A 911 call was made at 11:09 p.m. on October 15, 2015, to report a battery incident involving a relatively minor use of force. Police arrived nearly a half-hour later, found no evidence of a crime having occurred, and went on their way.

The reality of the situation, however, was quite different, according to a report on the incident later published by The New Orleans Advocate. In actuality, a car had blown through a stop sign just after 11 p.m. in the popular Marigny neighborhood of New Orleans. A 64-year-old man visiting from San Diego was nearly hit by the car and exchanged angry words with the driver, who a witness says subsequently assaulted the tourist. The victim was ultimately paralyzed.

According to an EMS report provided to the Times of San Diego, the emergency medical service arrived at 11:22 p.m., 13 minutes after the 911 call was placed. The ambulance left with the injured tourist at 11:30 p.m., eight minutes before a police officer reached the scene. Finding no victim, the officer marked the call “unfounded” — meaning that he or she found no crime had occurred — in the police department’s Calls for Service database.

This incident is a particularly egregious example of the effect that lengthy police response times can have on a city’s crime totals. Over the course of the hundreds of thousands of incidents that take place each year, long response times can lead to officers recording fewer incidents as crimes, which in turn can hurt the reliability of crime totals tallied by the FBI when the agency compiles national statistics. And ultimately, these delays can erode public confidence in the police.

For this piece, I analyzed 2016 data from three cities, New Orleans, Detroit and Cincinnati, and found that as response times go up, the likelihood that a crime will be found goes down. Indeed, in all three cities, when police took more than two hours to respond, they were over 2.5 times more likely to report they’d found no evidence that a crime had occurred.

Nationwide, about 86 percent of all major crimes reported by the FBI in 2016 were property crimes (theft, auto theft and burglary). Violent crimes (such as murder and armed robbery) were much less common across the country and often received faster police responses in the cities analyzed here. Looking more closely at 911 calls reporting property crime, therefore, can show how longer response times may deflate the number of crimes that get investigated and ultimately reported.

Lots of cities provide open access to Calls for Service data, but research into this subject is difficult because the data is not standardized and only a handful of cities provide information on the time of the initial call, the time of arrival, and the final status of the call. That determination of the incident’s status, referred to by police as its disposition, is made by the police and dispatcher. For instance, the disposition could be a finding that a burglary occurred and a report is needed, or that an alarm just went off because the wind blew a door open. Furthermore, the disposition can reflect an officer’s inability to locate evidence that a crime occurred either because no crime did occur or because no victim or witness was present when the officer arrived.

New Orleans, Detroit and Cincinnati do provide information for all of these parameters. Though the terms the cities use vary somewhat, this article will describe incidents lacking evidence of a crime as having a disposition of “unfounded.”

The chart below shows how longer response times may deflate the number of crimes reported in these cities — the chart measures the percentage of property-crime-related Calls for Service that were ultimately marked as unfounded compared to police response time in minutes. As response times got longer, the percentage of incidents deemed unfounded also increased.

In Detroit, only 16 percent of property crime incidents in which an officer arrived in under two hours received a disposition of unfounded, compared to 40 percent of dispositions following police response times of two hours or longer. Similarly, in New Orleans, 13 percent of incidents with a response time of under two hours received an unfounded disposition, compared to 46 percent of incidents with response times longer than two hours.

The problem was less acute but still apparent in Cincinnati’s data, which showed that 4 percent of 2016 property crime reports that were responded to in under two hours received an unfounded disposition, but 18 percent of such crimes where the response time was over two hours got the same designation. These three cities point to long response times as a contributing factor in the rate of recording of property crimes, though it’s hard to draw firm conclusions about the impact long response times have on national crime figures from such a limited sample.

Why might these cities be experiencing such lags? Most big police departments shrank during the last recession, and there is evidence that lower staffing levels mean dispatchers have fewer officers available to respond to incidents when they occur, which results in longer response times. Denver police, for example, noted in 2013 that there was a strong correlation between a drop in staffing in the years following the recession and rising response times.

At the same time, most police departments aren’t dealing with manpower shortages as severe as those in Detroit and New Orleans. While 64 of the 100 largest agencies that reported staffing data for both 2008 and 2016 declined over that span, the drops in Detroit (-22 percent) and New Orleans (-19 percent) were the second- and fourth-largest, respectively.

It’s also worth remembering that there may be good reasons for longer response times on some calls. For example, several cities, including Cincinnati, allow certain non-emergency reports to be filed online with the understanding that contact with police will occur hours or even days later. Alternatively, the dispatcher may be aware that a caller is unlikely to remain on the scene and prioritize accordingly, though this information would not appear in the publicly available data set. That said, longer response times were associated with higher percentages of unfounded incidents in all three cities even after accounting for different call priorities or when looking only at more serious crimes, such as robbery.

Ultimately, crime statistics can be confusing and misleading. A major challenge to better understanding how delayed police responses may affect reported crime figures is that national police response times are not formally collected and disseminated. Less than half of crimes that occur are reported to police, and long response times are a likely contributing factor to this trend of underreporting.