Forum Thread

simonsez

aesthetocyst wrote:

Look back to the question I was addressing, some players had asked whether the token RNG was picking a character first, and then a second RNG determined one of it's colors to spit out, OR whether the covers were treated separately, a single RNG choosing from amongst all character's covers in one big pool.

Did you ever try writing a sim in which you selected an outcome based on 93 possibilities, vs one where you arrived at one of those 93 possibilities by first doing a 1 in 31 RNG followed by a 1 in 3 RNG? I bet your distributions don't look any different.

Fightmastermpq

mohio wrote:

Bowgentle wrote:

rkd80 wrote:

"Best and least radical solution is to roll back dilution by offering more types of LTs, each with far fewer possibilities, allowing players to target fewer characters at a time."

That is an elegant proposal and will actually create a lot of decisions for players making the game more fun, while not impacting the bottom line in any way.

Of course it will impact the bottom line.
The only players who will open anything with less/no chance of OML are the ones with a champed OML.
Anyone else will only open the sort of token that gives them the best odds on OML.

Honest question...do you (or others?) think people would actually spend up to 100 cps for a token that had 15% chance at OML? That would be equal to current odds at pulling OML on a per cp basis. How about "just" 50 cp? I think people are a little more savvy than that, but I certainly could be wrong.

Now I know you're more addressing the idea of breaking all LTs into groups of 3s at 5% each (or something similar) and that everyone would pull from the group that had OML. Even if we assume this is true why would that have an effect on their bottom line? Isn't it possible people would be willing to spend more money chasing after his covers if they knew they had decent odds of getting him?

I would definitely spend 50CP on an OML only LT. I currently have him at 4/3/5 (with an extra red cover in queue.) Right now the only thing that will really make me more competitive in PvP is that last cover I need to champ him and be able to respec.

stochasticism

aesthetocyst wrote:

Added the identity of that beautiful formula, i = ln(1-c) / ln(1-p/k/w) . Stochasticism turned my halting, headscratching English into algebraic simplicity. Thanks, Sto!

Quite welcome. I lost some of the more depressing numbers we came up with from that formula but you can quite quickly learn things like 720cp for the last cover you need for a 5* is actually a good deal and is a better deal as more 5*s get added to the pool.

OneLastGambit

Bowgentle wrote:

rkd80 wrote:

"Best and least radical solution is to roll back dilution by offering more types of LTs, each with far fewer possibilities, allowing players to target fewer characters at a time."

That is an elegant proposal and will actually create a lot of decisions for players making the game more fun, while not impacting the bottom line in any way.

Of course it will impact the bottom line.
The only players who will open anything with less/no chance of OML are the ones with a champed OML.
Anyone else will only open the sort of token that gives them the best odds on OML.

Actually it doenst affect the bottom line, it shifts sales from one token type to another but it doesn't decrease the amount of tokens being acquired and used.

Vhailorx

OneLastGambit wrote:

Bowgentle wrote:

rkd80 wrote:

"Best and least radical solution is to roll back dilution by offering more types of LTs, each with far fewer possibilities, allowing players to target fewer characters at a time."

That is an elegant proposal and will actually create a lot of decisions for players making the game more fun, while not impacting the bottom line in any way.

Of course it will impact the bottom line.
The only players who will open anything with less/no chance of OML are the ones with a champed OML.
Anyone else will only open the sort of token that gives them the best odds on OML.

Actually it doenst affect the bottom line, it shifts sales from one token type to another but it doesn't decrease the amount of tokens being acquired and used.

It might shift the bottom line if extra tokens allowed players to be much more efficient with their cp. If fewer tokens are necessary to get the same number of target covers lad opposed to rng chaff covers), and if the prices aren't calibrated properly to account for the efficiency, then demi will lose money.

simonsez

aesthetocyst wrote:

Are you selectively responding only to that paragraph, simon?

