I'm not an expert but it seems to me that having a big fuck off gun is better than having a big book of statistics when a group of animals break into your house
You just need to game theory it out though.
If you as a criminal know that the likelihood that the owners of a house you intend to burgle own a gun is significantly above 0%, how likely is it that you yourself get a gun before doing the job?
Also factor in any laws that, oh, explictly state home owners can 'stand their ground' and not have any legal repercussions for executing a burglar.
Now factor in bringing a weapon with you automatically raises the length of any possible conviction.
Now factor in the associated risks of
sneaking in and maybe / maybe not alerting a homeowner who maybe / maybe not has a gun and maybe / maybe not can just kill you and you maybe / maybe not even realise you'd woken them up or that the house was occupied and you didn't realise.
Now compare that to just straight up pulling a home invasion and being in full control of the situation from the get go.
Ta-dah, you now have Home Invasion rates magically 3-4x higher than equivalent first world countries.
Same reason as when you make kidnapping a capital crime, you suddenly see the life expectancy of a hostage drop to slightly above zero, as risk / reward just favours killing the biggest threat to getting away with it.