While this is probably a good reason to own a weapon it probably is less responsible for reduced crime than is economics.
The gangs that ravage the urban areas of our nation are in the business of making money with reduced risks. This is why they concentrate their activities in the poorer parts of the cities.
Since the early 50's these gangs have gone out of their way to specifically target welfare recipients, and the elderly. They do this because these people are less able to call for help. If you are on assisance, and food stamps or EBT card, and I steal your new Iphone how do you report it without explaining where you got the money? If you are 100% disabled and I steal your rolex where did you get it? See the problem.
If you are cheating to get a handout, and have a part time job to buy luxury items how do you report your 67" flats screen TV stolen?
Today though, as the welfare has run out, the gangs are moving into areas where the welfare is still flowing. There we see increases in minority on minority crimes in Raleigh, Durham, Fayetteville, Charlotte, in NC as they come in to run the local gangs out or merge with them after peace treaties.
In the farm belts of tne East coast the Cartels of Mexico are establishing there Mexican worker protection and drug rings which is causing increased killings and attacks on Farm houses, and back road trailers.
While it is necessary for everyone to be armed because as the welfare runs out to protect your neighborhoods, the decrease of crime in Urban areas is not a result as much as it is a cause.