Selective in the sense that I'm responding to what I hoped would help me to understand these points you're trying to make about deducing whether this is a 1 or 2 stage RNG, and why you think fewer potential outcomes requires more iterations to yield a normal looking distribution. So far, I haven't gotten any closer, so I'll tap out.

Diarchos

Great reading all the information given in this thread.

I have a small concern though about the way this randomness works.

For example: I'm way in the 2-3 star transition with a lot of 4* on the roster.
I usually save up about 100 cp and open 5 classic legends pack and 5 of the latest.

What I've been seeing is that the game favors covers for the heroes that you don't have on the roster. This is basically the same with 2 and 3 stars.

About 7 out of 10 pulls I always get the ones that I don't have on the roster.

Maybe just unlucky but after about 70 pulls I'm starting to wonder.

mohio

Fightmastermpq wrote:

I would definitely spend 50CP on an OML only LT. I currently have him at 4/3/5 (with an extra red cover in queue.) Right now the only thing that will really make me more competitive in PvP is that last cover I need to champ him and be able to respec.

That's understandable since you already have a championed phoenix, but if all you had was that OML and still needed covers for all the other 5* would you still be willing to throw away the other covers you would be likely to get from opening more tokens?

I also have 12 OML covers and one expiring soon (2 days...), as well as 12 PHX covers and one expiring soon (so lucky lately...). I still don't think I would cost myself the possibility at more BSSM or GG (or even SS) covers, by spending more for chances at only PHX or only OML.

dsds

Diarchos wrote:

Great reading all the information given in this thread.

I have a small concern though about the way this randomness works.

For example: I'm way in the 2-3 star transition with a lot of 4* on the roster.
I usually save up about 100 cp and open 5 classic legends pack and 5 of the latest.

What I've been seeing is that the game favors covers for the heroes that you don't have on the roster. This is basically the same with 2 and 3 stars.

About 7 out of 10 pulls I always get the ones that I don't have on the roster.

Maybe just unlucky but after about 70 pulls I'm starting to wonder.

This I agree with. Most of these pulls are from players who have a very big rosters and aren't really missing that many characters.
In order to disprove this theory, you would also need results of players with less developed rosters. Do you mind posting your data here so that the statisticians can maybe find some use for your stats. And if any others who don't have a big roster can contribute, we may be able to see a pattern?

Edit: I mean the motive is there. So there is enough reason to suspect that this could be case, but we would need more data to prove. Data that only newer players can provide. Here's your chance to contribute new players!

Edit: Fact changed to theory. Too many stuff going on and used the wrong word.

Fightmastermpq

mohio wrote:

Fightmastermpq wrote:

I would definitely spend 50CP on an OML only LT. I currently have him at 4/3/5 (with an extra red cover in queue.) Right now the only thing that will really make me more competitive in PvP is that last cover I need to champ him and be able to respec.

That's understandable since you already have a championed phoenix, but if all you had was that OML and still needed covers for all the other 5* would you still be willing to throw away the other covers you would be likely to get from opening more tokens?

I also have 12 OML covers and one expiring soon (2 days...), as well as 12 PHX covers and one expiring soon (so lucky lately...). I still don't think I would cost myself the possibility at more BSSM or GG (or even SS) covers, by spending more for chances at only PHX or only OML.

It's definitely roster dependent. In your case you probably want both, but if you are no where near having Phx covered then the token with the best value is the one that has the lowest CP/OML cover cost. In classics he is currently 667 CP/cover while a 50CP OML token with a 15% draw rate would be only 333 CP/cover. This assumes the other 5* covers you would also earn hold no value, which for me with a champed Phx and only 5 covers for BSS/GG this is largely true. I could spend twice the CP to get that OML cover plus one of all the others, but those others don't add hardly any value since a 452 Phx is really no different from a 451 Phx, and the others are going to sit at 255 until they have probably 10+ covers.

