I see a lot of posts saying "X runs and still no drop"

WoW Classic WoW Classic General Discussion
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So I wanted to bring some light to the topic. How unlucky are we all?

First of all, it is correct to say that if the drop rate of an item is “p”, then it will take, on average, 1/p runs to see an item the first time.

But the probability of NOT seeing an item after 1/p tries can be quite large, which might be counter-intuitive.

Let’s take p = 0.05 as an example, a 5% drop rate. The expected number of runs is 1/0.05 or 20.

However, the probability of not seeing that item yet is (0.95)^20 ~ 0.36 which is a 36% chance. (Here we had a 95% chance 20 times in a row to NOT get the item).

In fact, if we plot the probability of not seeing a drop within the expected runs, for drop rates between 0.1% and 25%, we see that this probability only increases (up to a limit of 1/e) as the drop rate decreases.

(wolframalpha . com/input/?i=plot+%281-x%29%5E%281%2Fx%29+for+x+in+%280.001%2C+0.25%29)

So what does this mean? Well, if you want to make sure you see the item (just kidding, only with a 95% chance), you could solve for N number of runs:

0.95 >= 1 - (1-p)^⌊N⌋
–> N >= ⌈log(0.05) / log(1-p)⌉

For our example of a 1/20 drop rate, you would need to do 59 runs to see the item with a 95% success rate! That’s a lot more than 20 runs!

For fun, I decided to plot the curve of the number of “extra” runs (over the expected) that you would need to do to get your item (with a 95% chance), for different drop rates. It’s not so pretty!

(wolframalpha . com/input/?i=plot+%28log%280.05%29+%2F+log%281-x%29%29±+%281%2Fx%29+for+x+in+%280.001%2C+0.25%29)

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We did over 600 arena runs for SGC. The deal was I help my friend and I get the next one for off spec.

I don’t want to go back for mine.

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There is a 2.3‬% chance of that happening to you, given the 0.626% effective drop rate of SGC (accounting for the multiple bosses).

It should take 478 runs to have a 95% shot at it.

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That doesn’t make me feel any better.

Lucky us?

Are you using math with the assumption that it’s one boss?

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TL;DR - People don’t understand statistics and probability.

Bottom line is this, if something is a 5% drop, each time you do it you have a 1/20 chance of seeing it. That doesn’t mean after 20 runs you should see one. It just means each run you have a 95% chance of rolling the dice wrong. However failing doesn’t buff your chance of seeing it another time. That’s where the logic of “Well on average it should take” falls apart because you don’t build up a bad luck protection. Something could theoretically have an 80% drop rate and with the worst luck you could go 50 runs without seeing it. Statistically unlikely to happen but it is still a possibility.

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That is known as the Gambler’s Fallacy.

Tracking your history can be useful as we can calculate the probability of your series of events. It can also help you update your belief about the drop rate, if you believe it to be wrong.

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I think most people understand this at least at a basic level… just because they post their personal statistics doesn’t mean they don’t understand?

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I agree. I think probability is baked into human intelligence (not to mention the vast amount of education we have today). It can just get confusing / counter-intuitive when things get detailed. I don’t think they don’t understand it :stuck_out_tongue:

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I’m not so sure. If there’s something I am reminded of every single day for all 26 years I’ve lived as far back as I can recall, people are profound levels of stupid.

I kind of stopped using the term “Common Sense” because ironically, it turns out that it’s not all that common. Though depends how you view common sense, at face value you’d think it’s just basic sense everyone has but clearly not.

Think Einstein said something like “Common sense is just a collection of prejudices acquired before adulthood.” Which seems a lot more apt since some pretty basic things some people just do not know since they never dealt with them personally to acquire experience on how to deal with it. I.E when my girlfriend thought the way she dealt with a grease fire was to throw water on it and nearly burnt down her house when we were in high school which is something you’d imagine is just obvious to not do.

Or surprisingly how many people my age don’t know how to change a car tire despite it being something that everyone should know how to do before they’re 18, but if you’ve never dealt with a flat tire or didn’t have parents/grandparents who make damn certain to make sure you knew it, how else would you expect them to know it unless they on a whim just decided “I don’t know how to change a car tire, but I would like to.” and looked up a YouTube video and managed to sit through it all.

