Nothing was static, but all things considered, without escorts - and by dint of their success or otherwise, air superiority converting into air supremacy - even a ratio of one fighter to one supremely armed (and consequently manned) bomber was likely to be unsustainable due to the enormous difference in strategic materials, manufacturing manpower and time between the bomber and fighter... Not to mention the drain on maintenance and especially aircrew training, given it was eight+ men facing their mortality or capture, versus one.29 September 1939, 11 Hampden in 2 formations, the second of 5 intercepted, all shot down.
3 December 1939, 24 Wellingtons attacked warships, intercepted, no losses
14 December 1939, 12 Wellingtons, found convoy, spend 30 minutes trying to set up bombing runs in poor weather, 5 lost to flak and fighters
18 December 1939, 24 Wellingtons, bombed ships from 13,000 feet, perfect visibility, 12 Wellingtons lost, 2 fighters reported shot down.
Blenheim reconnaissance flights 20 September to 25 November 1939, 37 sorties, 7 lost.
The USAAF was aware of the early RAF raids, but noted the following would reduce casualties
1) Self sealing fuel tanks (The Wellingtons did not have them in 1939)
2) Increased defensive firepower including effective range, 6x0.303 inch versus 10 or more 0.50 inch
3) Tighter formations
4) Larger formations and/or raids.
5) Heavier airframes being harder to shoot down (Wellington Ia and Ic overload weight was 30,000 pounds)
6) Flying 10,000 feet or so higher
7) Flying faster, the Wellington Ia and Ic top speed was around that of the B-17/24 fast cruise speed.
Similar logic used when considering the Luftwaffe day raids on Britain in 1940
Without escorts present the interceptors had more performance available to trade off for firepower. A rule of thumb is in 1943 the 8th AF heavies shot down around 2 fighters for every 3 bombers shot down by fighters, in early 1944 that became 2 to 1 in favour of the fighters. The USAAF cause of damage reports reflecting an upgrade in average Luftwaffe fighter firepower. No doubt if figures could be calculated the ratio would move further in favour of the fighters during 1944 as more 30mm cannon were carried. During the Battle of Britain the exchange ratio was in the order of 1 RAF fighter to 3 Luftwaffe twin engined bombers, the RAF pilots had 8 rifle calibre machine guns firing at bombers weighing around 5 to 10 tons empty, the bombers single rifle calibre guns firing back but were in formation.
All the above ratios would require accurate bombing causing significant lasting damage to balance the bomber losses and/or enough interceptor losses to escorts. The USAAF calculation 300 heavy bombers being enough to drive average losses down to acceptable levels was done in 1942 at the latest and not revised, even as the defences were strengthened.
Nothing was static, radar made a big difference to bomber casualties once it was hooked up to a tracking and control system, in 1939 the German radar station phoned the airfield with what it was detecting and the fighters took a while to become airborne then were on their own. The Wellingtons were looking for shipping, not flying to a known location then returning. Think of the probable results in 1939 if it was 300 B-17E incoming, not worrying as much about bombs hitting non military targets alternatively the results in 1943 if it was 24 USAAF Wellington I incoming and waiting for absolutely clear weather.
The self defending bomber was a counterproductive WW2 myth.
The harsh teacher of war will often disprove a peacetime theory. But it seems odd to me that the penny of the ultimate lesson took so long to drop.