The controversy over race and policing reached a boiling point last week with deadly violence against police in Dallas and black men in Minnesota and Louisiana.

On the left and the right, sharply polarized narratives have emerged. In one, America is a white supremacist empire in which police killings are part of a systematic racist assault on blacks. In the other, most police shootings are justified and claims of racism are being used to stoke hatred of whites and cops.

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Meanwhile, a new study has found that, according to data from multiple cities and counties, police are not more likely to use deadly force against African-American suspects than white ones. Does this mean there is no racial bias? Not necessarily. Because blacks are arrested at far higher rates, they still account for a much higher share of those shot by police than their share of the population. Much of this disparity is due to differences in crime rates, but African-Americans — especially young men — may well be singled out over minor violations.

The study’s author, Harvard University economist Roland G. Fryer Jr., also has found that blacks are more likely than whites arrested under similar circumstances to be subjected to nonlethal force, from being grabbed or pushed against the wall to being handcuffed or pepper-sprayed.

What does this mean for the central narrative of Black Lives Matter — that black lives are devalued by police and society? The data don’t disprove claims of racial bias, but they do disprove the simplistic assumption that police shootings of blacks are primarily about race and that white people sail through police encounters unscathed.

According to a Washington Post database, 732 of the 1,502 people fatally shot by on-duty police since the start of 2015 were white, while 381 were black. Among those who were unarmed at the time of the shooting, 50 were black and 50 were white. Friends and relatives of some white victims of police shootings, such as Dylan Noble, a 19-year-old killed in Fresno, California, last month, have asked whether those killings get less attention because white lives were lost.

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Yet the fact that blacks generally experience more police maltreatment matters, too. Such interactions create a pervasive climate of hostility, perhaps contributing to lethal situations if African-Americans are more likely to see police orders as abusive and humiliating.

The issue of police brutality is hugely complex even apart from race. Cops are men and women to whom we delegate the dirty, dangerous, stressful job of dealing with crime and criminals. Some also treat their jobs as power trips and get vindictive in response to real or perceived disrespect. Add race and racial profiling, and the mix is explosive.

Right-wing hype about a “war on cops” is another narrative unsupported by data — the horror in Dallas notwithstanding. Killings of police have steadily declined in the last three decades, and this trend has continued in recent years. But the demonization of police, both by some Black Lives Matter activists and by some anarchist-leaning libertarians, is deplorable even if it does not lead to someone dying.

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A productive conversation on policing, race and violence would recognize both racial bias and the problems of police abuse across color lines — as well as the impact of crime, particularly in the black community, and the vital necessity of good policing.

If President Barack Obama used the remaining months of his presidency to initiate such a conversation, it truly would be a legacy to celebrate.

Cathy Young is a regular contributor to Reason magazine and Real Clear Politics.