Dylann Roof appears at a 2015 court hearing in North Charleston, S.C., after being accused of killing nine people inside Emanuel African Methodist Episcopal Church. (Grace Beahm/AP)

When it comes to mass shootings, President Obama and House Speaker Paul D. Ryan are in rare accord on a leading culprit.

Both point fingers at mental illness. And in poll after poll, most Americans agree.

But criminologists and forensic psychiatrists say there is a critical flaw in that view: It doesn’t reflect reality.

While acknowledging that some of the country’s worst mass shooters were psychotic — the Colorado theater gunman, James Holmes, with his orange-dyed hair; the Virginia Tech shooter, Seung Hui Cho, whom a judge ordered to get treatment — experts say the vast majority of such killers did not have any classic form of serious mental illness, such as schizophrenia or psychosis.

Instead, they were more often ruthless sociopaths whose ­behavior, while unfathomable, can’t typically be treated as mental illness.

U.S. Maj. Nidal Hasan, an Army psychiatrist, was convicted in 2013 of killing 13 people and injuring 30 others during a 2009 shooting rampage at Fort Hood in Texas. (Handout/Getty Images)

The oversimplification, experts say, is perpetuated by the gun industry and a society that assumes that the mentally ill are the only ones capable of deadly rampages. Now, with the White House and Congress prioritizing an overhaul of the ­mental-health system to try to curtail mass shootings and gun violence, critics say the country is chasing an expensive and potentially counterproductive cure on the basis of the wrong diagnosis.

“It would be ridiculous to hope that doing something about the mental-health system will stop these mass murders,” said Michael Stone, a forensic psychiatrist at the Columbia College of Physicians and Surgeons and author of “The Anatomy of Evil,” which examines the personalities of brutal killers. “It’s really folly.”

Stone maintains a database of more than 300 killers, most of them shooters of four or more people. He essentially breaks mental illness into two categories. In the first category are those with schizophrenia, delusions and other psychoses that separate them from reality and who are suffering from serious mental illness and could be helped with medical treatment. In the second are those with personality, antisocial or sociopathic disorders who may exhibit paranoia, callousness or a severe lack of empathy but know exactly what they are doing.

In a paper published last year, Stone found that just about 2 out of 10 mass killers were suffering from serious mental illness. The rest had personality or antisocial disorders or were disgruntled, jilted, humiliated or full of intense rage. They were unlikely to be identified or helped by the mental-health system, reformed or not.

[‘Damaged masculinity’ may help explain Columbine and other mass shootings]

These traits, by Stone’s analysis and definition, describe Eric Harris, the ringleader of the Columbine High School shootings in 1999; Michael McDermott, a software technician who killed seven co-workers in 2000; Nidal Hasan, an Army major who killed 14 people at Fort Hood, Tex., in 2009; Dylann Roof, who is charged with killing eight worshipers in a church in Charleston, S.C., last year; and many more.

“The whole notion of mental illness and mass shootings is so poorly understood,” said Liza Gold, a forensic psychiatrist at Georgetown University and editor of a recent collection of scholarly papers on gun violence and mental illness. “To address the reality of it, it’s like dealing with people in a parallel dimension.”

Here's a look at how President Obama has responded to mass shootings in the United States during his time in office. (Ashleigh Joplin/The Washington Post)

Around the country, at the federal and state levels, lawmakers have proposed or passed legislation linking mental illness to gun violence, saying the measures were needed to stop mass shootings. Some states, including New York, now require ­mental-health workers to report anyone they think is dangerous to a database used for firearms background checks. After the Virginia Tech shootings in 2007, Virginia passed measures to lower the criteria for commitment.

Almost every high-profile mass shooting in recent years has prompted plans and promises to reform the mental-health system.

Jonathan Metzl, a Vanderbilt University professor who studies the history of mental illness, has written that “insanity becomes the only politically sane place to discuss gun control.”

Earlier this year, in a tearful announcement of measures to stem the American phenomenon of mass shootings and gun violence, President Obama said, “We’re going to do more to help those suffering from mental illness get the help that they need.”

He proposed spending $500 million to expand mental-health treatment. His frequent legislative sparring partner on the Hill — the House speaker — is insisting that something be done to protect Americans from randomly being shot.

“We have seen consistently that an underlying cause of these attacks has been mental illness, and we should look at ways to address this problem,” Ryan (R-Wis.) said earlier this year.

The question is how.

[Are mass shootings contagious? Some scientists who study viruses say yes.]

In 2013, in response to the shootings at Sandy Hook Elementary School in Newtown, Conn., that killed 20 first-graders, Rep. Tim Murphy (R-Pa.), a child psychologist, proposed a far-reaching mental-health reform package to expand inpatient psychiatric care and relax privacy rules so family members of the mentally ill are able to access their health records. States would have lost federal grant money if they didn’t pass laws forcing people to get outpatient treatment. The bill, which had Democratic co-sponsors, stalled amid concerns about patients’ privacy and the involuntary-treatment provision.

Murphy revised and reintroduced the bill last year, backing off the involuntary treatment requirement. Sen. Chris Murphy (D-Conn.) also has proposed a reform package, although he has not linked it to mass shootings, saying he was “uncomfortable having mental health framed as a response to gun violence because it risks drawing an inherent connection between mental illness and violence, which doesn’t exist.”

