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%.