Hi Tac,
The vibrations induced by multiple rapid fire weapons lead to a dispersion that's far greater than the individual weapon's error, and the uneven firing sequence of unsynchronized weapons contributes to this.
I've not seen any figures for typical variation of the cycling peroid of machine guns, but I'd say it's great enough to turn the bullet stream into a random sequence within seconds. You can watch it happen on old films showing Il-2s strafing ground targets: One second, both wings spit flames at the same time, the next second they alternate :-)
I think Widewing is accurately describing the first salvo when the gun mounting is in rest. Probably dispersion ramps up to the full value a few cycles after that, but I'm speculating here. Probably the RAE report on their vibration problems with the quadruple machine gun turrets would give the details ;-)
I think for the P-38, the service manual describing the gun calibration procedure would give the desired result with regards to dispersion, so we could be able to find out if we're lucky and someone discovers a copy of that manual.
Regards,
Henning (HoHun)