About the whole "Japanese atma farming theory" thing, there's a bunch of holes in it.
The theory claims at certain atma have a better chance to drop at certain times. These times are supposedly linked to the Japanese times.
First issue would be the time windows the drop rate would improve. Assuming the average person has work from 8 to 5 and goes to bed from 12 to 7, there's a maximum of 6 available windows open for said person. If you'd subtract daily necessities, such as hygiene and food, the amount of available windows are usually less than available. One could argue whether Square-Enix may or may not design it like this. But a design like this is simply not fair for a lot of players as the "best windows" aren't available to them at all for certain atma.
Secondly would be how the theory is linked to a "mechanic" outside the game. With this I mean real life time. It would be more reasonable if the theory was linked to the Eorzean time. But one Eorzean hour lasts about 3 to 4 minutes. Which is nowhere near enough to finish a single FATE from start to finish.
Thirdly is the data. I tried googling for the data of samples they took to create this theory, but I haven't encountered it yet. Supposedly they asked for other players when they obtained specific atma. Without any data sheets available anywhere, this raises the following questions: How many samples were taken? How many samples did get an atma drop? How many samples didn't get an Atma drop? More importantly: How many samples were not recorded?. From reading just reddit, it seems like they only took samples they were looking for and didn't regard samples they didn't want. Samples they didn't want would be players not obtaining an atma with the very same fate. If you're still confused, imagine this: 100 players on a specific FATE. 10 players get a drop and all 10 report they have one. 90 players didn't get a drop and didn't bother to report. Although extreme, this example would mean the droprate would be 100% for this particular FATE for a specified time. While in reality 90 didn't get it.
Lastly would be post theory release. Once the theory was made public, a massive horde of players started doing FATEs in specific regions during certain hours. If the amount of participants would multiply by 10, then obviously the amount of ATMA drops would be multiplied by 10 as well. On average anyway. With the massive increase of atma drops simply due to numbers, the amount of reports of the theory being "legit" also increases. These same believers would also not farm outside those hours. As they cannot be bothered. So at the same time the amount of FATE participants for areas outside the theory time will diminish as well.
tldr; too many holes in the theory, believe it if you feel comfortable with it.


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