So what's the math/logic behind the percieved discrepencies between % and actual rate

Honest question here, as I know there's an explanation for it (Either scientific or mathematical) that explains the phenomena wherein we see things with a high % chance yet seem to see a lot of fails.

I.E., gathering:
95% chance of success per hit. Missing one hit every time for the last 5 times.
33% chance of proc per hit. Never seeing the proc activate upon any of the last 15 hits. etc.

Basic things like that wherein the percentages wind up not matching the actuality - or even feel like they come close to it (Honestly feel like I'm at a 60% success rate at 95% on both characters.)

Note: This is not a complaint. I am more curiously about the psychology, mathematic, or scientific aspects that define this better.

Appreciate it!

Gambler's Fallacy - https://en.wikipedia.org/wiki/Gambler%27s_fallacy

There are generally two things at play, one psychological and one technical. The psychological aspect is called confirmation bias (we remember the strings of failures at 95% and forget the multiple times we HQ with less than a 20% chance, things like that). This also involves us forgetting that everytime we fail at 95%, someone else more than likely just got a 5% HQ.

The technical aspect is that computerized random numbers aren't truly random. They have to be programmed in some way, and while I don't know the details of this game's RNG, sometimes what happens (as an example) is that the program generates an incredibly long string of numbers when it's started and each time a "roll" is called for, it takes the next roll in the sequence.

Obviously, for an MMO, it's going to be more complicated than that, since the servers need to handle hundreds upon hundreds of random numbers at any time.

To summarize what's already been said... Each time you roll to see if you hit or not (as in your first example) you have a 95% chance to succeed, you also have a 5% chance to fail. Because each of these attempts is rolled separately you actually have the same odds every single time. In many cases it's likely with such odds that the rolls will seem to favor you, but they really don't.

The percentage tends to normalize over a larger sample of attempts that will produce a number that reflect the percentage rate.

The percentage of this game is clearly not what it states and its been frustrating ever since the start of FF14. I assume the game was designed to appear favorable but is in fact a gil or time sink, hidden by ''probability''.

Roll a dice with 100 sides and I swear to you you'll very rarely get that 5% be it negative or positive, even less chances to get 2 in a row. And look at the materia system. 33% means you should in theory win 3 times out of 10 but failing 20 times in a row is obviously a problem no matter how unlucky you are. Seeing the high number of people fail the same amount is obvious that the system cheats itself.

In my opinion, consider the amount stated to be about 10% to 20% lesser than what it states.

If you flip a coin 10 times, how often will you see 5 heads and 5 tails? What about 100 times? 1000?

People are really bad with probability and statistics. Over a very large number of samples, the observed data will approach the expected.

Sometimes, RNG takes a dump on you.. But we also tend to have more memory of the bad runs than of the normal or even good runs. When making my lucis tokens, I just kept chanting myself to remember the law of large numbers.. Throw myself at the crafts enough times and I WOULD get my tokens.

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Originally Posted by Rock_Biter

Gambler's Fallacy - https://en.wikipedia.org/wiki/Gambler%27s_fallacy

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This was an interesting read.

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Originally Posted by Hito-Shura

And look at the materia system. 33% means you should in theory win 3 times out of 10 but failing 20 times in a row is obviously a problem no matter how unlucky you are.

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And that is wrong.
33% mean that you have a 67% fail chance regardless how many times you try it.

I can't edit my post, but I did just think of one example of unfair RNG that did get fixed. It used to be that if you crafted with all NQ mats and no quality increasing actions, you would never see a HQ result. After one patch, the HQs suddenly started appearing.. And it felt really weird and highlighted that there was inaccurate reporting of the true HQ chance before, but perhaps only at 1%.

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Originally Posted by Hito-Shura

Roll a dice with 100 sides and I swear to you you'll very rarely get that 5% be it negative or positive, even less chances to get 2 in a row. And look at the materia system. 33% means you should in theory win 3 times out of 10 but failing 20 times in a row is obviously a problem no matter how unlucky you are. Seeing the high number of people fail the same amount is obvious that the system cheats itself.

In my opinion, consider the amount stated to be about 10% to 20% lesser than what it states.

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I'm sorry, and I mean no disrespect, but you are completely wrong.

