The science itself — like most attempts to link brain biology to behavior — is murkier.
In recent decades, researchers have made extraordinary strides in understanding the workings of brain cells, neural circuits and anatomy.
Yet drawing a direct line from those basic findings to what people do out in the world is dicey, given the ineffable interplay among circumstance, relationships and personality.
What scientists — from such diverse fields as psychiatry, neurology and substance use — can say is that the arrows seem to be pointing in the same direction. A number of brain states raise the risk of acting out violently, and the evidence so far, while incomplete, suggests that C.T.E. may be one of them.
Dr. Samuel Gandy, director of the N.F.L. neurology program at Mount Sinai Medical Center, said his research showed that rage and irritability “are far and away the most prominent symptoms” among former players with likely C.T.E. His group has identified 10 of 24 former players who probably have the disease.
Scientists at Boston University, who reported the findings on Mr. Hernandez, have described similar behavior in many of the more than 100 players they have evaluated. The caveat for both research efforts is that these samples are selective: Almost all of the players had signs of possible C.T.E. before being studied, which led the players and their families to participate and to donate their brains for research.
It may still be that most of the athletes in violent sports who develop the signature brain pathology, especially at modest levels, are no more irritable than anyone else. But an important hint to the contrary comes from a more mature corner of brain science: dementia research.
People with advanced dementia often begin to act in uncharacteristically aggressive ways, as many caregivers can attest. In a recent study of dementia patients, Swedish researchers found that 97 of 281 dementia patients had a history of aggression.
Those who acted out earliest in the progression of their disease had so-called frontotemporal degeneration — that is, damage concentrated in the frontal and temporal lobes of the brain. This is where C.T.E. shows up, too.
In frontotemporal degeneration, “a purported association has been made with criminal behavior,” said Kevin Bieniek, a research fellow in the Dickson Neuropathology Lab at the Mayo Clinic College of Medicine in Jacksonville, Fla. “Different disease, but some clinical and pathological parallels to C.T.E.”
All of this is far from definitive, given the wide variety of factors that affect motivation and impulsive behavior. Substance abuse is a prominent example. Mr. Hernandez was no stranger to illicit drugs, according to testimony at his murder trial.
Studies strongly suggest that people who are mentally unstable, particularly those with severe paranoia, are more likely to become violent when under the influence of alcohol or other drugs.
The link between steroids — such as testosterone — and rage is another confounding factor. It is rarely clear in mature athletes whether they have used performance-enhancing drugs, or how much.
“Testosterone aggravates aggression in the absence of pathology,” Dr. Gandy said. “If there’s pathology, it’s likely to make things worse.”
As cases like Mr. Hernandez’s and others continue to move into the courts, judges will be making decisions based on limited, piecemeal scientific evidence. These won’t be easy decisions to make.
The only way to diagnose C.T.E. is at autopsy. A number of scientists, including Dr. Gandy’s group, are working to refine brain imaging tests intended to detect the signature pathology in living patients.
Those tests are not yet definitive. Over the past decade, many courts have been reluctant to admit brain scans as exculpatory evidence.
“There’s no serious argument about whether violence comes from the brain,” said Owen Jones, director of the MacArthur Foundation Research Network on Law and Neuroscience at Vanderbilt University.
“It’s just hard to make a credible claim that a particular brain injury has caused a particular act of violence.”