Profile of MMX

Interesting. Do you have scatter values? I've tried the Pershing a few times and at vet 0 it seems like it has much worse scatter than a HE Sherman. It seemed kind of underwhelming at vet 0 but decent at Vet 2 or better.

Both tanks have an angular scatter of 6, but the Pershing pulls ahead due to having a lower distance scatter (4.2 vs 5.5). Hence the size of the HE-Sherman's scatter cone is roughly 25% larger than that of the Pershing.



AOE Profile (upper panel) and size of scatter area (lower panel) as a function of distance

Idk how to improve these icons right now, because imo they are fine. What about UI indicator on the portrait with picture of current shell in the gun?

though the icons are quite easy to distinguish side by side they are still very similar and i always found it difficult do discern if i have HE or AP ammo loaded in the heat of the battle... maybe if the explosion effect for the HE shell was a bit more distinctive either in shape or color this would help a bit

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Great guide, as usual! I was actually planning on doing something like this but you beat me to it.

Some points you might want to consider adding:

• FoW scatter: Units firing into the FoW suffer a penalty that increases the area of the scatter cone in which shots may land. This is basically a multiplier (for most units 1.25, or 25%, but for certain units this is significantly larger, e.g 2.5 for the ISU-152) that acts on distance_scatter_ratio and scatter_angle, but not on distance_scatter_max. Hence, for most tanks the scatter cone only gets wider when firing into the FoW due to distance_scatter_max still acting as a hard cap, but not longer. Also, distance_scatter_ratio also appears to be capped at 1 (obviously, since for values greater 1 a shot fired in front of the tank could in theory scatter behind it), but some tanks like the SU-76 or the ISU-152 can be affected by this.
  
• Moving scatter: This one is another modifier that in contrast to FoW scatter increases both angular and horizontal scatter, by doubling distance_scatter_ratio (again still capped at 1), distance_scatter_max and scatter_angle. Hence, stopping before a shot not only increases the chance to hit due to higher accuracy, but also by greatly decreasing scatter.
  
• Veterancy: While scatter reduction through Vet was removed for all Tiger variants in the latest patch, quite a few other units, such as the King Tiger, PzIV J or T-70 will still gain a bonus to scatter when vetting up. This again acts on distance_scatter_ratio, distance_scatter_max and scatter_angle and thus greatly reduces the area of the resulting scatter cone. Very powerful especially against infantry, but obviously also increasing the odds to connect that lucky scatter shot at max range.
  

great matches, fantastic final series... overall an awesome tourney! grats to pfc for winning the trophy and big shout out to all the casters and mapmakers for making this possible!

that's some interesting analysis, thanks a lot for sharing!
as hannibal already pointed out we've both been working on very similar scatter and AoE-related projects lately, and i think your approach is a good way to do it.

after reading over your methodology, i'd suggest a few edits to your formulae to get a bit more accurate results though:

i think the approximation you used for the double integral under the AoE curve is quite crude and calculating the precise "volume" is actually not much more complicated than what you've already done.
instead of approximating the area under the curve with rectangles and integrating to get the volumes of the resulting cylinders, you can split the complete area into right trapezoids and calculate the precise volume for the corresponding cone sections via pi*h/3*(r^2+rR+R^2), where r and R are the inner and outer radii and h is the damage at each radius (n, m, f)

with respect to the scatter cone, there is one important varable that you may have missed from what i've read: distance_scatter_max.
this will cap the horizontal scatter you get from distance x dynamic_scatter_ratio (this even caps the FoW multiplier!) and lead to smaller actual scatter areas, especially at max range.

apart from this i think your method works great to get a somewhat reliable impression for raw or "on paper" performance of arty pieces and a handy gauge for comparison. however, relating this to in-game performance is a bit tricky, due to the sheer volume of additional variables factoring in here, as pointed out by others already.
i've been working on a simulation to get actual squad sizes and formations into the equation for quite some time, which i plan to release soon(tm). with a few modifications this would probably work well for artillery and indirect fire, too.