Preamps do make a difference of improvnig your range for RadarBox.
Fenris we are software guys here so we don't fully understand what you have written either but your calculations do not set with reality.
Everybody who has bought the preamp kit from our site has had an improvement in range. Depending on location, some customers have picked up 30-60% more aircraft.
For reference, I'm an RF engineer with more than 25 years of experience, so the calculations are correct in terms of the theory.
However, there are other effects going on too, so what I have calculated is not the whole story, it is also necessary to know what the RB ADC/FPGA combination (the receiver back end) does in the presence of multi-path signals and in the presence of time-overlapping signals at different strengths. And its selectivity, the ability to reject other local signals on various other frequencies.
Perhaps I'll write something a little more detailed when I have time, as always no one is required to read it, it will be for information only.
What I will say is that improving the system noise figure by a couple of dB could, under some circumstances, create the increase in aircraft received you mention simply because the radiated pattern from an aircraft can sometimes lead to signal loss at less than the theoretical maximum range because of nulls aligned with the direction to the RB in question. A few dB in that case can make the difference between a low enough error rate to receive a complete message and missing that message. It's all about statistics, there are very few certainties involved. The same situation twice may result in successful reception on one occasion and not on the other.
That's why I was pointing out that it's up to the individual to decide if that £200 is worth spending, and that will depend on how much coax they need to run, and how cluttered their horizon is. There is naturally their perception involved too.
Did I say this wasn't easy? I'll say it again then - this isn't easy!