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TLDR: The drop rates of both adjacent and uncompleted maps are far higher than we've been told. It seems that adjacent map have ~4-5 times the chance to drop over a non-adjacent map (when both are completed), and if the adjacent map is also uncompleted, then it's ~9 times the chance in comparison to the non-adjacent. This is of course if you're running a map that is adjacent to the uncompleted map (so it can drop naturally).
Background
In the 3.2 patch notes is a change:
"You are now twice as likely to obtain maps you have not yet completed on the Atlas as maps you have. This is intended to help players who choose to play solo complete their Atlas."
This raised some confusion and so I asked Bex to clarify what this actually means in the form of concrete examples.
In this question to Bex one of the examples is about how the changes affect the chances of uncompleted (adjacent) maps vs completed (adjacent) maps vs completed (non-adjacent) maps;
NOTE: I have changed this example to simulate the new 3.6 atlas for the sake of simplicity and understanding/picturing the case. You can check the original from the thread linked above.
We have no completed maps in tier 6
We run Cage (T5 map), which has 2 adjacent T6 maps: Burial Chamber and Necropolis. When a +1 map drops, the chance of it being either of them is 1/2.
If we then complete Burial Chambers, the chances are now 2/3 for Necropolis and 1/3 for Burial Chamber to drop.
If we then also complete 2 extra T6 maps that are not adjacent to Cage (such as Vault and Lair), the chances are now 2/5
Burial ChamberNecropolis, and 1/5 for each of the other T6s.
In her response
Another thing that this answer confirms is that if a map is uncompleted, it only has twice the chance to be found (assuming you are running a map adjacent to it) in its tier in comparison to other maps in its tier that are not adjacent.
However, ever since 3.2 patch hit live, every now and then someone mentions that they're getting way more adjacent maps than other maps in the same tier when they're farming a specific map. For example in 3.5, people farming T16 Burial Chambers in 3.5 will find more T12 Necropolis maps than other T12 maps even if all of those maps are completed. I and many others have felt this but never really bothered to actually test this theory and just kind of shrugged it of as "it's probably just rng".
There has not been a patch that would even hint anything towards adjacent maps being favored over non-adjacent maps, unless the adjacent map is also uncompleted. I went through all patch notes since 3.2 and didn't find anything on this topic, but there is of course a chance that I missed something. So correct me if I'm wrong.
Now, couple months ago /u/ACTPOHABT asked me in my discord for verification on his observations that lead him to a conclusion that adjacent maps have a higher chance to drop regardless if the map is uncompleted or completed. In more specifics; he had obtained twice the amount of T6 Phantasmagorias and T6 Temples from a batch of 700 T7 Arcade maps in comparison to non-adjacent maps while having all T6s completed, which should not happen.
The second observation was from having Desert Springs and Shaped Belfry as his only T15 maps in his Atlas while having all of the rest maps in his Atlas completed, and an Eldered T16 map. And by running T14s, T15s (Desert Spring + Shaped Belfry) and the Eldered T16 for Uber Elder spawns he got 50 Pit of The Chimera maps and 15 of the other Guardian maps. Pit of The Chimera is adjacent to Desert Springs.
So obviously something is off. I asked him if he wanted to run an exclusive test just to test the theory and pinpoint somewhat the actual chances of the drop rates, and he was in.
TEST 1 Spreadsheet
We needed a map that is easy to sustain in low tiers to make sure we're getting a lot of returns and a good sextanting position to really ramp up map drops. We decided to do this test on T1 Atoll, as it's enjoyable, easy and linear/fast layout to run for a test like this, has good sextants and had 2 adjacent T2 maps; Arid Lake and Iceberg.
The setup:
Quad tab (576) of T1 Atolls
Full Atlas completion minus T3 maps (to downgrade all +2 drops from the map boss to T2)
Map rolling method: Alch / Chaos with 4 sextants (just to get more map drops)
The assumed result of T2 maps obtained based on what we've told by GGG should be close to equal amount of all T2 maps;
1/6 Arid Lake
1/6 Iceberg
1/6 Thicket
1/6 Pen
1/6 Dungeon
1/6 Armoury
RESULT
To our shock after he had finished the quad tab of Atolls, he had nearly 70% of T2 map drops being Arid Lake or Iceberg. Something is definitely wrong. How on earth can it be that adjacent completed map seems to have 5 times the chance to drop compared to other maps in the same tier that are non-adjacent?
The final results were 228 Arid Lakes (35,74%), 200 Icebergs (31,35%), 66 Thickets (10,34%), 53 Pens (8,31%), 48 Dungeons (7,52%) and 43 Armoury (6,74%) out of total 638 T2 map drops.
This suggests that adjacent map has ~4-5 times the chance to be found in comparison to non-adjacent maps in the same tier.
With 95% confidence the actual drop rate of the adjacent completed map Arid Lake in this scenario is within 32,0% - 39,5% based on this amount of data.
TEST 2 spreadsheet
Somewhere around the halfway mark of this test it was already clear how uneven the drops were, so we got interested in what would happen when one of the adjacent map is also uncompleted. We wanted to test this but Actpohabt decided to finish the first test first. We also saw this being a great opportunity to mimic the example that I gave Bex (in terms of setup, but at a different tier, which shouldn't matter).
Setup:
Quad tab (576) of T1 Atolls
Full Atlas completion with these exceptions:
only 4 T2 maps allowed to drop;
Iceberg (adjacent, uncompleted)
Arid Lake (adjacent, completed)
Pen
Dungeon
Map rolling method: Alch / Chaos with 3 sextants (just to get more map drops)
So if everything was working like in the example I gave bex, the distribution of maps should be something like;
2/5 Iceberg
1/5 Arid Lake
1/5 Pen
1/5 Dungeon
RESULT
375 Icebergs (56,56%), 201 Arid Lakes (30,32%), 46 Pen (6,94%) and 41 Dungeon (6,18%) out of 663 total T2 map drops
This suggests that uncompleted adjacent map has ~9 times the chance to be dropped in comparison to completed non-adjacent map in the same tier.
With 95% confidence the actual drop rate of the adjacent uncompleted map Iceberg in this scenario is within 52,8% - 60,3% based on this amount of data.
CONCLUSION
Most of this test was streamed by /u/ACTPOHABT in his stream, but he wasn't aware that twitch deletes old vods after a time unless they're saved as highlights so most of the proof of the actual completion of this test is lost, sadly. Here is a video of him doing some of the second test and here is a video of him analysing the data at the end, in case you're interested.
The spreadsheets Test 1 and Test 2 include calculated 95% confidence intervals for the results and it's fair to say without reasonable doubt that map drop mechanics calculations are not like we have thought. Either bugs/mistakes in the drop mechanics calculations, GGG has forgotten or decided not to tell us the real numbers, or something has changed since 3.2 and were not documented in patch notes.
It seems that instead of twice the chance for locked maps in comparison to completed maps is actually ~9 times, and even completed adjacent maps are over 4 times more likely to be found over non-adjacent maps in the same tier.
Again, I'd like to thank /u/ACTPOHABT for questioning the known rules and willing to run the actual tests after that, and thanks to Xayazi (dont know his reddit username) and /u/ZaneDX for helping with calculating the confidence intervals.
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