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Please tell me that’s a copy pasta…

Let’s not turn this into an iamverysmart thread. Trying to bring some fun on this topic while we suffer through our grinds for loot!

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I never saw one drop in the time it took me to get a hoj, of which I lost 3 rolls before winning one. But there’s an easier solution. Just get the tombstone from scholo. That’s what I was using before I got R10.

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:frowning: and no that’s with multiple bosses

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On our quest for SGC we brought in anyone who wanted HoJ to extend time between lock outs. We got so many HoJ we even gave one to a priest.

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A guild mate of mine has run arena farms trying for his SGC since launch. He’s sitting just shy of 400 arena clears right now and hasn’t seen it. Another guild mate got it in his first night of trying for it.

My guild has gotten 4 bindings to drop from Garr, and 0 from Baron Geddon.

RNG is RNG. Sometimes you’re lucky, and sometimes you’re just not.

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Hunters will wish they farmed one when they get to nef

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After reading your post I’m convinced you’re one of them.

Statistics is about analyzing past data whereas probability is a theoretical branch of math that looks to the future. They’re on complete opposite ends of each other as far as what they deal with.

Put into WoW lingo statistics is about throwing 500 people into a dungeon and them reporting back that it took them an average of 32 runs to get a 5% drop rate, but probability is saying that if an item has a 5% drop rate you should see one every 20 runs.

Actually it does. The keyword, of course, is “should” because nothing is guaranteed in probability because that’s not what it’s about.

See, when you say stuff like this I just think “That person doesn’t understand probability”.

Actually it’s improbable to happen, not statistically. Statistically would be “All my friends took 1-4 runs to get the item and it took me 50”. Statistics require data, if you’re just using assumed drop %s you’re calculating theoretics, which is what probability is.

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Inaccurate. Probability is directly derived from current statistics. They’re not opposite ends so much as two complimenting forces that feed into each other. Statistics over how much dungeons being ran and how often items appear feeds into the probability of seeing that drop. Meanwhile, probability of an item appearing feeds into the statistics regarding how many have seen it, or how many have it.

No, probability stands the first part but doesn’t extend to the other. Probability just means the odds of it dropping. It implies nothing about “should see in X attempts” past people mistakenly thinking it does. If your probability of seeing an item is 5%, that’s it. Your probability of seeing it is 5%. It doesn’t imply “And going off that you should see it in 20 attempts.”

Wrong. If something is 5% likely to happen, it doesn’t mean after 20 times it should happen. Nor does probability even imply that. It just simply states “You have a 5% chance of seeing it.” NOTHING more.

Here’s a common scenario used to explain probability. A bag of marbles with different marbles and your odds of pulling a specific marble. What happens with drops though is if you pull out a green marble while fishing for a blue one, it doesn’t remove the green one from the pool. The green one goes back in and you keep fishing. Each attempt carrying a 5% likelihood you might pull the blue one. But this in no way implies within 20 attempts you should pull a blue one.

Oh cute, I’m being judged by a guy who named himself after one of the most well known Vanilla PvPers who I’m in the process of explaining why they’re incorrect to. I’m sure your opinion holds so much value and weight to me. . .

Both can be used here. If I have an established 1% chance to die from something, you can both say it’s statistically unlikely and improbable. They both work while not being exactly interchangable terms. Or if you’d like from vocabulary dot com " The adjective improbable also means statistically unlikely to happen" For the full context: " Since improbable means something is unlikely but not impossible , your optimism allows you to keep hoping. The adjective improbable also means statistically unlikely to happen. You might be afraid to fly, but the odds of a plane crash are so low that such an event is improbable ."

Probability is a calculation of odds based on statistics, sure the 5% was a theoretical number I used for simple discussion and wasn’t pertaining to a specific item. Except drop rates are calculated through statistics so they aren’t entirely theoretical outside of we have no concrete tables from Blizzard stating the exact drop rate of items.

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No where in this analysis have you factored whether the player has a lucky rabbit’s foot in his bags.

Pfff.

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Incorrect. There is a ~0.67% chance of SGC dropping. There is a ~9.09% chance of Gorosh spawning and he has a ~6.89% chance of dropping SGC, for a ~0.63% chance of SGC dropping on any given run. The chance of going 600 runs without seeing SGC is actually several orders of magnitude greater than 0.015%.

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when it comes to loot drops, the more superstitious you are, the better.

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