"You don't need a gun, the police will protect you!"

Right.
...Cincinnati police officers will no longer respond in person to the following reports:  criminal damaging, dog bites, lost property, lost or stolen license plates, phone harassment, property damage or found property.

Police will no longer respond to assault reports, unless a suspect is still present or the victim requires medical attention, breaking and entering reports unless a suspect is still present, menacing reports "unless suspect is expected or threatens to return or is part of the elements of domestic violence" or theft reports "where there is no possibility of immediate apprehension".
Make you a bet: especially if you use a weapon to protect yourself from someone they won't show up for, they'll be right on your ass.