The idea that numbers alone were responsible for the defeat of the LW in the west is really a myth. Obviously numbers played a part (as they do in all battles), but not as big of one as people would tend to think. The allies had a massive numerical advantage in aircraft on the western front from 1941 onward as the Luftwaffe transferred aircraft to the eastern and mediterranean fronts. In 1941 and 42, a lot of this numerical advantage was in fighters, but after the failure at Dieppe many RAF fighter squadrons were transferred to other theaters to support the ground combat taking place elsewhere.
Allied fighter strength did build up again following this, but it was split up between British and American units, split between different air forces within both nationalities (ADGB vs. 2nd TAF for the British, and 8th vs. 9th AF for the Americans). These splits meant that in the late war years, it was very rare to see all the allied fighters concentrated on any one mission or task. And with missions ranging from V1 defense of GB, fighter bombing of france, bomber escort to germany, and fighter intrusions and escorts to Norway these forces were fairly spread out when on operations.
At the same time, the Luftwaffe had taken steps to increase their fighter presense in the west, primarily to counter daylight bombing by the 8th AF. As a result, the fighter vs. fighter odds in actual battles tended to far greater in 1941/42 then in 1944. In spite of these decreased odds, the allies had far greater sucess in these battles in 1944, and when the allies did focus all of their fighter forces on one concentrated objective (air superiority and bombing of the normandy area for D-day) again, the Luftwaffe responded by transferring even more fighter units to the west. The result of this concentrated battle was far different in 1944 then it was in 1942.
To illustrate this, I'm going to show some numbers from two large scale air battles, one that took place in 1942, and one from 1944. I've chosen these two because I have good records from both sides for these dates, making it possible to make an accurate analysis.
The first that I've chosen is the Dieppe raid of Aug 19th, 1942. The allies attempted to make a landing at Dieppe in France and the RAF was tasked with providing fighter cover, as well as attacking German targets in the landing area. The Luftwaffe put the maximum possible effort to oppose this landing with both bombers and fighters of their own, resulting in a large and concentrated air battle that lasted most of the day.
The RAF flew 2600 total sorties, and of this 1800 were Spitfire Mk. Vs and around 150 were the new Spitfire Mk. IXs. The reported 106 total aircraft lost for the day, of which 88 were spitfires! Luftwaffe fighters claimed 96 aircraft destroyed, which would indicate that most of the RAF losses were to enemy fighters.
In opposition, the Luftwaffe mounted 377 Fw190 sorties, and an unknown number by bomber units in the area (mostly Do217s). They reported 48 aircraft lost, 20 of which were fw190s.
Despite the incredible numerical advantage, the RAF suffered much higher losses - particularly in fighters. This can be primarily attributed to two factors - first the Luftwaffe pilots of JG2 and JG26 generally had much more combat experience then their allied counterparts, second the Fw190 had a massive speed advantage over all the allied fighters present at the low altitudes where most of the combat was fought that day.
The second combat I've chosen is that of April 8th, 1944. This was a large scale raid by the 8th Air Force, with a large scale Luftwaffe response. The target for half the bombers was a number of Luftwaffe installations in NW Germany, the other half of the bombers would hit aircraft factories in the Brunswick area - deeper in northern Germany.
The 8th AF dispatched 644 bombers, evenly split between the two targets. 780 fighter sorties were flown as escorts and fighter sweeps, once again fairly even split between the two bomber streams. The Luftwaffe concentrated their fighter response entirely on the deeper penetration, and as a result only 4 of the B-17s which were striking the closer targets were lost, while 30 of the B-24s hitting Brunswick were lost. Also as a result of this, 376 of the US fighters didn't see any LW fighters in the air. Only the 330 B-24s and 408 escort fighters would be involved in the ensuing air battle.
I don't have an exact total of Luftwaffe sorties for the day, but I know from kill and loss reports that they employed the following JagdGruppen in combat on that day:
I, II, III JG1 - 129 fighters
Stab, I, II, III, IV JG3 - 105 fighters
I JG5 - 29 fighters
Stab, I, III JG11 - 68 fighters
I, II, III JG26 - 129 fighters
II JG27 - 12 fighters
II JG 53 - 23 fighters
III JG54 - 37 fighters
III JG300 - 16 fighters
I, II, III JG302 - 67 fighters
Sturmstaffel I - 17 fighters
The total comes to 632 fighters (all Bf109s and Fw190s). Luftwaffe serviceability tended to run around 50%, and 8th AF intellegence reported that around 300-350 Luftwaffe fighters were seen. It seems likely that this was a fairly accurate estimate of the number of LW sorties flown that resulted in contact. In terms of fighter odds, we are looking at around 1.5:1 in the actual combat area, as opposed to over 4:1 seen in the previous battle.
Ultimately, the Americans lost 22 fighters, but 9 of those were losses to flak or crashes due to pilot error/malfunction from the fighter units that never made contact with the Luftwaffe.
Luftwaffe fighter losses for the day were 78 with 42 pilots killed and 13 wounded. A devastating total, particularly in pilots where you are seeing nearly 20% of those who were in action that day killed or wounded.
US bombers made claims for 60 kills, and US fighters 88. The fighters were ulitimately credited with 57 kills after reviewing the claims and gun camera film.
We can see from this, that in early 1944 the typical 8th AF bombing mission was generating far lower odds then those that existed in 1942. We can also see that the results achieved were FAR better. In particular, allied fighters were achieving much greater sucess against their german counterparts. The three main reason for this were: allied bombers were a far more serious threat and so german fighters were more focused towards attacking them, allied pilot quality and tactics had improved during the war while german pilot quality had declined, allied fighters were now as fast or faster then their opponents and possesed better high altitude performance which is where most of their combats were taking place.
When the allies did again focus all their fighters for D-Day (achieving odds closer to those seen at Dieppe, then over Germany in the first half of 1944) the Luftwaffe was shattered. Bomber losses to fighters which had been increasing throughout 1944, dropped off an June and never recovered. The luftwaffe made further attempts to build up a large force and strike at allied bombers as well as at the allied tactical fighters, but were never able to regain control of their airspace which had been lost in 1944.
In light of this, I think it's silly to write off the Luftwaffe's defeat as being a case of simple numbers. As we can see, the allies had a huge numerical advantage from early on in the war but continued to suffer defeat at the hands of the Luftwaffe. The big key to sucess for the allied airforces in the west was improvments in pilot training, tactics, and aircraft. At the same time, the Luftwaffe saw little improvement in their fighters, and a decline in the quality of their pilots.
