great at statistics though, would have to crunch numbers so I can't say for sure if that's right.

- Case in point, if you look at their regular items, you'd think each would have a ~20% drop rate based on logic and the Heroic data (it picks one of 5 items on the table to give you all with equal weight). It seems in the Normal mode data things are a bit fishy with that Leather mantle.

Originally Posted by Mormolyce
Ah, now that I think of it - it's possible the mount doesn't show up if you already have it.
That is definitely not true, I got at least 3 Azure Drakes (don't ask why I ever went back to Malygos).

9. Originally Posted by mrbreck
You read all of that and you chose to pick out that one word and flip out? You are being overly pedantic concerning semantics. All they are saying is that the likelihood of some event occurring is higher as your sample set increases. "Cumulative" may have been a poor word choice, but the information presented is valid and you know it.
Consider the random variable X = number of tries needed to get the mount. Then the distribution function F also known as the "cumulative distribution function" gives the value F(x) = probability it drops in x or less runs.

So it's definitely a good word choice

10. Originally Posted by voidspark
It's cool, it actually is difficult to understand, I wasn't being snide/sarcastic about that. Really interesting though if you get into it more!
Definitely threw my brain for a loop. But hey, I learned something new!

11. Originally Posted by Niku
So I am currently farming for the Drake of the North Wind in Vortex Pinnacle and I have cleared the place 77 times since I started counting.
The drop chance is 0.78% according to wowhead and I'll trust that it's either that or close to it. I'm using this article http://wow.joystiq.com/2010/01/13/dr...ity/#continued to calculate the probability for the mount to have dropped during the course of my 77 runs (at the moment: 45.28075 percent). But seeing as I am not even remotely talented when it comes to mathematics, my mind is having an issue wrapping itself around the whole ordeal.

Everytime I kill the dragon the drop rate is it's fixed 0.78%, that does not rise or fall on any new kill. On the other hand, the number of times I have killed him rises and I should have had an overall increase chance for it to have dropped... so should I get more excited about the next run and the run after that? The drop rate is unchanged, but it feels as if I have a higher chance to get it everytime... but I don't.
When I am at 500 runs and let's assume for arguments sake I have not had it drop yet, the chance that I would have seen it within the number of my runs is now at 98%. In such a scenario, should I expect it to drop any run now? Or is that foolish since the probability is still 0.78% which doesn't seem promising at all.

Ultimately I don't know what to ask. I believe it boils down to "Should I get more excited since it's more likely to drop?".
Lets just take a moment to explain Blizzard probability theory. I will take something that is near and dear to my heart, which incidentally they are removing for WOD, and that is probability to hit.

Back as recently as Cata there was no need to hit cap, in theory, for a Paladin tank. You could go into a raid and happily go about your buisness with 6% chance to miss and, again, in theory get along just fine. With 6% chance to miss you would THINK that in 100 swings you would miss roughly six times. You would continue to think this until the 20th or 30th time you saw your shield of the righteous miss at the pull in strings of 7 to 8 misses when you were tying to build threat.

So here is the reality of Blizzard probability. If you have a .78 chance that your item is to drop according to Blizzard. What this means that is somewhere between your first and 100th pull someone else will whisper you how they got it their very first try. Oh and Obama care will miraculously work, and the Muslim radical world will opt for a play nice attitude towards other religions.

Meanwhile you will be on your 1-100th set of 100 pulls and 6 years later get your drake in a goody bag on your healer in a random heroic.

Hope that helps clear up Blizzard math. I think they must hire designers who are missing a finger or a toe and cannot actually count to ten without it.

12. The drop chance is not "according to Blizzard". It's according to real data collected by Wowhead. A streak of bad luck does not mean that the numbers are false.

13. Originally Posted by judgementofantonidas
Back as recently as Cata there was no need to hit cap, in theory, for a Paladin tank. You could go into a raid and happily go about your buisness with 6% chance to miss and, again, in theory get along just fine. With 6% chance to miss you would THINK that in 100 swings you would miss roughly six times. You would continue to think this until the 20th or 30th time you saw your shield of the righteous miss at the pull in strings of 7 to 8 misses when you were tying to build threat.
Your chance of missing a 6% attack 7-8 times is positive but astronomical. However besides exaggeration (7-8 misses in a row 20-30 times) I think one thing you are missing is the dodge/parry chance (expertise).

If you had the model where you could miss 17% (8% hit, 9% expertise) of the time, then your chance of a 5 streak miss on your shield would be 1 in 7043, which is small, but definitely realistic if you're looking at how many pulls you can be doing in a month. More likely you're losing threat by 2-3 miss streaks and then it feels like 7-8 times.

14. Originally Posted by voidspark
Your chance of missing a 6% attack 7-8 times is positive but astronomical. However besides exaggeration (7-8 misses in a row 20-30 times) I think one thing you are missing is the dodge/parry chance (expertise).

If you had the model where you could miss 17% (8% hit, 9% expertise) of the time, then your chance of a 5 streak miss on your shield would be 1 in 7043, which is small, but definitely realistic if you're looking at how many pulls you can be doing in a month. More likely you're losing threat by 2-3 miss streaks and then it feels like 7-8 times.
Nope. Nice try discrediting my statement. Logged it, counted it, confirmed it with my raid at that time. Then I hit capped and said screw it.

15. Originally Posted by judgementofantonidas
Nice try discrediting my statement.
As I wrote:
Your chance of missing a 6% attack 7-8 times is positive but astronomical.
You probably won the lottery. Though I doubt you had it happen 20-30 times.

