In the year since its program has been fully in place, Kansas City has had a significant decrease in homicides. The city had averaged 114 homicides a year over a four-and-a-half-decade period through 2013. And the number of murders hovered over 100 in the roughly five years before NoVA’s inception. But murders plummeted to 80 last year, a 20 percent drop from 2013. While assaults with guns also decreased last year, overall assaults increased.

Whether those changes were linked to NoVA is difficult to say, because fluctuations in crime are almost always a result of multiple factors. At the same time, a report released recently by the University of Missouri-Kansas City found that while crime decreased drastically early last year as NoVA was fully in place, the drop tapered off. It is too soon to determine if decreased crime will be a long-term trend, the report said.

In other places, the success of the algorithms has been spotty or difficult to assess.

John S. Hollywood, a senior operations researcher at the RAND Corporation, said that in the limited number of studies undertaken to measure the efficacy of predictive policing, the improvement in forecasting crimes had been only 5 or 10 percent better than regular policing methods.

The Memphis police force, a pioneer in predictive policing, has worked with the University of Memphis for about a decade to forecast crime by noting time and location of episodes and information about victims. Officers then flood those areas with marked and undercover police cars, and also increase traffic stops, the department said.

But violent crime has proved stubborn in Memphis, and the city continues to be one of the most dangerous places in the nation, according to F.B.I. data.

In Kansas City, NoVA officials gather about 30 to 40 patrol officers about once a quarter to discuss and examine intelligence gathered on the street — details not necessarily captured in official documents. The information often comes from informal conversations that officers have with people on the street about things like who is arguing and who might have committed a violent crime.