jorgen_cab
your claim is incorrect. 20 shots at .20 has a greater dispersion than 8 shots at .5. i reckon that you correctly remembered but misconstrued the variance of the binomial- misconstrued because in this case it is mu, not n that is being held constant.
Yes.. I constructed a program to do some actual statistical tests... since doing it in the game are a bit difficult. Lower size will get a small extra leaking except for the 87% size which actually seem to produce better result in most realistic instances than 100%
From my tests... for example...
Missile salvo size: 5
Missile salvos: 50.000
Missile Speed: 10000 km/s
PD tracking Speed: 5000 km/s
PD to hit modifier from fire-control: 0.9
Size 100, 10 shots, about 45% hit ratio : Average about 4.10 hits per salvo
Size 87, 12 shots, about 39% hit ratio : Average about 4.17 hits per salvo
Size 50, 20 shots, about 22.5% hit ratio : Average about 3.99 hits per salvo
Size 25, 40 shots, about 11.2% hit ratio : Average about 3.92 hits per salvo
Size 17, 60 shots, about 7.6% hit ratio : Average about 3.94 hits per salvo
So... the most effective gun seem to actually be 87% as far as I can tell from a leaking perspective in real terms. The 87% gun are weaker at around 75-100 tracking speed if grade bonus is 100. This interval will then change depending on grade bonus... so it depends... but differences is small and in general the 87% seem better since it get more benefits unless you are in a 25-30% interval.
You can change the numbers above of course but in general the same result will stand and the differences will diminish fast as salvo size go above the turret shot ratio. Although in realistic terms the differences in leaking from a 100% to a 17% gun are so small that other considerations such as fire controls, turret design versus ship design etc should be more important.
If you are often engaging rather small salvos of around 4-8 missiles then having a large 100% quad turret might not be that useful and too big for some ships. You might need more fire-controls and smaller turrets.
To put the above in more real terms... If you are engaging 100 incoming salvos each with 5 missiles the 100% size turret will miss 90 missiles out of 500 while the size 17% turret will miss 106 missiles.
If anyone want to do their own testing you can use this little .NET app if they wish... I provide no support..
https://www.dropbox.com/s/kj1kz6r9aemtpz7/Aurora_PDtest.exe?dl=0