Math, Materia, and How to Succeed at Melding

[ChiefCurrahee]

From what I've seen the melding chances are not correct. It took me over 1200 materia to get my gamblers crown and a double meld with tier 1 materia is supposed to be around 42 percent chance. It wasn't even close to 42 percent, some times i would fail 35+ double melds in a row. I did keep track for a while and it seemed the average was about 15-20 percent chance. More closer to 15 percent imo but no where even close to 42 percent. It wasn't uncommon to fail 15 double melds in a row, finally get a double meld, then fail another 20 in a row.

The materia melding system is garbage. If you are unlucky you get screwed over while a small amount of people seem to consistently have good luck and reap the rewards from it. Would like to see a more balanced, less RNG system put in place.

P.S. This is a repost from another materia thread but i felt it applied to here too.

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.

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%?


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.

[morpheus]

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.

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.

[Alzelia]

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.

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.

[Alzelia]

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.

(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.

[ChiefCurrahee]

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.

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.

[Onisake]

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

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

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%?

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.

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.

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.