May I point out a few mistakes in your assumption Marjak?
You say the Luftwaffe knew exactly how many fighters they had in the air? Not true for 1944+ at least.
You say the Luftwaffe knew how many enemy aircraft they downed? Not true at all.
You say the fighters depleted their whole ammo altogether? Not true at all. Many get shot before they even have the possibility to fire a single bullet, many see no combat action at all, many do a single pass, fire let's say 1/4 of their bullets and have to rtb damaged... the fewest will ever get the chance to shoot all their bullets.
You assume that the number of damaged bombers is the same like the number of downed bombers? Usually not true.
Of course you can, Mike. No problem.
You don`t have to know exactly how many fighters you have in the air. You`re right, the only important value is the numbers of 20mm bullets fired on that day, and I`m pretty sure that the weapon attendance could come up with this when asked before.
As for the number of downed bombers, at least they officially presented numbers every time. I`m aware of the fact of exaggeration but anyway LW officials could count the wrecks on one particular day, so it`s possible to operate with a minimal value for statistical purpose.
As for the damaged bombers. I don`t assume that it was the same number. I only wanted to include into the statistic the fact that damaged bombers were possibly hit by 20mm bullets as well.
Anyway, this was just an experiment. I never said that the LW did calculate such things on a daily basis. I even doubt that they actually did, but at least it`s possible to come up with a statistic like this. And who knows, maybe an angry Göring bashing his fighter pilots for incompetence and cowardice once asked in a rhetorically manner "WTF they are hitting out there?". And so a pencil pusher tried to come up with a number.
But maybe a guy who knows about statistic can help us.
We have two known parameters (number of 20mm bullets fired and number of bombers that were downed for sure (the wrecks that can be counted - the minmal value)
We know that it took 20 hits of 20mm to down a bomber (at least this was an official LW test trial)
We have two unknown parameter (the number of damaged bombers and the number of hits those damaged bombers received).
And we don`t know how many bullets were fired on fighters.
Is it possible to create a reliable statistic according to this when the latter parameter do have a huge variance? (but also for the damaged bombers you have a minimal and a maximal value, the same for hits on these bombers, statistically less then 20, so 1-19).
Also, let`s do not forget that my assumptions for this statistic are based upon the numbers of one particular day. But of course it`s possible to use the numbers from a long-run analysis as well. I guess that when you have to counter allied bombers on an almost daily basis, you have some statistical material to operate with.
Cheers