American gun ownership = 36% of the population.
British = 6% of population.
Difference = 30%.
So if guns saved you 100% of the time, the 30 extra percentage points of gun ownership would make burglaries 70% as common in the US as in the UK.
But since the figure was only 90%, then that makes it a 27% difference. (90% of 30%).
Therefore 100%-27% = 73%.
Sorry if that doesn't make any sense. I'm so tired I'm basically sleep-typing and higher reasoning and mathematical functions aren't available to my brain. I'm not entirely sure I did the math right the first time, I think I may have grossly oversimplified and created a false equivalency between percentages, but... tired. Don't know.
That's what I was thinking anyway.
The burglary rate in both countries is identical
The only thing preventing a burglary from happening is the presence of a gun, which has a 90% chance of prevention
Obviously both of those are horrific over simplifications but for the sake of maths...
There are x burglaries per 100 people. The ones targeted against a non-gun-owning household are succesful. Therefore there will be 0.94x burlgaries in the UK, 0.64x in the US
The ones against gun owning households have a ten percent chance of success. Therefore there will be 10% of 0.06x = 0.006x burglaries in the UK and 10% of 0.36x = 0.036 burglaries in the US of gun owning households.
Total burglaries in the UK then is 0.94x+0.006x = 0.946x
Total burglaries in the US is 0.64x+0.036x = 0.676x
(0.676/0.946)*100 = 71.45
So the burglary rate in the us should be 71.45% of the burglary rate in the UK.
I think what was making it look so wrong was that I was assuming the gun ownership rate in the US wasy waaaaaaaaaay higher than 36%. I guess the "guns owned per capita" figure was throwing me off, must be a shed load of houses with multiple guns.