Edit: Also there is no way in hell you were exp capped as a paladin tank in Cata, so you still had to suffer that.

16. I sorta got a grasp of it now (Not the mount *sad face*). Thanks guys!

17. what it means in simple term is that u could be super lucky to have it in ur first run, without even knowing it exists. or, u can be super duper unlucky, never owning it for the rest of ur life :P

18. You gotta think way more simplistic about this.

Zero shots fired hit zero targets.

Thats all, really. Thats all you need to keep going.
Dont go off the slippery slope of Gambler's Folly thinking more shots fired = increasing chance each time it hits.
Just know that no shots fired = no chance of hitting, and you're good.

19. Sounds like you're suffering from the Gamblers Fallacy.

20. Originally Posted by Niku
So I am currently farming for the Drake of the North Wind in Vortex Pinnacle and I have cleared the place 77 times since I started counting.
The drop chance is 0.78% according to wowhead and I'll trust that it's either that or close to it. I'm using this article http://wow.joystiq.com/2010/01/13/dr...ity/#continued to calculate the probability for the mount to have dropped during the course of my 77 runs (at the moment: 45.28075 percent). But seeing as I am not even remotely talented when it comes to mathematics, my mind is having an issue wrapping itself around the whole ordeal.

Everytime I kill the dragon the drop rate is it's fixed 0.78%, that does not rise or fall on any new kill. On the other hand, the number of times I have killed him rises and I should have had an overall increase chance for it to have dropped... so should I get more excited about the next run and the run after that? The drop rate is unchanged, but it feels as if I have a higher chance to get it everytime... but I don't.
When I am at 500 runs and let's assume for arguments sake I have not had it drop yet, the chance that I would have seen it within the number of my runs is now at 98%. In such a scenario, should I expect it to drop any run now? Or is that foolish since the probability is still 0.78% which doesn't seem promising at all.

Ultimately I don't know what to ask. I believe it boils down to "Should I get more excited since it's more likely to drop?".
The probability per drop remains the same. You aren't any more likely than you ever were.

This is the part that's 45%, so pay attention, it's fairly simple.

The odds that you'll have done it 77 times without seeing a drop are (according to that site, apparently, i don't have the patience to do the math at this point) about 55%. So, in a sample of 1000 people, around 550 will have not seen it after 77 attempts. Each time that you do it, the likelihood that you will see it becomes higher not per attempt but in the entire sample of your attempts.

In other words, it starts being really unlikely that you haven't seen it after a few hundred tries. That doesn't affect drop rates in any way, but it means that your probability of having seen it in x attempts, including this attempt will be higher. This is why trying a bunch of times will get it for most people.

One of the things about WoW that's unfortunate is, in 7 million players, there's like a .00001% chance that even doing it 100,000 times will never see it. Which, while it seems meaningless, is 70 people. So, probability states that about 70 people will never get it even if they do it once a day for the next 273 years.

Functionally, this means that even with very high drop rates, anything that has a random drop chance is, statistically, impossible for all players to get. In fact, a fair number of people (approximately equal to most people's total 'friends they've ever made in a lifetime' amount) will almost certainly have no chance to ever get it.

RNG adds excitement to the game, but always understand that it's existence means you may be one of the 70 people (from my example, it's actually a higher or possibly lower number depending on droprates) who will, after 273 years, never see it.

Therefore, be happy if you see it, because you could have been one of those 70 At least that's how I try to look at it.

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Wow, just saw a lot of people with seemingly little math education arguing pointlessly.

Let me try to explain something here.

Your chance for this mount to drop is (according to existing data) about .78%.

No matter how many times you kill it, your chance to get it on that kill will still be .78%.

Your likelihood of getting it from any given kill will never increase (except eventually Blizzard will probably raise it to 2-3%, most things eventually have) above .78%

However.

If 100 players kill the boss one time, the statistical likelihood that one of them will have gotten it nears 100%.

Now: what does this mean, and what does it not mean.

IT DOES NOT MEAN:

That you are more likely to get it.
That you are "due" a drop.
That it has to drop eventually or otherwise it won't actually be .78%.

IT DOES MEAN:

That your chance to be a member of the group "In the extremely small group of people for whom it didn't drop at least once out of 100 chances" is very small.

Now, to further this point.

You _still_ aren't any more likely to get the mount than you were before, because like someone said, you can't factor past events into probabilities for the future. Why? Because the chance of me waking up on November 18, 2013 is 100%. It already happened. That quantum state in this matterverse has already collapsed into a stable wavefront and is no longer accessible from my position in relative spacetime. It no longer has a probability. The cat is now either alive or dead. It is no longer a probabilistic event; "LurkerOnly wakes up on November 18, 2013" is, from my perspective, a collapsed event that is no longer accessible and can only be observed. It is 'actual'. I'm sorry, I know that this will completely cause some of you to think "this guy is insane", but this is just general relativity, 100 years old theories.

So, like I said. Remember that, in terms of probability, there is nearly 100% chance that out of 7 million subscribers trying once a day for 30 years, one person will never see it drop. That person could be you. Just be happy if you see it, and don't let your disappointment increase each time it doesn't drop.

In a very real sense, the next time you kill the boss and try to get the mount, will be the first time you've ever done it. Try to approach it with the same hope but understanding of its unlikelihood, and don't get too bummed out if you don't see it. .78% is kind of a low chance, after all.

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