Numbers Don’t Lie

I’ve speculated in the past about the drop rates of certain champs in different crystals but it wasn’t until this 5* featured that I decided to put pen to paper. What I found was astounding.

I have opened 3 5* featured crystals in the past few weeks and all of them have produced a 5* Thor Jane Foster. Assuming every champ has the same drop rate, the probability of pulling a TJF is 1/24. Here is where it gets interesting... Opening crystals are independent events. To find the probability of multiple independent events all occurring, you simply multiply their individual probabilities. So, the odds of getting a TJF is 1/24, multiply that by the probability of getting a second TJF on your next pull (1/24) and you get 1/576. That’s pretty unlikely but plausible. Now, take that probability and multiply it by the probability of getting a third consecutive TJF (1/24) and you get 1/13,824. That’s 0.007%. Again, that’s pretty unlikely but still plausible. I very well could be the unluckiest person in the whole MCOC community.

Here is where I find issue.... I have an alliance mate that has had similar luck. 3 5* Beasts in a row from 5* featured crystals. Again, independent events. The odds of my 3 TJF (1/13,824) multiplied by the odds of his 3 beasts (1/13,824) and you get 1/191,102,976!!!! That’s an astounding 0.000000523%. But it gets worse! Those are bad enough odds that this scenario can happen to two different people within the MCOC community for any given crystal, but when you take into account the fact that we are in the same group of 30 people out of the tens of thousands of people that play this game, the numbers really take a turn for the worse.

With all that being said, I can’t help but think that there are most likely similar stories out there where people have experienced this kind of luck. At some point we can’t just keep saying “that’s RNG for ya!” and we have to realize that maybe different champs are more likely to drop than others despite the assumption that they are all equal.

Anyways, rant over. Let me know what you all think. Maybe I’m off my rocker or maybe you agree with me. I’m interested to hear all sides.

Comments

PsyLife

I appreciate your going in to the numbers, but technically there is an equally likely chance that anything could happen. The chance of getting three of the same character in a row are 1/576, or about 0.2%. In reality, there are 13, 824 possibilities for three rolls, 24 of which would be the same three consistently. To have at least two of the same would be a 1/24 chance. That’s pretty high. While it might seem like you have bad luck, try a poll to see how many of the featured pulls were good. The bigger the population, the better the results.

DNA3000

I have opened 3 5* featured crystals in the past few weeks and all of them have produced a 5* Thor Jane Foster. Assuming every champ has the same drop rate, the probability of pulling a TJF is 1/24. Here is where it gets interesting... Opening crystals are independent events. To find the probability of multiple independent events all occurring, you simply multiply their individual probabilities. So, the odds of getting a TJF is 1/24, multiply that by the probability of getting a second TJF on your next pull (1/24) and you get 1/576. That’s pretty unlikely but plausible. Now, take that probability and multiply it by the probability of getting a third consecutive TJF (1/24) and you get 1/13,824. That’s 0.007%. Again, that’s pretty unlikely but still plausible. I very well could be the unluckiest person in the whole MCOC community.

Here is where I find issue.... I have an alliance mate that has had similar luck. 3 5* Beasts in a row from 5* featured crystals. Again, independent events. The odds of my 3 TJF (1/13,824) multiplied by the odds of his 3 beasts (1/13,824) and you get 1/191,102,976!!!! That’s an astounding 0.000000523%. But it gets worse! Those are bad enough odds that this scenario can happen to two different people within the MCOC community for any given crystal, but when you take into account the fact that we are in the same group of 30 people out of the tens of thousands of people that play this game, the numbers really take a turn for the worse.

This is a common problem with statistics, namely what's sometimes referred to as the significance problem. The easiest way to explain it is with an example.

Suppose I were to pull Hulk, Beast, and Archangel in that order from the featured crystal. What are the odds of that specific sequence happening? The same computation you did should still work: 1/24 * 1/24 * 1/24 = 1/13824. But you can do that for any sequence of champs. Is the conclusion that all possible openings are virtually impossible to happen?

In fact, all possible openings *are* very rare. If I pick any three champions at all and ask "how long would it be before you opened three crystals in a row that matched my picks" that would be a very long time: matching three picks in a row is extremely unlikely. But the catch is I'm picking three first, and then you're trying to match those picks. That's very hard. But if you open three crystals *something* has to happen. You're going to get three champs, of course. Now if you look at what you open and after the fact try to determine how rare that was, this is a completely different situation. Now, you aren't actually looking for three Jane Fosters. You're looking for anything your pattern-matching brain will think is "significant."