Each individual 'roll' of the die is a separate random event, so your chance of rolling 1 on a 100 sided die is 1% the first time you do it, and the second, third, fourth..., the 1 millionth, etc... The chances of a sequences of 1's occurring is lower and you can calculate that %chance based on the number of 1's in the sequence vs the number of other possible outcomes. But the thing is, it's still possible that it could happen, it's just more and more unlikely.

33% doesn't mean that in theory you should win 3 out of 10, 10 is a small sample of 100, even with 100 tries, you may get 33 out of 100 (33%) but that's only one possibility. Statistically over a very large sample (1,000,000s of events) a 33% chance will be borne out, but not necessarily over a shorter sequence of 10 or 100 events.

This is why a 1% drop rate is often seen to be so miserly. Over the entire course of play for all players, that item drops at 1%, but any individual player could go several hundred attempts before seeing the drop happen, while another could get it on their first try.

Is funny people remember clearly those 95% miss here and there but forget those 2 HQ in a row with 15%

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Originally Posted by Myrhn

Is funny people remember clearly those 95% miss here and there but forget those 2 HQ in a row with 15%

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Confirmation bias

your asking for math and logic for RNG. Closest thing you will get is statistics...

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Originally Posted by Hito-Shura

The percentage of this game is clearly not what it states and its been frustrating ever since the start of FF14. I assume the game was designed to appear favorable but is in fact a gil or time sink, hidden by ''probability''.

33% means you should in theory win 3 times out of 10 but failing 20 times in a row is obviously a problem no matter how unlucky you are. Seeing the high number of people fail the same amount is obvious that the system cheats itself.

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Congrats to the North American Public Mathematics Education Program.

Are we just throwing statements into the wind or does someone have data that actually proves "Seeing the high number of people fail the same amount is obvious the system cheats itself?"

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Originally Posted by Dante_V

The percentage tends to normalize over a larger sample of attempts that will produce a number that reflect the percentage rate.

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That's called the Law of Large Numbers, btw.

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Originally Posted by Mycow8me

your asking for math and logic for RNG. Closest thing you will get is statistics...

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Um, statistics is logic and math.

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Originally Posted by raela

unfair RNG

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RNG is not fair or unfair. It's random.

Threads like these time and again show that people do not understand randomness, statistics, or basic math. *sigh*

statistics is anything but logic, it only exists to prove that something will eventually happen the only question is when.

You could argue the formulas are logic I guess.

I appreciate al ot of the responses here! It makes a lot of sense, just been a while since I studied these catagories so I'm glad to see the way it connects in the background. XD It's easy in the frustration of "**** I just hit my third miss in a row at <insert high percentage here> this is bull****" but a lot of you with a bit more knowledge helped remind me of how the statistics actually work (Taking things less as a cumulative and more as a singular incident wherein the probability of it happening is statistically the same but the probability of that sequence of events might have been statistically lower.)

The wiki article was a great read too. Thank you very muhc for that! o/

Here's the devs description of it: http://forum.square-enix.com/ffxiv/t...Random-Comment

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Originally Posted by Mycow8me

statistics is anything but logic

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Well, this depends entirely onto what level of advanced mathematics you are willing to go. There *are* systems of logic - most of which are supersets/generalisations of classical logic - which allow you to reason about/with probability, uncertainty, or randomness.

This is where we get into probability. Let's say that we flip a coin 10 times, each next event is of course a 50% chance of getting heads. However if you want to calculate the chance of getting heads 10 times in a row, you would have to take 1/2 times itself by 1/2 ten times, or 0.5*0.5*0.5...and so on.

The end result would be 1/1024, or 0.00097 (0.097%, almost a tenth of a percent).

So the chance of you missing 5 times in a row at 95% success rate item?
Take the 5% failure rate and multiple it by five times, which looks like:
.05*.05*.05*.05*.05 = 0.0000003125

Therefore, the chance of you failing a 95% success rate item five times in a row can be viewed as that sucks mate.

