I'll add to this. I would argue that the BoB was an example of the much vaunted German doctrine of 'Auftragstaktik'. In a simplistic form this was the practice of senior commanders and their staff (Goering, Jeschonnek, Schmidt, with the exception of Goering an inexperienced bunch, the latter two were too young to have served in WW1) telling their inferiors what the overall objective was and them allowing them to get on with the operational planning to achieve this.
The problem was that this planning was disbursed onto mainly the two' Luftflotten' involved in the battle.
Luftflotte 2 was commanded by Albert Kesselring, an artillery officer who had held a staff appointment in WW1. His Chief of Staff, Wilhelm Spiedel, had commanded a company of storm troopers in WW1.
Luftflotte 3 was commanded by Hugo Sperrle, the only senior Luftwaffe commander to have anything like the equivalent experience in air operations to his RAF opponents. His Chief of Staff, Gunther Korten, had been an infantry officer in WW1 and his chief of operations, Karl Koller, had been teaching at the Munich police academy in the five years before the BoB.
Given these factors it is hardly surprising that there was no overall strategic vision and there was no coordination of tactics within the Luftflotten, let alone between them. These were mistakes that could not be made when fighting a centrally directed air force, the Battle itself being run principally by two of the architects of the air defence system they now managed.
Incidentally, throughout the period we British call the BoB, roughly 50% of Bf 109 sorties were 'Freiejagd' and not escorts at all.
There were problems with the escort role.The Luftwaffe bombers did not fly like the Americans in defensive boxes that occupied nearly as much air space vertically as horizontally , they flew in a broad front formation, much more difficult for the fighters to cover.
Then there is the intention. By the time of 'Big Week' it was made clear to the fighters of the 8th Air Force that their mission had change, they were no longer to prioritise the safe return of the bombers, they were to shoot down Luftwaffe fighters, lots of them, as many as possible. The Luftwaffe in 1940 never adopted any such policy, in fact it never adopted any coherent policy at all.
Cheers
Steve