Some public schools have played around with the idea of "performance-based" compensation, where teachers get paid more if they deliver better outcomes (unfortunately generally measured by standardized test scores) than would be expected on average, given the students coming in. This is mean to be about a 'value add', so teachers in schools with high socio-economic status students who were already going to score well don't get automatically paid more -- it's about an estimated 'improvement'.

I'm broadly aware that some health policy people want providers to be paid for caring for patients, not on a per-procedure basis. Get paid more for keeping your patients healthy and living longer, not for racking up more visits.

Does such a thing exist for policing? I think critically we need a mechanism for collecting crime stats that isn't fully dependent on the police themselves -- but at a high level, paying police to reduce actual crime, and shrinking their budget when crime actually increases, seems like a path to at least get what we pay for.

The only crime statistic that is pretty reliable is the murder rate. The vast majority of murder victims are found.

For lesser crimes the numbers can't be trusted. Many victims don't bother to file reports because they're afraid or they don't believe that law enforcement will act. Some police forces even have an unofficial policy of discouraging victims from filing official reports in order to minimize workload and make their statistics look better.