For some areas repeatedly hit hard with crime, police intervention can shut down lawlessness and keep it down. But for others, police involvement just shifts the trouble around.
A mathematical model, based on Los Angeles data, helps distinguish the two kinds of hot spots (citing this paper). It turns out that there are two "sharply distinct" catagories of crime hot spots.
Crimes in one location encourage more crime in that location from other criminals. "Data has shown, for example, that the house next door to a house with a broken window is more likely to be robbed." When the criminals are drawn only locally to a location by prior crime, police action can wipe out of crime hot spot for good.
When criminals are drawn to a crime hot spot from distant locations by prior crime, for example, to place with a reputation for being a drug market, police action will only cause the hot spot to relocate (if more than one police action is present, usually roughly midway between the police crime suppression actions). There is a critical value for this distance that distinguishes the two kinds of hot spots, producing distinct catagories of them.
Burglaries typically have an impact on crime rates in a 2 kilometer radius, and tend to be highly local according to the supporting data for the study.
So, if you want to know if police action will reduce total crime, you need to know how far away from the crime hot spot criminals come to commit crimes. If this distance is more than the critical value, police action at the hot spot is unlikely to be effective at reducing total crime. If the distance is less than the critical value, the broken windows theory works.