EDIT: For your 33% proc chance, failing at 15 times, would be .67*.67 up to 15 times, which results in a 0.00246, or 0.246%

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Originally Posted by Eidolon

I appreciate al ot of the responses here! It makes a lot of sense, just been a while since I studied these catagories so I'm glad to see the way it connects in the background. XD It's easy in the frustration of "**** I just hit my third miss in a row at <insert high percentage here> this is bull****" but a lot of you with a bit more knowledge helped remind me of how the statistics actually work (Taking things less as a cumulative and more as a singular incident wherein the probability of it happening is statistically the same but the probability of that sequence of events might have been statistically lower.)

The wiki article was a great read too. Thank you very muhc for that! o/

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You bet. I felt the same way when I first experienced this in-game. "F@$#!ing game is cheating me!"

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Originally Posted by Zykor

So the chance of you missing 5 times in a row at 95% success rate item?
Take the 5% failure rate and multiple it by five times, which looks like:
.05*.05*.05*.05*.05 = 0.0000003125

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Actually, that's the chance that if you only do something five times that you'll fail all five of those times. If, on the other hand, you do that 95% success rate activity a thousand times, the chances that somewhere within that thousand a string of five failures in a row will occur is much higher.

That's why people think the percentages on gathering are off, because it's the sort of activity that gets repeated thousands of times. Overall the percentages come out about right, but people remember streaks of rare events in a row.

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Originally Posted by Malevicton

Here's the devs description of it: http://forum.square-enix.com/ffxiv/t...Random-Comment

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A interesting read. It reminds me of that vsauce guy's youtube channel.

He(Micheal Stevens) made a good video on what is random-ness:
https://youtu.be/9rIy0xY99a0

I found it a bit surprising that even things like dice aren't completely random. Another MMO was talking about the same subject. It seems like things that are truly random rarely "feel" random. It seems like if they alter programming so that you can't get a re-occurrence of the same number in a row would make it "feel" more random, but actually it would be less random. So, I'd imagine, most game companies seem to be against the idea of making things less random since people would probably take issue if they found out.

although 0.0000003125 seem very unlikely
yet, the probability are calculate base on large sample size almost to infinity
to closer to the infinity end, the more likely to stick to probability value
for example the chance of winning lottery is extremely low
but there are always someone win it
it is the population is so large even the probability are low, it could eventually happen

I am not very good with statistics, but I can help on the programming side.

There are some well know algorithms in use by a lot of companies for RNG. Sometimes, these algorithms tend to have strange behavior when looked at in a relatively small time frame. One algorithm when set to mod 10, for instance, has a tendency to favor the the low end (i.e. 1 and 0) over the short term, but eventually evens out. These behaviors could have something to do with the architecture its' run on, or quirks in the programming language, etc.

Think of how some of the abilities work for a gatherer (for instance). If we worked on a completely even distribution, with rules in place to keep certain values repeating constantly, then having a 75 percent chance to hit a node will never activate the ability that requires 4 hits in a row. So what people expect to happen in 4 hits (i.e. 1 hit missing) is a bad idea.

So the only choice with this specific game design is to allow, or even encourage streaks so some extent. This is why I think they chose the model they did. Rest assured, all well written RNG algorithms do even out eventually, even if it is infuriating in the end.


(Written fast, so please excuse any errors)

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Originally Posted by Zykor

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But with the sample sizes involved in crafting and gathering those numbers are actually pretty significant. The chances of it happening right on the craft that it happens are astronomically low, but those types of streaks are supposed to appear as the sample size grows (law of large numbers). Part of the problem is that people look at the streaks in a vacuum ("omg failed 3 95% in a row what are the odds?!" Well how many other attempts went normally before that happened?).

Going with your coin flip examples, the odds are 1/1024, so if you repeated it 1024 times it ought to have happened at least once. It's not guaranteed to have happened by any stretch, but 1024 is the number by which it would have been likely.

Similarly, we're supposed to get streaks in crafting/gathering every now and then. Not every craft or gather, but that's where confirmation bias comes into play. The odds look so anomalous that they stick out in peoples minds. If you were to actually do the coin flip experiment 1024 times (though that would obviously be boring) you would forget most of the results, but would likely remember ones like 10 straight heads or 10 straight tails. So even though people get different kinds of streaks at different times, most of which are relatively reasonable over long periods, they just naturally blank out the filler (filler being the crafts/gathers where nothing of note happens).