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.