first off, kudos for taking the time and sharing the aoe estimations! this kind of data is what the discussion needs imo, since actual in-game tests - as valuable as they are - always suffer from low sample size, huge variability and, in turn, often quite a bit of confirmation bias. that being said, please allow me some comments on the actual data:
looking at the aoe curves, it appears you have neglected the aoe_max radius (at which the aoe damage falls from aoe_far to zero), which adds quite a significant portion to the overall area under the curve. now i might of course be wrong on how the aoe_max is actually implemented in-game, so if you have more info on that i'd be glad to hear.
also, i'd be interested how you derived the dmg/area values, since i've done something similar myself recently to calculate some sort of aoe damage index, also taking the scatter area into account.
EDIT: Just saw how long this post got. It's rather technical, so have fun reading...
EDIT2: Fucking hell I just realized that the circle calculations have a mistake. Slipped with the cell logic, will correct that soon.
EDIT3: Fixed it, will fix the original post now too.
Thank you very much. I also agree that the theoretical AoE calculation is better than in game tests when comparing units with the same scatter values.
First off: Yes, max_aoe_range (or how it is called) is neglected. I wrote this half a year ago and I didn't know how and if at all this stat is implemented, since many units don't really have it. At the time I left it out because the calculation in Excel overall is a bit tricky to implement and removing it later could be a huge pain. You actually just reminded me of that, I forgot that I did not do this at the time. Is this stat just used to increase the AoE with the minimum AoE value (as it would logically suggest)? I can't remember if I just saw a lot of units with the max AoE range stat being either "0" or the far AoE distance anyway. Also, if someone knows if the attribute editor is up to date in that regard that would be great as well. With some clarity on that regard I could implement this now.
To the AoE damage area values:
I'm not 100% sure about my calculus (plus how to write it for Excel) anymore, so I made approximations to closely estimate the area. The actual difference to a real calculus is minimal and only given if the actual distance points for the AoE are not covered by the increments that my Excel calculates automatically (which is to be expected though).
The "area under plot" is a first calculation to get more info about the plot. It just incrementally adds up the averaged damage for each radius increment. For example, the Tiger post does an averaged 116 [(120+112)/2] damage on the first 0,1 meters, adding 11,6 damage to the area under plot. This is done for each increment. Functional area under plot caps exceeding damage at the red bar, in this case 80 HP. So here, only 8 damage would be added.
This can give a quick impression about AoE performance, but neglects that the AoE is a circle and outer increments have more area than inner ones. That's what I mean with "circle estimation". It basically does the same, but beforehand calculates the actual area of each of the circle segments. For example, the most inner segment has an area of 0,0345 m^2 and a capped damage of 80, giving it 3 total damage. The most outer segment has an area of about 1,8 m^2 and 24,5 damage, adding 44 total damage. In my opinion though, this overestimates the outer rims as they usually don't matter that much. But it can still give an impression about overall performance.
That's why I gave both values, the "area under plot" and the circle damage (as well as the curves).
For a more complete calculation of tank performance you would need to know how exactly scatter is calculated (since also Vipper's guide is a bit thin on that). Then take the inter-model-distances and make a statistical model for the fight that ideally also accounts for re-targeting of other models if they are killed. This is basically way more than I am capable of doing though. And even this would still not account for clumping of squads in a real fight.
I think the curves and some area estimations are a bit more practical here and give okay-ish results for the amount of work you need to put into.