How many possibilities are "significant?" Well, look at your own post. You thought three Jane Fosters were significant. You thought three Beasts was significant. I'll bet you think three anything in a row is significant. What are the odds that if you open three crystals you'll get three champs identical? Well, there are twenty four possible ways that can happen: three Beasts, three Archangels, three Jane Fosters, etc. Twenty four different champs in the crystal, twenty four different ways to have all three identical.

So really, the odds of you seeing a "significant" set of three was actually 24 out of 13824, not 1 out of 13824. Which is one out of 524. It is the same number you get if you assume the first champ can be anything, and then the next two have to match it: 1/1 x 1/24 x 1/24.

Except: you've probably opened more than three featured crystals. I'll bet that most of those openings were not three identical champs in a row. So you didn't have one shot at landing on a one in 524 possibility, you've actually had many shots at that. The odds of you seeing this were actually N out of 524, where N is greater than one. What's more, there are people who post about getting two out of three being the same, which is even easier to happen. Your triple pull is just one out of many different possibilities that people consider "significant" and when you look at the odds of any of those things happening the odds are actually not all that bad.

And then, there's another error: the idea that since you're just a couple out of tens of thousands of players makes the odds worse. They actually make the odds better. Consider that tens of thousands of players don't post their pulls. Because while all pulls are equally (un)likely, most aren't interesting to human eyes. When someone pulls three different champs, they don't talk about it. Only those that actually see apparently significant to human eyes pulls actually posts about it. So what are the odds that out of tens of thousands of players two would be in the same alliance and both pull triples within a short window of time? Well, the odds of one player doing that is one in 524 as previously mentioned. What are the odds of two people in the same alliance of thirty people doing that. The odds are actually about one in 665.89 (math: (1/524)^2*(523/524)^28*30*29/2). In other words, one out of every 666 alliances that contain players who actively open featured crystals will have two people who both pull triples.

Out of thousands of alliances, the odds of this happening are actually very good. For any one player the odds are rare, but collectively out of all the many players and alliances, it is bound to happen multiple times. And we only hear about the rare time it happens, not the thousands of times it doesn't happen.

To put it another way, the odds of winning the Powerball lottery are astronomically low: one in 200 million+. So does that mean the Powerball lottery must have rigged the contest, because the winner couldn't possibly have won fairly and must have cheated? No, because there ultimately has to be a winner eventually (they keep going until someone wins). The odds of any one person winning are low, but the odds of a winner existing at all is eventually very high. So there's a difference between asking what are the odds of something happening to you, and asking what are the odds of something happening at all. You *saw* the rare occurrence first, then *retroactively* asked what the odds of that happening are. That's an alternate version of the significance problem.

Colinwhitworth69

Plate of shrimp.

Nick1109

I'm in a post full of Harvard grads.

Djin

Statistically speaking there's always a chance for unlikely events to take place.

PsyLife

So DNA3000 just took my post and elaborated it.🤣 Jk I couldn’t of explained that myself, plus I’m on mobile.

DNA3000

So DNA3000 just took my post and elaborated it.

Inspired by a true story.

Plinko

Reality is that I opened my 6th 5* class awakening gem today after exploring variant 2. My second cosmic in a row even though I have no use for it. After getting 4 mutants prior in a row that I couldn't use. As for the 3 to 4 2015 rank up gems. 2 cosmics and a tech. I could use mutant, science, or skill. So more things I can't use. And a cosmic r5 gem. Which I could use every type besides that one at the moment. I don't believe it's real rng. I believe it's coded to be dependent on your inventory. 95% of the time you'll get things you can't use right away. You'll probably use it eventually. But kabam wants you to buy those deals every day to rank up the champs you want. They don't want you taking shortcuts with a gem. They make more money that way. It's simple business.

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SlashingSunset

I do feel the same way as well sometimes. I mean, all of the time. My first 5* was a Beast back then, and I was so excited to open my second 5* when that time eventually came. I actually pulled him a second time. Good times!
There's def something weird going on with those Crystals.

lowlevelplayer

@DNA3000 Sometimes I wonder what your day job is. Are you a math professor or just another math guy

PsyLife

@lowlevelplayer Teaching people math on the forums.

Demonzfyre

@CoachLed go move defense.

