[Tony Williams]

There were three ways to improve the hit probability in WW2 (in no particular order):

1. Minimise the time of flight of the projectiles - achieved by a combination of a high muzzle velocity and a good ballistic coefficient of the projectiles. However, other things being equal, increasing the muzzle velocity involves reducing the rate of fire and increasing the weight of gun and ammo, so you can carry less.

2. Increase the rate at which projectiles are fired by increasing the number of guns or speeding up their rate of fire (N.B. The Luftwaffe preferred to fit 2x low-velocity 30mm MK 108 rather than 1x high-velocity 30mm MK 103 for the same weight, because the MK 108 combo put shells into the air at three times the rate). However, that requires a bigger ammo capacity and more weight again.

You will appeciate that Nos. 1 and 2 are in conflict with each other, within any reasonable weight limit. As with virtually everything else, the best solution is a compromise between conflicting factors.

3. Fit gyro sights - which made a huge difference to the hit probability of the average pilot with no weight penalty - brilliant!

A final comment: the hit probability is not the same as the kill probability. Within any given weight limit, an armament designed to maximise the hit probability is likely to have a reduced kill probability because it will be firing smaller and less destructive projectiles.