Math, Materia, and How to Succeed at Melding

In other words, if you want good gear be prepared for tons of failure first. Don't come on the forums crying that you blew up your only double melded chest piece trying to get a triple. We're only going to laugh at you.

Do you have any info for moon phases? Most of the people that I play with tend to think that a full moon increases your odds, while a new moon decreases them. A friend triple melded a pair of hands for me yesterday during full moon phase, on an item I already had double melded a long time ago. What do you folks think?

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Originally Posted by ChiefCurrahee

Just because something says you have 42% chance to create a successful result doesn't mean 42 out of 100 WILL be successful.

It's pure Random Number Generation (RNG) per individual item. You can have 100 melds @ 42% positive meld rate and fail all 100. Yet you still have a 42% chance in a positive result.

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With a pool size as large as 1200 if it was 42% chance you would think you would see it start equal out after a while? Or maybe not only did i get unlucky, but i kept getting unlucky over and over and over again. What's the odds of someone having this bad of luck over and over again on something with a 42% chance. Now, what are the odds that the 42% number might not be correct considering the information i posted along with others.

This post was very insteresting to read and conforted me a little, since I've been blowing up Sarngas left and right. So thank's the OP for that.

Anyway, I recently applied these notions to try and double meld a weapon with 2 Mind Materia III, so I decided to post my results here and hopefully help some ppl in their melding quest too.

I tried to use the lower tier materias, but didn't always have them. I noticed that the success rate when as low as 28.00% and as high as 30.00%, so I used the 28% value to do the calculations.

Obviously, one would expect 1/.28 = 3.57 weapons would be enough, so I made 4.
For this, the probability of me failing the 4 weapons in a row, would be (.72)^4=26%, which is still very high.
And so indeed I failed these 4.
Then I decided to make 4 more.
Now, the probability of me failing the 8 weapons in a row would be (.72)^8=7%, which is fairly low.
I failed the first 3 and got it at the last one.

The probability of all this happening was around 10%.
It seems to be really really just bad luck, but I can't seem to wonder if there isn't something more or (being a Software Engineer myself) if there's something wrong with their random number generation algorithm XD


EDIT: okay, to be fair, after this incident, i just double melded 3 weapons in a row XD
You're forgiven, SE!!

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Originally Posted by Alzelia

TLDR

What all this boils down to is this very simple fact:
You wanna take a risk, do it yourself.
You wanna be safe, buy it.

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PROMOTE THAT MIQOTE! NOWZ

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Originally Posted by morpheus

With a pool size as large as 1200 if it was 42% chance you would think you would see it start equal out after a while? Or maybe not only did i get unlucky, but i kept getting unlucky over and over and over again. What's the odds of someone having this bad of luck over and over again on something with a 42% chance. Now, what are the odds that the 42% number might not be correct considering the information i posted along with others.

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Without giving me PERFECTLY accurate numbers for you're success rate it is impossible to determine if the 42% is correct. Human memory is flawed, especially when dealing with such a large sample size.

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Originally Posted by morpheus

With a pool size as large as 1200 if it was 42% chance you would think you would see it start equal out after a while? Or maybe not only did i get unlucky, but i kept getting unlucky over and over and over again. What's the odds of someone having this bad of luck over and over again on something with a 42% chance. Now, what are the odds that the 42% number might not be correct considering the information i posted along with others.

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(WARNING: the math up ahead will get much more complicated than what I have been using previously. Skip ahead to the blue text to skip the math)

I figured I would elaborate a bit further about probability over increasing sample populations, like the one you describe above. I have often said that it is in the long run that eventually your overall odds will get closer and closer to the 42%. With a probability of success at 42%, you would expect 504 out of the 1200 to be successful melds. However, random chance is involved, so you may not get this number. There is a statistical process to determine the chances of, for example, getting 450 out of 1200. To figure that out you'll need to use a cumulative binomial probability.

The first thing we need to do is figure out the probability of getting exactly 450 successes. To do this we use the binomial formula:

b (x; n, P) = C * P^(x) * (1-P)^(n-x)

Where:
x = The number of successes = 450
n = The number of trials = 1200
P = Probability of success = .42 (42%)
C = The number of combinations that will give us 450 successes.

Here is the formula to find C:

C = (n!) / [x!(n-x)!]

The formula above only gave us the probability of finding exactly 450 successes. However, we are looking for the chance it will be 450 or less. So we need to figure out the chances of exactly 449 successes, 448, successes and so on, and then add them all up.

Luckily, you can do this problem in excel, go to any frame and type " =BINOMDIST(450,1200,0.42,TRUE) " Hopefully you noticed that each of the numbers in the parenthesis corresponded to one of the numbers I used above. If you use TRUE it will figure out the cumulative probabilities up to 450, if you use FALSE, it will figure out the exact probability of getting 450. When I plugged everything in, excel gave me an answer of .083%


So out of 1200 double melding attempts at 42%, you should expect them to succeed with 504 of the attempts. Some people might get more, some might get less. We would expect to get a cluster of numbers around 504. What I used all the math for, was to determine how widely spread that cluster of numbers would be. What I found is that 98% of the time, the number of successes would be between 464 and 544.

