Vault/LT Token "Streakiness"

Unknown

simonsez wrote:

carrion pigeons wrote:

That's because clustering *isn't statistically improbable*. That's my point.

Then your point is invalid. This isn't subjective. It's just math. If you pull 10 tokens, the probability of getting 3 MrF blues, and 3 Falcrap yellow is ridiculously small, if every cover actually did have an equal chance of being pulled. And when practically every person who posts pulls shows clustering that is unlikely, I stop giving the benefit of the doubt.

Pairs and triplets can't be evaluated in themselves, but within the larger context of the total set of possible draws. They're much more likely than people think.

It's just the birthday paradox. The odds of any two people having the same birthday is very small (around 0.27%, assuming equal distribution of birthdays), but it becomes much larger as you add more people. The odds of two people sharing a birthday reaches 50% when you reach 23 people and 90% around 40 people.

As for the "invisible vault" idea - we can probabilistically determine the truth of this through some creative math. We can also rule them out with a much simpler process at the extremes. If the hypothesized hidden LT vault had 80 items, we would expect that 8 out of those 80 would be 5*s. Therefore, if anyone has ever opened 144 LTs in one go without any 5*s or 152 tokens in one go with fewer than 8 5*s, we can discard the 80-vault idea. 7 5* draws from 152 is "only" the bottom 0.8%, so it's not actually that unlikely by a purely random process.

But the best argument against an "invisible vault" is that vaults are a huge psychological incentive for people spend money. It might not make economic sense to implement for something like LTs, but why would they use it and not tell us? After all, many people are actively calling for a streak-breaking mechanism.

Unknown

Which is not to say that chances are definitely even or that RNG is correctly distributing covers. There's a history of anti-consumer practice in this game that this kind of activity would not be inconsistent. I only point out the math to suggest that if we need better data to make this accusation than we currently possess.

I tried to gather some data on LT draws a few weeks ago that showed that we could potentially gather enough data to make this claim. But it relied on user-reported information that I would not sufficiently confident in (a 20% under-reporting of LT draws would be enough to push it past the significance level). If someone puts out a survey that was restricted only to people who recorded their draws meticulously, we can be much more confident.

CrookedKnight

If you got enough people to report on every LT draw they make (e.g. the "your latest legendary pull" topic) then you wouldn't need an especially long history to at least evaluate whether certain characters are more likely than others overall (streakiness would still have to be done per individual, though).

simonsez

Malenkov wrote:

It's just the birthday paradox.

I don't see any analogy at all. If the odds of someone getting "x type of clustering" is .27%, the odds of 40 people having the same sort of unlikely clustering sure as hell isn't 90%.

Malenkov wrote:

but why would they use it and not tell us?

It's hard to rationalize the things they do when they often seem nonsensical, but maybe they're thinking that when people see a video of KD pulling 8 Gwen's from a 40 pack, people will mistakenly believe the chances they can do likewise are far greater than they actually are. Which would spur more sales? 100 people who all get 0-3 Gwens, or 100 people where 2 people get 8, and the rest get 0-2?

simonsez

Malenkov wrote:

I only point out the math to suggest that if we need better data to make this accusation than we currently possess.

I agree with you. I'd love to get more data. I just push back against those other folks who blindly accept that pulls are purely random, despite more evidence suggesting they're not, than they are. If you go back to when 5*s first came out, there were dev-verified pull streaks that had probabilities in the neighborhood of one in 10s and even 100s of millions... if what they're telling us about pull rates is true. Which is why I don't believe they are. My "invisible vault" theory is just a guess... could be anything.

Unknown

CrookedKnight wrote:

If you got enough people to report on every LT draw they make (e.g. the "your latest legendary pull" topic) then you wouldn't need an especially long history to at least evaluate whether certain characters are more likely than others overall (streakiness would still have to be done per individual, though).

This is an interesting idea, but I'd have to wait for that thread to get much longer than it currently is. The last time I evaluated it, I had a sample of 400 pulls. That thread is over 200 replies, with many reporting multiple pulls. I'll get on that right away.

Unknown

simonsez wrote:

Malenkov wrote:

It's just the birthday paradox.

I don't see any analogy at all. If the odds of someone getting "x type of clustering" is .27%, the odds of 40 people having the same sort of unlikely clustering sure as hell isn't 90%.

I mean that it's a reasonably analogy for clustering in any series of pulls, not necessarily across individuals. The chance of two people having the same birthday is analogous to the chance of drawing the same two characters, so the number of pulls is similar to the number of people. As you increase the number of people, the chance that any two people will have the same birthday increases faster than a naive assumption about the math.

The "common sense" way of thinking about this is that pulling a duplicate out of some small number of draws (let's say 10) is pretty unlikely. But it's actually not.

This article has a calculator at the end that uses the square approximation which will ballpark the numbers for us: http://betterexplained.com/articles/und ... y-paradox/

Put in days=25 (we're ignoring 5*s for simplicity).

And then put people = 10.

The result is that there's a 83% chance that you'll get at least one duplicate (or more).

It *seems* wrong, but it's actually about right. The Wikipedia article goes into more detail: https://en.wikipedia.org/wiki/Birthday_problem

Unknown

Malenkov wrote:

CrookedKnight wrote:

If you got enough people to report on every LT draw they make (e.g. the "your latest legendary pull" topic) then you wouldn't need an especially long history to at least evaluate whether certain characters are more likely than others overall (streakiness would still have to be done per individual, though).

This is an interesting idea, but I'd have to wait for that thread to get much longer than it currently is. The last time I evaluated it, I had a sample of 400 pulls. That thread is over 200 replies, with many reporting multiple pulls. I'll get on that right away.

Reading through the responses, I get the feeling that people are somewhat more likely to report if they get successes (good 4*s and 5*s), so it might be slightly skewed towards the higher end.

EDIT: Yeah, I think there's too many people who only report because they got some crazy draws. Even after the first 3 pages, we're past the significance level in the other direction (e.g. enough to suggest that the rate is actually higher than >10%). So, basically the opposite bias from my earlier poll.

So, yeah, we still need a full accounting of draws, not just good/bad streaks. Maybe we can get a set of volunteers (whales and also non-whales) to track and anonymously report exactly what they're drawing.

carrion_pigeons

simonsez wrote:

carrion pigeons wrote:

That's because clustering *isn't statistically improbable*. That's my point.

Then your point is invalid. This isn't subjective. It's just math. If you pull 10 tokens, the probability of getting 3 MrF blues, and 3 Falcrap yellow is ridiculously small, if every cover actually did have an equal chance of being pulled. And when practically every person who posts pulls shows clustering that is unlikely, I stop giving the benefit of the doubt.

It really isn't.

When practically every person who posts pulls shows (individually) unlikely clustering, you have *a normal distribution*. It really is just math. You are many times more likely to see "unlikely" clustering than you are to see a distribution with none.