In fact, once I get my last OML cover I'm planning to save my CP until I can pull 260 Latest LTs (maybe even more because RNG). As this is the number of pulls you need to get 39 (3 of each character) 5* covers given a 15% draw rate. I feel like 3 champed Latest 5*s (whoever they are 9 months from now) would add much more value to my roster than using it on classics and slowly covering my BSS/GG/IM/Cap/Banner and adding a handful of levels to my OML/Phx.

*Note I also have a 4/4/4, lvl 435 SS but it's not worth considering in this conversation because he is just that bad.

**It's also worth noting that for any of this to make sense D3 must keep moving Latest characters to classics with both 5* draw rates staying at 15%. Given precedent that's unlikely to be the case, but year-long plans that are disrupted by last minute changes are just another part of the game.

Fightmastermpq

dsds wrote:

In order to disprove this fact

Let me stop you right there.

1) It's not a fact, it's a hypothesis.
2) This hypothesis is based on evidence that is anecdotal at best.
3) You don't present a theory with little to no evidence to back it up, and then submit that someone else must disprove this theory else it be considered fact.

The burden of proof is on you, go collect your data on pulls from smaller rosters with a large sample size and show us any correlations you find.

dsds

Fightmastermpq wrote:

dsds wrote:

In order to disprove this fact

Let me stop you right there.

1) It's not a fact, it's a hypothesis.
2) This hypothesis is based on evidence that is anecdotal at best.
3) You don't present a theory with little to no evidence to back it up, and then submit that someone else must disprove this theory else it be considered fact.

The burden of proof is on you, go collect your data on pulls from smaller rosters with a large sample size and show us any correlations you find.

yes you are right, it is a theory. Wrong choice of words. My bad.

But a lot of threads are based on theory because we really can't prove anything. We just get close to the truth but we never really know. So we are basically going in circle here.
And I have made an effort to ask others with smaller rosters, that's all I can do.

I can't prove it myself because I have every 3,4,5* character except for 5hulk and 5america.

Fightmastermpq

dsds wrote:

Fightmastermpq wrote:

dsds wrote:

In order to disprove this fact

Let me stop you right there.

1) It's not a fact, it's a hypothesis.
2) This hypothesis is based on evidence that is anecdotal at best.
3) You don't present a theory with little to no evidence to back it up, and then submit that someone else must disprove this theory else it be considered fact.

The burden of proof is on you, go collect your data on pulls from smaller rosters with a large sample size and show us any correlations you find.

yes you are right, it is a theory. Wrong choice of words. My bad.

But a lot of threads are based on theory because we really can't prove anything. We just get close to the truth but we never really know. So we are basically going in circle here.
And I have made an effort to ask others with smaller rosters, that's all I can do.

I can't prove it myself because I have every 3,4,5* character except for 5hulk and 5america.

Look, aes did a ton of work here and actually compiled a pretty substantial sampling of pulls - probably the largest that we have. His conclusion......

aesthetocyst wrote:

c. Is MPQs RNG "honest"? Yes. The RNG is honest, in that any large enough dataset will begin to resemble the published odds. The larger the dataset, the greater the resemblance.

If you are going to claim that isn't accurate you are going to have to present a good deal of evidence to support it. Even if what you hypothesize were true you would increase draw rates for the newest characters that even the vets and forumites might not have rostered, but we don't see that. Let's stop making theories based on feelings and anecdotes and presenting them as facts. If you are suspicious track your data, and request others do the same...then come back with the data when you have something worth discussing.

dsds

Sorry i didn't mean to sound unappreciative. I appreciate all the effort you have put in. No doubt that is a pretty huge project to do.

We all have confirmation bias whether it be for or against or whatever. I am not saying that it couldn't happen to me, I could very well be bias as well. I am just doing some constructive criticisms here. Like anything scientific. You publish your findings and other people will try to find something wrong with it. If everyone says yes that is correct and it's undisputable, then there would be no progress. I mean we are all human after all.

