Not proportional to cost.
Having it fitted we are looking at £500 or about.
I did install it because even if overkill, hey, it is my life, and I can afford it.
But considering how many fires are, and how many lives this would save.. I think this is overkill.
There are about 44 deaths by fires in Scotland per year.
Lets assume the US number of 55% reduction is correct.
There are 2.53 million households in Scotland.
Let's assume all those 44 deaths are residential, and no firefighters, etc (so best case scenario for alarms)
This would save 24 lives.
The battery ones last about 6 years really, not 10, and the installed ones are very expensive to install.
The cost? 8.8 million pounds per life.
While life is quite valuable, there are many things than can be done for less money to save lives, and actuaries would agree.
I would say, fix potholes, put lights on dangerous intersections, do colon cancer screenings sooner, etc etc.
If you fit them yourself, it is better value, still quite expensive, but I did it for £200
Sources:
https://www.nfpa.org/News-and-Research/Data-research-and-tools/Detection-and-Signaling/Smoke-Alarms-in-US-Home-Fires#:~:text=The%20risk%20of%20dying%20in,to%20trigger%20a%20smoke%20alarm.
https://www.nrscotland.gov.uk/statistics-and-data/statistics/statistics-by-theme/households/household-estimates/2021