Sen. Murphy’s bill is competing with legislation sponsored by Sen. John Cornyn (R-Tex.) that would require courts, not ­mental-health professionals, to determine whether someone should be prohibited from buying guns. Democrats say that would make it tougher to seize firearms, but the National Rifle Association supports Cornyn’s measure.

There may not be much chance of any meaningful reform passing in an election year. Still, both parties seem determined to get something done.

“The reality is, so many of these mass shootings could have been prevented,” Rep. Murphy said in an interview. “The issue is identifying these people sooner and getting them the help they need.”

But psychiatrists and criminologists who specialize in mass killings say these cumbersome and expensive efforts would have little effect in stopping mass shootings. They fear that the country will be given a false sense of security and that when the shootings persist, the mental-health system will be blamed again.

Critics are especially concerned about increased stigmatization of the mentally ill, fearing that they will avoid treatment so their medical records aren’t entered into databases, some of which have derogatory category titles such as “the mentally defective file.”

‘So deranged, so evil’

Underlying the disconnect between the legislative ideas and the scientific reality, experts say, are fundamental misconceptions about the connection between serious mental illness and violence.

Studies show that the mentally ill do present a higher risk for violence than others, but overall they account for just 3 to 5 percent of violence in the country — and only 1 percent of gun violence against strangers. They are far more likely to be victims of crime.

There are many groups perpetuating the myth of the mentally ill mass shooter, experts say.

One is the news media, which looks for and raises the mental-illness story line after major incidents, sometimes without confirmation but with profound effects. Readers of news articles linking mental illness to a mass shooting “reported significantly higher perceived dangerousness of, and desired social distance from, people with serious mental illness in general,” according to a paper by researchers at Duke and Johns Hopkins universities.

Another is the NRA, whose officials, in fighting off tighter gun-control policies, have called mass shooters “so deranged, so evil, so possessed by voices and driven by demons that no sane person can even possibly comprehend them.”

And most Americans agree, with 63 percent blaming mass shootings on the failures of the mental-health system to identify sick people before they act, according to a Washington Post-ABC News survey last year.

“I think it’s the human inclination to explain behavior that is frightening and tragic as the result of mental illness, because it’s very hard to understand that individuals do not have to be mentally ill to do something frightening and tragic,” said J. Reid Meloy, a professor of forensic psychiatry at the University of California at San Diego who studies mass killings and consults with the FBI.

Mass shooters come in different forms. Some are depressed about their lot in life. Some are enraged by personal slights and seek revenge. Others are paranoid, including Roof, who voiced deep hatred of blacks and other minorities in a manifesto on his website and allegedly told his African American victims: “You rape our women, and you’re taking over our country. And you have to go.”

But that doesn’t mean they have a “significant impairment in reality testing,” as Stone put it in his analysis of mass killers. They plot methodically. They know what they are doing.

“Consequently, they often have not had significant interaction with either the mental-health or law enforcement community,” the Congressional Research Service said in a long report on mass shootings that raised questions about the connection to mental illness. “Nonetheless, following mass shootings, policymakers often propose providing increased funding to bolster” the background-check database.

It’s a dead end, researchers argue.

The book on mental health and gun violence that Gold edited included a paper on mass shootings with this conclusion: “Reactive attempts to reduce gun violence by focusing on people with mental illness represent an intervention with no supportive evidence of practical efficacy.”

‘People in crises’

What might work?

A first-of-its-kind law in Connecticut offers some lessons — and obstacles.

In 1998, a disgruntled state lottery accountant fatally shot four employees at the agency’s headquarters. A year later, the state passed a law that allowed police to seize guns from people deemed imminently dangerous to themselves or others, based on tips often provided by family members or friends. More than 2,000 guns were seized in the first 10 years after the law took effect, according to a state legislative research report.

A 2014 analysis of the seizures in the Connecticut Law Review found that 80 percent of those who had guns taken away — most were men — had no history of mental illness. “The profile that emerges from Connecticut’s experience is that of people in crises,” the analysis said.

Marital conflicts. Financial problems. Grief. Disputes with co-workers.

“The risk factors are the circumstances,” the article concluded, “not the person and not a diagnosis.”

Two other states — California and Indiana — have passed similar laws, which allow for both seizures and a temporary prohibition on purchases. Public health experts say these measures, if adopted widely, could have a significant effect on gun violence and mass shootings, particularly because shooters often drop hints about their plans to family members and friends, who could then report them.

The NRA opposes such measures. And mental-health experts also question them. People with failing marriages, financial troubles and problems with co-workers are everywhere. So are people with personality disorders.

How could a system be devised to triangulate the risk and identify real threats? Not easily. Or ever.

“From a psychiatric perspective,” Gold said, “I don’t think you can design an intervention to prevent mass shootings.”

But some of the mental-health reforms being promoted to reduce gun violence — increasing the number of in­patient beds, raising funding for schizophrenia research, improving community mental-health services — may deserve support anyway.

“If the result is better funding and treatment for mental health, is that a worthy outcome?” said Meloy, the forensic-psychiatry professor who consults with the FBI. “I think so, even if the means to get there were somewhat duplicitous.”

Correction: An earlier version of this story identified Nidal Hasan as an Army captain. He was an Army major.