GregP
Major
Sorry to be blunt Greg. These statements are wrong. Everything you said here is completely at odds with all wartime analysis by the scientists and statisticians for the various commands.
"Loss rates go up with time in hostile airspace" Of course it does! The longer fish are around your hooks, the greater number of fish you will catch. Put another way, the longer you fish, the more fish you will catch. Predator-prey models which have been around for over a hundred years predict this to be the outcome. These models have 5 key components: prey availability, prey density, search time, handling time and satiation. The longer prey is available to a predator (measured in units of time), the greater the likelihood it is attacked and eaten. Handling time includes the act of capture as well as consumption. Satiation is the point at which the predator no longer wishes to use energy capturing prey due to being full. The air warfare analogy to satiation is the combination of fatigue and running out of fuel.
"loss rate go up with distance" distance is a function of time, see above.
"loss rates go up with weather" poorly stated, perhaps, but aircraft crash rates absolutely went up with bad weather. Surely you aren't arguing otherwise?
Jim
Depends on circumstances.
Statisticians calculate values that have everything to do with aggregate numbers and almost nothing to do with your circumstances. Being an engineer, I should know. Statistics can be correctly calculated and still have nothing to do with your circumstances; they're just statistics that generally predict outcomes. They don't predict YOUR outcome. They only predict probability if 1) the original assumptions are correct and 2) you try the experiment MANY times randomly. After a certain number of random trials, your outcomes should generally reflect the probabilities IF 1) and 2) are correct. There is almost nothing random about a wartime aircraft mission.
So, in general, the more time you spend over enemy territory, the greater the chance you will be found and attacked ... true. But, you can seriously affect the outcome by changing the circumstances. We all know that large streams of bombers were detected and attacked with flak and fighters, sure.
Go research how many times a flight of ONE fast photo-reconnaissance aircraft was successfully found and attacked and get back with me. It isn't very often. So, sure, I'll agree with you for large formations of escorted bombers. But I disagree strongly with your contention for small formations of fighters and/or fast bombers with a specific target. They almost always got through, and were planned so they also usually got through with the element of surprise.