[Jens]

Longer range IMHO doesn't necessarily mean to have more time for combat (hitting the enemy) or am i wrong? A shorter range to the destination give an opportunity to fly more sorties per day, and so to shoot/bomb at the enemy several times more. An Example for this effect seems to me the Eastern Front and to some degrees the battle of britain.
Also numerical superiority in planes doesn't mean to have numerical superiority in the air? It depends mostly on the sorties you fly, if you can achieve numerical superiority.

IMHO if i get Galland and others right, one of the main failures by Luftwaffe was the planning of the Normandy Air Battle. The transfer of the JGs from Reichsluftverteidigung were not well organized (Communication between and Leading staffs and unit commanders) and had not enough material/ground support. Very much fighters seem to have crashed at bad shape airfields and other reasons.