I've been collecting data on how many FATEs it takes to get Atma for the ARR Relic Weapons cause me and my partner both started out with very bad luck with them dropping at all. I also haven't done any statistical analysis in a long time so I thought it would be a fun, relatively simple refresher.
So far I have 20 Atma, 10 from North Shroud and 10 from Central Shroud. I'm not doing t-tests cause I can't be bothered to look up the relevant tables. I'll do z-tests instead with acknowledgement that my statistics will be suboptimal.
In the North Shroud, I got 10 Atma in 41 FATEs. In the Central Shroud, I got 10 Atma in 31 FATEs. With a 95% confidence interval, I can say the drop rate in North Shroud is 24.39% +/- 13.15% and the drop rate in Central Shroud is 32.26% +/- 16.46%. Obviously I would need to go a lot longer to get actually decent data but oh well? You can't make me?
Testing if the drop rates are the same between North and Central Shroud because I got weirdly lucky with Central Shroud, a one-tail z-test puts the z-value at -0.738 and the p-value at 23.03%. Not nearly low enough to be confident that there is a difference in drop rates, but the low amount of data means this is fully expected. That being said, I am VERY confident they wouldn't make different drop rates for different maps. That would be ridiculous.
Now, the reported drop rate by the community is 25% for Atma, but I do not know if we have a definite source beyond "that's what it seems like". With my 20 successful Atma drops over 72 FATEs, that's a drop rate of 27.78% +/- 10.35% (CI again 95%). Obviously within range of the 25%, but again, I wanted to practice stats cause I haven't done that in so long. And it's gonna take a while to get all the data from 120 Atma drops for all 10 ARR Relics.
The z-value came out to 0.526 and the p-value came out to 59.89% for a two-tailed z-test against 25%. Which is basically what is expected so far. That z-value would need to be > 2 to start feeling like there's a difference.
Despite my rough initial luck with the Atma and my partner's abysmal luck, it is looking initially like the drop rate is indeed 25%. I will continue to update with more calculations as my bored ass gathers more data.
And if anyone is dumb enough to help me with collecting data, that could be neat. Perhaps we could do some chi-squared tests between the various maps. You'd just need to count how many FATEs you do in each map and how many Atma you get in said maps while having the appropriate weapons equipped.