I have pretty much the same theory as lozarus.
I also found there are different "hard cap" for different guns.
I found H39 had one at 96, where I totally saw a day/night difference in my average spread. Seemed the bismarck also get better spread regularity at that level, but I cannot be 100% sure.
I also seemed to notice a tightening in O2 guns around 93.
For H44, I,ve noticed a day/night difference at 113, altough I must say the 44 spread never was that awful.
As far as other nation goes, my experience is quite limited, as I only noticed that possible "hard cap" for the first time in a yammy, with gunners that leveled to 96 also.
A friend spoke to me about the L1, which 96 would seem to be the magical level for its gun too.
My hypothesis is that the guns recognize a "true ability" and works a bit like stairs. Between x and y true ability, the spread will stay about the same, then once you climb a step, you see a first big difference.
I didnt do any pushed research on that tough, its merely the observation of a player in the course of its grinding on the server.
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