EDIT: After all that, I think I'm done analyzing probabilities of melding to make sure SE's numbers are correct. From now on all my future work on this will be based on the assumption that the percentages SE gives are accurate. However if someone could provide me with UNBIASED data I'll work out the probabilities and Standard deviation for them.

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Originally Posted by Resheph

Do you have any info for moon phases? Most of the people that I play with tend to think that a full moon increases your odds, while a new moon decreases them. A friend triple melded a pair of hands for me yesterday during full moon phase, on an item I already had double melded a long time ago. What do you folks think?

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I don't think the moon phase has anything to do with melding. I believe the percentages given by the game are completely accurate. I believe that the exact same meld will give the exact same percentages. However I plan to do some testing to check what the actual factors for melding are. I'll list what I think actually does influence your chance of double melding.

Possible factors

HQ versus NQ gear

What materia is already equipped

Materia tier (mind IV vs mind iii)

Materia sub-tier ( mind iii (11) versus mind iii (15))

Materia type (trying to put 2 different materia on the same item)

Item level

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Originally Posted by Alzelia

I don't think the moon phase has anything to do with melding. I believe the percentages given by the game are completely accurate. I believe that the exact same meld will give the exact same percentages. However I plan to do some testing to check what the actual factors for melding are. I'll list what I think actually does influence your chance of double melding.

Possible factors

HQ versus NQ gear

What materia is already equipped

Materia tier (mind IV vs mind iii)

Materia sub-tier ( mind iii (11) versus mind iii (15))

Materia type (trying to put 2 different materia on the same item)

Item level

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As far as i like your Thread, you should consider gathering information about moon-phase and directions as well. SE denied that the 12 has anything to do with it, but wanted to keep it a secret if moon-phases do.

Actually moon-phases and directions had an effect in FFXI, so why not in FFXIV? If not this, the moon-phases didnt need to be there at all.

All triple-melds tier IV i made, including the 5-meld tier I for the crown happend during new-moon btw. i tried it also on different phases, as on full-moon i never got a 4-meld tier I. As i mentioned in a different thread i cant prove it, SE did not deny it. So gathering info's about this, may could help to clarify this topic as well.

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Actually moon-phases and directions had an effect in FFXI, so why not in FFXIV? If not this, the moon-phases didnt need to be there at all.

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Actually it never did in FFXI. Took down synth data for over a thousand synths back then.
People just like to believe in whatever they want.
(And because the programming team is different.)

I double-melded Colosseum Loincloth x 2 out of 5 before new moon started.

End of the day, it's a "religion". Just believe in whatever makes you feel good. No need for proof. Even if there is proof to the contrary, people will still think moon phases have an effect.

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Originally Posted by Nero

As far as i like your Thread, you should consider gathering information about moon-phase and directions as well. SE denied that the 12 has anything to do with it, but wanted to keep it a secret if moon-phases do.

Actually moon-phases and directions had an effect in FFXI, so why not in FFXIV? If not this, the moon-phases didnt need to be there at all.

All triple-melds tier IV i made, including the 5-meld tier I for the crown happend during new-moon btw. i tried it also on different phases, as on full-moon i never got a 4-meld tier I. As i mentioned in a different thread i cant prove it, SE did not deny it. So gathering info's about this, may could help to clarify this topic as well.

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I'll add a category for that in my records, but it would take a data set of at least 2 thousand melds before I could say anything conclusively about it.

Honestly, this sounds to me like a "Self-fulfilling Prophecy." That is, you believe that a new moon will give you a better chance at double melding, so you decide to wait till the new moon to attempt the meld. And since you do more melding during a full moon than any other time, you get more melds during a full moon. This encourages that belief, and it just goes in a vicious cycle.

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Originally Posted by Alzelia

Honestly, this sounds to me like a "Self-fulfilling Prophecy." That is, you believe that a new moon will give you a better chance at double melding, so you decide to wait till the new moon to attempt the meld. And since you do more melding during a full moon than any other time, you get more melds during a full moon. This encourages that belief, and it just goes in a vicious cycle.

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I get what you are pointing at, which is logical. Problem with that is.. i tried to 5meld for the crown during all moon-phases, while i burned around 200 STR tier I Materia's. Same goes for the tier IV triple meld.. ich tried them a lot, no matter which phase.. when they started to work out at new-moon, i stood on that which does not mean that i never tried on other phases again.

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Actually it never did in FFXI. Took down synth data for over a thousand synths back then.
People just like to believe in whatever they want.

