very interesting read, thanks for elaborating a bit further on this. i've actually done something similar to estimate the aoe performance by calculating the volume integral of the area under the aoe-curve (in practice i dissected the curve into triangles and squares and added the volumes of the respective cylinder and cone segments , which turned out to be easier in excel). this should, in theory, give the same results than your methods, albeit mine seem to be quite a bit off (e.g. for the tiger i get an area of 170.7 DMG*m and a volume of 1314.3 DMG*m^2)
then, in order to factor in the unit's scatter, i've divided this volume by the respective scatter area at set distances (e.g. 10, 20 and 40 m) to get an aoe performance value for comparison.
however, as you've already pointed out, unit spacing add another huge layer of complexity to the actual aoe performance that would be very difficult to calculate precisely. i've done some numerical simulations with excel before concerning heavy tank aoe here..
, which seem to correlate quite nicely with the theoretical aoe performance derived by the above method.
still, i'm also not sure about the exact way how scatter is calculated, so if you - or anyone else - has more info on that i'd be much obliged.