Here's my own experience though. I am pretty tired of the grind recently, so there was one new 4star release that I didn't do moon knight. And it so happens that I get that character a few weeks after his pve. Then there's the other user that I agreed with that got more new characters as well. So that's at least two people here that see this. It is such a small sample size, it's very likely a coincidence, but this is something that can be considered. There is a motive for this. 1000hp per roster slot is quite a bit. If it gets even 1% of the mpq population to buy a new slot, it's quite a bit of money.

If you dismiss everyone's criticism, there would be no progress and we would further from the truth.

Please don't take it personally, This is just how scientific progress works. If you don't think the theory is good, then don't try to disprove it and leave it at that. I am not calling anyone out to disprove it. I am just stating a criticism that is constructive with no ill will.

dsds

Let me stop you right there. My criticism is really on characters that are not on your rosters like the other player stated. It wasn't to do with covers you are missing. So for instance someone who says they have 1 cover of professor X and can't get any would not be a counter to the theory because he already has one or more covers of that character in his roster. The theory comes from the fact that it will encourage you to buy more roster slots. It's also not a guarantee you will get it, just a higher chance.

It's safe to say not too many people would prefer 1 cover of a character they don't have on their roster because that character is unusable for a significant period of time and would be wasted, if they didn't buy an extra roster slot. They would much rather have a cover of a character they have covers for so they can use that character right away. You see those types of posts randomly everywhere like the DDQ clash ones where they beat someone only to get a cover of someone they don't have and they complain how they can't use it for 6 months. For sure your suggestion to hoard would help too if this theory is true because if you hoard, you're much less likely to get a single cover of something you don't have.

Also I didn't state that RNG would "flip" and force you to waste covers by giving you too many covers you already have. that is just your own assumption that I would think that. My theory is simply that if you don't have at least one cover of a character, your odds of getting that said character may increase. My criticism for the theory is that the people who submitted the data may already have at least one cover of every character available in the 4-5* land, so you don't see the pattern, that is all.

agarber

Aes, thanks for nice job! Though I have a correction from math point of view. These

aesthetocyst wrote:

b. Each of a character's 3 colors are completely separate possibilities.[/b] That is, separate database items. I have seen players ask from time to time whether, when a token is opened, the character is selected by RNG, and then the color determined by a 2nd RNG. Similarly, players often ask why we can't have colorless covers, or convert one color to another. Well, only the devs know the code involved and the database structure, but distributions of pulls indicates that each color of each character is a completely separate item. In any sizable dataset, plotting the distribution of individual character colors by quantity pulled yields a normal distribution. Plotting the distribution of characters by quantity pulled (that is, disregarding colors entirely) yields a non-normal distribution.

actually are both "non-normal" distributions though one (or both) can look like that.

TL;DR: Math is easy.

The normal distribution (or bell curve which is density of the normal distribution) come from the Central Limit Theorem https://en.wikipedia.org/wiki/Central_limit_theorem

In simple words it is the following. If X1, X2, ... , Xn are equally distributed independent random variables, then their average is a normal distribution with certain parameters.

What does that mean in case of LT pulls? Let's say we have chosen one 4* - IW, and we are pulling LT 100 times. Then each random variable will give us value 0 (if we did not pull her), or 1 (yes, one more IW). Then we take the average of 0's and 1's after 100 pulls, and this will give us an outcome for one experiment for average of 100 random variables. Now if you take 100 average outcomes and plot them, you will get something close to a normal distribution (actually not really, as rate of convergence could be not that fast).

In your experiment, first value was the average of measured random variables for IW, second - for Flaptain, and so on. The problem is that they are not independent. If you pulled 50 IWs in 100 LTs, there is no way you could pull 51 Flaptains from the same 100 LTs, and independent random variables give non-zero probability for that.

Now come my speculations, as I am not an expert in statistics or probability

So, why "almost" normal distributions appear? Reason for that is the following. Though the measurements you have plotted are not independent, if you throw away small part of them, then remaining will be "almost" independent because pulling each 4* has small expectation, so large deviation from average for each is also almost impossible, and thus it is highly unlikely to be affected by the boundary "you can't get more than 100 4*+5* from 100 pulls".

