8th Air Force Raid on Lille 9 October 1942. From the Official History by Craven and Cate, initial bomber gunner claims 56 destroyed, 26 probable, 20 damaged, revised (no date when) to 21 destroyed, 21 probable, 15 damaged. The USAAF fighter escort made no claims, 4 bombers were lost plus a fifth written off. Craven and Cate researched the German archives and found Luftwaffe units operating in the west lost 11 aircraft that day with a further 11 with more than 60% damage (write off damage level). That is 22 aircraft from all causes of all types for all units. At this stage about 40% of the Luftwaffe aircraft losses were non combat related. After looking at the Luftwaffe fighter loss statements Craven and Cate conclude one (1) was the most likely number of fighters shot down by the bombers.
The above story is what many people initially interested in the USAAF rebound to after learning the B-17 (with an occasional little help and comic relief from its sidekick B-24), did not shoot down millions of axis interceptors just on test flights. Research tends to be left there, replaced by assumptions and estimates, the famed I know it is true as seen and proved on TV several times a night, ignoring the lead in the show has the great God Scriptwriter on their side, more and more necessary as seasons progress. Research largely confined to maximising audience share.
If anyone thinks the following is incorrect, provide the evidence, not the feelings.
The reality is the exchange rate USAAF heavies versus Luftwaffe interceptors changed over time. In To Command The Sky by McFarland and Newton they note that in Q4/42 5.8 heavy bombers were being lost per 100 cases of reported combat and this had climbed to 11.6 per 100 cases in Q1/44. In the book Brute Force by Ellis he lists the figures as in 1942 2.3 bombers lost per 100 combats and in mid 1944 17.7 bombers lost per 100 combats. Mostly as a reflection in the increase in average Luftwaffe fighter armament.
The interest in the 8th Air Force and B-17, along with the small number of raid days and the relative lack of non USAAF heavy bomber activity in 1942/43 makes it remarkably easy to obtain a good set of USAAF losses with causes for the period, down to serial number level and match them with Luftwaffe losses. Apart from the individual bomb group and other web sites things like B-17 Flying Fortress List by David Osborne, Mighty Eighth War Diary by Roger Freeman and the USAAF Statistical Digest (the latter acting more as a sanity check). The horrible grind that shows how even 1% losses times a mission every second day gives nearly 50% casualties in 3 months when measured against the starting force size.
Statistical Digest 1942/43 ETO
effective sorties, 20,883 heavy bomber, 5,533 medium/light bomber, 25,451 fighter
Combat flying hours, 162,059 heavy bomber, 23,735 medium/light bomber, 59,015 fighter
thousand rounds of ammunition used 651x0.30 and 27,761x0.50 heavy bomber, 5,533x0.50 medium/light bomber, 18x0.30, 1,265x0.50, 23x20mm fighter
enemy aircraft claimed destroyed in the air, 3,543 heavy bomber, 33 medium/light bomber, 458 fighter
US aircraft lost to enemy aircraft, 737 heavy bomber, 18 medium/light bomber, 171 fighter
When it comes to the Luftwaffe There are books like Day Fighters In Defense of the Reich by Donald Caldwell, for the study
A) Auswertung der Einsatzbereitsch der fliegenden Verb. Vom 1 August 1943 bis November 1944", which are the fighter losses for all units in the west and Reich. The figures quoted from this source actually stop on 19 April 1944.
B) Generalleutenant Josef Schmid "Day and Night Aerial Warfare over the Reich 1943-44", first published in 1954. Schmid was the commander of I Jagdkorps which controlled most of the fighters defending Germany. In checking his figures with the text of McFarland and Newton it looks like at times Schmid does not include write offs in his casualty list.
C) British translations of captured German Documents, "German Air Force Losses in the West 1 September 1943 to 31 December 1943" also losses for the area of Luftflotte Reich for the same dates and for the west and Luftflotte Reich for the period 1 January 1944 to May 1944. These are the documents from the Luftwaffe Quartermaster General and give cause of loss.
In summary it looks like the best rule of thumb for the 8th Air Force is for every 2 B-17s or B-24s destroyed by Luftwaffe fighters 1 Luftwaffe fighter was destroyed by the bomber's gunners. With the initial (1943) ratio being around 1.5 to 1 until the Luftwaffe gained experience in intercepting the B-17/24s then moving to a higher ratio as fighter firepower was upgraded then higher again as Sturm units and 30mm cannon came into use. It means in 1943 the 8th Air Force heavy bombers shot down around twice the number of Luftwaffe fighters as the USAAF fighters, while overclaiming by around an average of 7 to 1.
For on the ground, no claims until January 1944, the 8th AF fighters are credited with 4,250-23-2,886, the bombers 3,079 destroyed or damaged. The 9th Air Force 2,216-147-1,894, all by fighters. The USAAF Statistical digest reports MTO 7,003 enemy aircraft destroyed on the air, 2,494 on the ground, Pacific Ocean 575 and 219, Far East Air Forces 4,502 and 1,796, China Burma India 1,202 and 711, Alaska 89 and 24. Air to air claims end to have less overclaiming than air to ground ones.
The reported average of 18 to 20 hits of 20 mm cannon to bring down a B-17 is via causing structural failure, that is no fire, compared with 2 to 3x30 mm hits. US firing trials at Aberdeen using German 20mm incendiary rounds versus 40% full B-17 fuel tanks showed the chance of causing a fire per hit was 10% at 50 metres dropping to 2% at 2000 metres. Apparently a 13mm round's chance of starting a fire was 40% of the 20 mm. So the average number of hits to bring down a B-17 (and by implication other 4 engined types) would have been under the 18 to 20 figure, given the ones lost to fires.
In early 1944 the average Luftwaffe fighter in the west was given an armament upgrade as seen by the 8th counting the holes in returning bombers and noting what caused them. To Command The Sky by McFarland and Newton gives the statistics for the ratio of cannon shell to machine gun bullet hits for damaged bombers. The data reported on starts in August 1942 and ends in June 1944. The figures are date, cannon shell hits per 100 machine gun bullet hits.
8-12/42 40, 1-4/43 77, 5-8/43 70, 9-12/43 81, 1-2/44 88, 3-4/44 127, 5-6/44 135.
The Luftwaffe quite consistently month by month awarded 2 B-17 kills for each 1 actually shot down, the B-24 ratio was more like 1.8 to 1.