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So did i, since i was a Bonecrafter.. and now? you believe it didnt have an effect, i did believe it had an effect. SE themself stated "may it does, may it does not". Who is right? you or me?

Exactly my point of gathering data about it.

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Originally Posted by morpheus

With a pool size as large as 1200 if it was 42% chance you would think you would see it start equal out after a while? Or maybe not only did i get unlucky, but i kept getting unlucky over and over and over again. What's the odds of someone having this bad of luck over and over again on something with a 42% chance. Now, what are the odds that the 42% number might not be correct considering the information i posted along with others.

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Sure you can expect to see an out come around 42% AFTER THOUSANDS and THOUSANDS of attempts.

However it's a probability of success. So some people after thousands of attempts will find they only had a 35% success rate while someone else might find they had a 50% success rate.

The 42% you're seeing is just the chance of probability that EACH item you attempt will have a positive out come, but has a 58% chance to fail. It's just a roll of the dice and hope you come out on top.

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Originally Posted by tymora

End of the day, it's a "religion". Just believe in whatever makes you feel good. No need for proof. Even if there is proof to the contrary, people will still think moon phases have an effect.

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Thank the 12 i'm an athiest.

I still plan on updating this, I've been a bit busy though

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Originally Posted by ChiefCurrahee

Just because something says you have 42% chance to create a successful result doesn't mean 42 out of 100 WILL be successful.

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ehhh. yes and no. It should be close to 42 within tolerance. if you do 100 attempts and you are supposed to get a result 42% of the time, you should expect to get that result between 39 and 45% of the time. anything beyond that And i would say it's not really 42%.

more later

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Originally Posted by ChiefCurrahee

It's pure Random Number Generation (RNG) per individual item. You can have 100 melds @ 42% positive meld rate and fail all 100. Yet you still have a 42% chance in a positive result.

For all those people who don't understand you can do an experiment. Go buy a 10 or 20 sided die

pick 2 random numbers for the 10 sided die and 5 random numbers on the 20 sided die. This will give you 20% of the numbers on the face of the dice. Roll the dice 100 times and record your results. How many times did your randomly picked numbers show up? 20% on the nose? Was it less than or greater than 20%?

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the results will vary between the two die. using a RNG (http://stattrek.com/statistics/rando...generator.aspx) i just did a quick test. 100 attempts to get a number between 1 and 20. i had 6 instances less than 20. Doing this 4 more times i got 14, 9, and 23, and 18. so out of 500 attempts i had an average of 14% success. that's 6% off. and 500 is a fairly large sample size. at what point do we say we have enough samples to be statistically significant? at what point do we say it's not within tolerance to say that this is not 20% success rate?

doing the same test between 1-20 and looking for instances between 1 and 4 i had 21 instances. doing this 4 more times i got 19, 23, 15, and 18. that's a 19.2% success rate. this is much much closer to what is expected. it would be difficult to argue that this is not an accurate rate.

so one is perceived to be more accurate than the other. even though they are technically exactly the same. Why is this? It's a simple mater of scaling.

IE: in the 100die example there are 100 possible outcomes. when you attempt 500 times, that's 500*100=50000 possible outcomes. in the 20 sided die example there are only 10000 possible outcomes. IE: as an individual i need to increase my sample size by at least 5x on the 100 sided die to see a comparable scaling.

So when a success% is displayed, is it for the individual or the server? in this case it is most likely for the server. because we don't accurately see this rate unless we have an absolutely massive sample size.

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Originally Posted by ChiefCurrahee

The game doesn't keep track of every meld you make, and if you fail 4 times in a row the 5th isn't a guaranteed success for a 20% positive meld rate. It just means that every item you meld has a 20% chance to roll the magic numbers on the dice.

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the perceived problem is our die is just too large. when it says 20% is it 20/100 4/20, 200/1000? because this makes a large difference on the small scale. the average player probably won't attempt more than 20 times because they aren't likely to be able to afford it. so it should be normalized to show this percentage over 20-100 attempts. not over thousands.

title should be changed to Meth Materia and Melding. Stop overthinking it guys

Seriously. Just get a whole mess of mats, a whole mess of materia, and start crafting. Make bigger piles for crazier melds. You might get what you want out of it, or not.

Yeah I do think the title is a bit misleading. It doesn't really tell you how to be successful at melding, as well it couldn't, since melding is entirely based on luck. If anything it teaches you how to manage expectations and not smash up your keyboard lol. As far as anything rng related goes, its just a simple roll of the dice. Probability, unfortunately, deals with infinity; that makes it a bit harder for our brain to wrap around. Since we think in terms of finite numbers, all statistics can tell us is the chance of failing every time out of a finite number of attempts. Its useful for humans, since we never plan on doing anything to infinity. Regardless, the probability of success will always remain the same no matter how many times you repeat it, thus the only real way to succeed at melding is to do what OP said:

1) Do it a billion times until you win

or

2) Buy it.