Punishment increases → murder decreases

 From the FreePress:

...Five years ago, ...police activity and staffing fell in big cities (where most of the crime is), as demoralized cops left the force. ...new policies—from chokehold bans to “no-chase” policies—further constrained police activity. ...

Unsurprisingly, murder soared.

But now, following a political backlash, policing is back:

In those cities where activity has recovered—New York and Washington, D.C., for example—murder has fallen. In cities where activity remains low, like Seattle, murder is still high. 

However, police "have focused on bringing murder down, while sidelining other, less significant crimes. This helps explain surging public disorder, which has remained high even as homicide has dropped." 

BOTTOM LINE:  When criminals substitute away from high-punishment crimes, we say those crimes are "deterred," one of four justifications for punishment (Google):

1. Retribution: This philosophy centers on the idea of "just deserts," meaning that offenders should be punished because they deserve it, and the punishment should be proportionate to the severity of the crime committed. It aims to achieve justice by making the offender suffer for the harm they've caused.
2. Deterrence: Punishment can aim to prevent future crime by discouraging both the individual offender and others in society from committing similar acts.
   • Specific deterrence: Intends to discourage the individual offender from repeating the crime due to the fear of further punishment.
   • General deterrence: Seeks to make an example of the offender to dissuade others from engaging in criminal behavior.
3. Incapacitation: This approach focuses on preventing future crime by removing the offender from society or limiting their ability to commit crimes. Examples include incarceration, house arrest, or even capital punishment.
4. Rehabilitation: This goal aims to prevent future crime by altering the offender's behavior and addressing the underlying causes of their criminal conduct. Rehabilitation programs can include counseling, educational and vocational training, or treatment for substance use disorders.