Halley

You: How could I win 5* Thor Jane with 0.000001% ??
Kabam: Lucky you!! Congratulations! You win the game, like you did as a sperm long time ago!! It's a miracle, right? Enjoy & dont need to thank us!!
🎊🎊🎊🎉🎉🎉💯💯💯

tklmc

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c(now 19) usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster

Demonzfyre

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster

So if RNG is what it's supposed to be, what should you have?

Kerneas

You all are thinking too small. You think that pulling 3x the same thing in a row is barely possible. But on the greater scale it is a normal phenomenon. If a million crystals are opened (and this happens), quite often happens that 3 same champions are opened by one person in a row

frzbr

from november 2019 to january 2020, i got 5 5* king groot in a row... and 6 4* magneto in a row ( counting both magnetos )... my first 6* was HT, and 2 months later, my 2nd 6* was HT again... i know its an rng but maybe something is brokens... lol...

tklmc

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster
So if RNG is what it's supposed to be, what should you have?

It could be more variable. I think RNG is not randomized and works with a code that increases the chance of pulls which you need the least

CoatHang3r

Well this thread pretty much proves that numbers are so good at lying people have built entire belief systems around the lies they tell.

DrZola

Ally mate pulled 4 6* Karnaks in a row from basic 6*.

I offer this example only because I suspect the number of 6* pulls to be (and to have been) significantly less over time than 5* pulls. That may mean an extreme result like L100 Karnak is likelier than not because of a smaller sample size. Or maybe not.

I don’t think there’s any reasonable doubt that the drops are randomized. But I do wonder what “randomized” actually means sometimes to the game’s basic chance engine.

Dr. Zola

Demonzfyre

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster
So if RNG is what it's supposed to be, what should you have?
It could be more variable. I think RNG is not randomized and works with a code that increases the chance of pulls which you need the least

How can RNG be more variable? What about it says it has to be that?

Do you have proof that code is enforced in the game?

Plinko

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster
So if RNG is what it's supposed to be, what should you have?

A variety and not the same thing you can't use every time you roll.

PsyLife

Actually, if you were to get variety, it would be less random. Check this out: https://www.daxthink.com/think/2017/2/27/apple-made-itunes-shuffle-less-random-to-make-it-more-random

This is an example that actually disproves your point but enforces your thoughts. Kabam should change the rng system to get better business like apple did.

Demonzfyre

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster
So if RNG is what it's supposed to be, what should you have?
A variety and not the same thing you can't use every time you roll.

@Plinko that's not RNG.

Plinko

I think exactly same as Plinko, RNG is not as it suppose to be. I have 29 5* champs and only tech is howard:(( So I have 15 tech t4c usefulness in my inventory, last week I need mutant t4c and opened 5 t4 class crystal hoping mutant catalyst then what I saw is 4 tech and 1 cosmic that are the most unnecessary t4c's for my roster
So if RNG is what it's supposed to be, what should you have?
A variety and not the same thing you can't use every time you roll.
@Plinko that's not RNG.

That’s not an argument. Do you take every carny and used car salesman’s word for it when they tell you something. You have no proof that they don’t do it just as I don’t have any that they do. I have results from pulls to go on and that’s pretty strong evidence to me and many of the others experiencing the same thing. If you work for kabam or are friends with them that’s fine. But to say it’s impossible for them to have a system that isn’t highly dependent on your inventory is laughably naive.

_I_

if a person gets hit by a speeding vehicle yet survives we term it as a miracle but if the same person dies we term it as accidental death. but the probability of that hit n run victim to die or survive was always 50% at the instance of being hit. the outcome of the event just ends up being a source of relief or dismay depending on the result.
so I do not feel the Kabam guys have done such rigorous maths so as to design such a cunning way that some champs are to be thrown down at us more frequently than the rest of the champions. its more abt the randomness becoming a reoccurring event n not some casino styled treachery.
As I said before too that what u see in videos of end game players or players who spend regularly to buy champs, their pool or variety of possession of champions is due to their opportunity to have more chances to roll the dice or simply put as they are opening more crystals. The higher the no. of chances they are taking the greater the access to the probability of pulling a desirable champ. A player who can open only two 5 * crystals a month vs a player who will buy units n attempt those cavalier crystals @200 units a piece will obviously have higher chances to pull a desirable champ out of his many items.So the more u stake n gamble the more u will feel rewarded in the form of variety.This game is either for the patient guy or the impatient guy. A patient guy will just sit out like we sit out while fishing n bait the catch. An impatient guy will say forget fishing let's go buy the fish n eat it too.But at the end if the day target is to eat the fish. To eat it for free or buy it to savour its taste is our choice. Nothing else.

unknown

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