Their names have become both a litany and rallying cry: Michael Brown. Tamir Rice. Eric Garner. Walter L. Scott. And now, Freddie Gray.

Since Brown was fatally shot in an encounter with a Ferguson, Missouri, police officer in August, so many unarmed black males have died in police confrontations that even President Barack Obama noted this week that "it comes up, it seems like, once a week now, or once every couple of weeks." Calling such encounters "a slow-rolling crisis, he added, "This is not new and we should not pretend it is."

But determining how prevalent such killings are is no easy matter. The use of police force — against minorities and whites alike — is so poorly monitored that there is no precise accounting of how many citizens are killed by officers, much less their ethnicity or other crucial details.

What official data exists suggests that the number of killings by police officers has crept upward only slowly, if at all, in recent years. Since 2009, one regular if incomplete measure, the FBI’s account of justifiable homicides by police officers, ranged from 397 to 426 deaths annually before jumping to 461 in 2013, the latest reporting year.

Federal experts have long acknowledged that that estimate is too low, and a handful of more recent, unofficial reports — online databases compiled and fact-checked by volunteers – place the toll much higher, at about 1,100 deaths a year, or three a day. Yet they do not suggest that the pace of police killings or the racial composition of victims as a group has changed significantly in the past two years or so.

A number of criminologists believe police homicides are near their nadir. In New York City, for example, 91 people were fatally shot by police officers in 1971 — and a record-low eight in 2013, the last year for which figures are available. In Los Angeles, officers used "categorical" force — gunfire, chokings and other violence that could lead to death — in 84 of nearly 149,000 arrests in 2012, down 17 percent in seven years.

That data suggests that any perception that higher numbers of unarmed African-Americans are being killed by the police in recent months is driven by citizens’ postings of unsettling cellphone videos and pictures, like that of police officers dragging Freddie Gray, his legs apparently not working, into a van.

"People are shocked by all these shootings," said Peter Moskos, a former Baltimore police officer who is an assistant professor at the John Jay College of Criminal Justice at City University of New York. "But they’ve always been there."

But it also means that lethal force by the police is a steady problem that is causing police departments across the country to debate whether they need to change procedures and training.

At the riot-scarred intersection of Pennsylvania and West North avenues in Baltimore on Tuesday, Robert Wilson, a Baltimore high school graduate, said the frustrations that sparked civil disorder there spread well beyond those who took to the streets this week.

"What the media doesn’t understand it is that growing up in this society is poverty, it’s police brutality, it’s rat-infested houses, it’s your friends dying," Wilson said.

For most officers, firing a gun is among the rarest events in their careers. But training and the law-enforcement culture condition officers to regard themselves as perpetually threatened. And while many officers on high-crime patrols learn to sense and respond to danger, experts say, less-experienced officers may see their training as a license to use force — not a restriction.

Some criminologists say the very nature of police work and training can inure officers to the violence they see, and make excessive force seem reasonable in risky situations. Last October, Milwaukee’s police chief fired a 38-year-old officer who had shot and killed a mentally ill man during a fight — not because the shooting was deemed unjustified, but because he had not followed training in handling citizens with mental illness that might have avoided the fight altogether.

"So much police training, from beginning to end, deals with police facing the fact that even the most innocuous circumstance can result in an officer’s death," said Michael Jenkins, a University of Scranton assistant professor of criminal justice. "I understand that stress in their day-to-day lives. But as a profession, they need to place that potential for harm within its proper context."

For years, the FBI report on justifiable police homicides and other federal estimates of police homicides have understated the problem. Only recently have online databases compiled by volunteers begun to produce a more accurate picture. Two of the more prominent ones, Fatal Encounters and Killed by Police, each logged about 1,100 police-related homicides in 2014. Their totals are higher when police-related deaths, such as fatalities in high-speed car chases or suicides in standoffs, are included.

Because the records of killings are drawn mostly from news media reports, some crucial details, including the race of officers and suspects, often are missing.

Yet even those spotty numbers shed new light on the nature of police killings.

Fatal Encounters, maintained by D. Brian Burghart, the publisher of The Reno News and Review, may be the most meticulous aggregator of reports of killings by police. The data, covering killings from 2013 to the present, reinforces federal statistics in one broad respect: In police homicides in which the victim’s race is identified, blacks account for about three in 10 deaths, and whites roughly half.

"Blacks are three times as likely to be killed by cops as are whites, on a per-capita basis," said Moskos of John Jay.

But part of that is because of crime in predominantly black neighborhoods.

"Blacks are four or five times as likely to be victims of homicides, and they are five times as likely to feloniously kill a cop," he said.

Crowdsourced data goes well beyond federal statistics — and offers intriguing results.

Relying on data gathered by Fatal Encounters, The New York Times ranked states by their rates of police-involved homicides per 100,000 residents. The result: Among the lowest were populous states like Massachusetts, Michigan, New Jersey and New York whose big cities — rightly or wrongly — are often seen as crime-prone. And some of the states with the highest rates — up to six times greater, in fact — were less populous and generally western states like Montana, New Mexico and Oklahoma.

Why? Medical care could be one reason; shooting victims in rural areas may be far from a trauma center and unable to get care, Jenkins said. But sociological factors also could be at work.

"We know the South and Southwest are generally the most violent areas, per capita, compared to the rest of the country," he said.

Even within individual states, some police departments have a record of killing suspects at rates far higher than others. On both government and crowdsourced databases, some big cities like Phoenix and smaller ones like Albuquerque and Oklahoma City stand out for the unusual number of police killings reported relative to their size.

And homicide victims are not cut from one cloth. In the 18 months ending last December, at least 18 percent of police killings documented in the Fatal Encounters data involved victims who were mentally ill, and an additional 7 percent involved drugs or alcohol. Burghart and some experts said the true share probably was higher.

That fact is important, they said, because it suggests that police homicides could be reduced if officers were better trained to recognize and deal with mental instability — or, for that matter, any of the circumstances that end in needless deaths.

"Too much of police investigations into killings revolves around the immediate circumstances," Jenkins said. "We need to step back and ask what got us to that place. What got the person who is now deceased into the position where he acted the way he did? And those questions are not being asked."

Michael Wines and Sarah Cohen, New York Times