In your case for colored chars you have 93 outcomes (right?), so these "additional" chars that bring dependency problem are not visible. In case of 31 uncolored chars, they are more visible and that is why you can see non-normal plot.

agarber

aesthetocyst wrote:

Sure, sounds good to me! In your opinion, could we abuse another term to explain the emergence of bell curves, as iterations increase into a sufficient multiple of the number of possible outcomes, as a good ol' fashioned "regression to a mean"? If you keep piling on the iterations, the average distribution of the outcomes will increase, and the extreme low and highs will be watered down.

Don't think this will work. As I got from Wikipedia, "regression to the mean" also deals with two or more independent measurements of the same random variable, and in our case they still depend on each other, though not too much.

Actually, it seems that you should get something close to a Binomial distribution https://en.wikipedia.org/wiki/Binomial_distribution

Looks like a bell curve, and it should converge to it if you fix p, increase n, and scale it correctly. There is a part of Wikipedia article that claims exactly that.

Addition: Though outcomes are not independent still... It is like a question "how we can treat dependent random variables as independent". I don't know the answer Google did not help me till the moment

agarber

aesthetocyst wrote:

Look at probability distributions and discrete random variables, see if those float your boat?

Anyway, I found how one check whether RNG is "fair enough". One can do that using chi-squared tests http://wiener.math.csi.cuny.edu/Statist ... at013.html
Though it uses R language, and I am not sure it is free. Probably Google Docs can do something like that

However they use 150 tries for a regular dice (6 faces), so for our 100 outcomes we should use at least 2500 pulls... Or 50000 in case the number of tries must be quadratic in number of options.

The other option. It could be close to a Poisson distribution https://en.wikipedia.org/wiki/Poisson_distribution
which is also a certain limit of binomial... But I can't find any confirmation to that as well...

DTStump

agarber wrote:

aesthetocyst wrote:

Look at probability distributions and discrete random variables, see if those float your boat?

Anyway, I found how one check whether RNG is "fair enough". One can do that using chi-squared tests http://wiener.math.csi.cuny.edu/Statist ... at013.html
Though it uses R language, and I am not sure it is free. Probably Google Docs can do something like that

Yes, R is free. As a matter of fact I have it installed on my PC, so if you'd like me to run a few tests, I could. I would just need the dataset, of course.

OneLastGambit

dsds wrote:

Sorry i didn't mean to sound unappreciative. I appreciate all the effort you have put in. No doubt that is a pretty huge project to do.

We all have confirmation bias whether it be for or against or whatever. I am not saying that it couldn't happen to me, I could very well be bias as well. I am just doing some constructive criticisms here. Like anything scientific. You publish your findings and other people will try to find something wrong with it. If everyone says yes that is correct and it's undisputable, then there would be no progress. I mean we are all human after all.

Here's my own experience though. I am pretty tired of the grind recently, so there was one new 4star release that I didn't do moon knight. And it so happens that I get that character a few weeks after his pve. Then there's the other user that I agreed with that got more new characters as well. So that's at least two people here that see this. It is such a small sample size, it's very likely a coincidence, but this is something that can be considered. There is a motive for this. 1000hp per roster slot is quite a bit. If it gets even 1% of the mpq population to buy a new slot, it's quite a bit of money.

If you dismiss everyone's criticism, there would be no progress and we would further from the truth.

Please don't take it personally, This is just how scientific progress works. If you don't think the theory is good, then don't try to disprove it and leave it at that. I am not calling anyone out to disprove it. I am just stating a criticism that is constructive with no ill will.

The highlighted section is the problem with your method. Any scientific analysis cannot be done on a personal experience. It needs quanitifiable data and opinion is not reliably quantifiable. I think everyone involved here would be perfectly fine with you providing data analysis from a significant and representative data set which disproves or questions the theory, but that's not what you are doing.
Provide evidence and people will agree but simply stating your experience is different is not a valid enough point to be considered scientific constructive criticism.