Backstopping the Boston study that was the subject of my last blog (“Disturbing New Study”), a different team of researchers reported this week that National Football League retired players are four times more likely than the general population to die of brain diseases.

Dr. Ann McKee, a pathologist and co-director of the Center for the Study of Traumatic Encephalopathy at Boston University, told the Los Angeles Times that the new research “opens new avenues for research and validates our neuropathological findings…. It raises our concern about the risk of CTE, dementia and ALS and the way these conditions overlap.”

McKee’s team studied the brains of four military vets and four athletes, all of whom had been subjected to previous concussions, and compared them with four people with no history of brain damage. All the vets and the athletes showed symptoms of chronic traumatic encephalopathy (CTE), but none of the others did, the team reported last May. After showing that they could replicate that degenerative brain disorder in blast-exposed laboratory mice, the team concluded that everyone who suffered a brain injury — even a mild concussion — could be at risk of developing degenerative brain diseases later in life that can lead to memory loss, bad judgment, depression, outbursts of anger, thoughts of suicide and potential dementia.

The new study, reported Wednesday in the journal Neurology, was much broader. A team from the National Institute of Occupational Safety and Health, which is part of the Centers for Disease Control, tracked 3,439 retired football players with five or more seasons in the NFL.

The bad news is that they found these athletes four times as likely as other men their age to die of Alzheimer’s disease or amyotrophic lateral sclerosis (ALS), better known as Lou Gehrig’s disease. And it found that the league’s speed players, those who built up more speed before they made a tackle or were brought down by one, were at even greater risk.

The good news is that the risk is still relatively small. Among the 3,439 players the researchers tracked, 1,116 died during the study period. Of those, only 27 were found to have a neurodegenerative disease as an underlying or contributing cause of death.

“Although the results of our study do not establish a cause-effect relationship between football-related concussion and death from neurodegenerative disorders, they do provide additional support for the findings that professional football players are at an increased risk of death from neurodegenerative causes,” the study concluded.

Still, it was enough to shake up the NFL, which announced on Wednesday a $30 million contribution to the Foundation for the National Institutes of Health to support “research on serious medical conditions prominent in athletes and relevant to the general population.” It was the largest single philanthropic donation ever made by the NFL in its 92-year history.

“We hope this grant will help accelerate the medical community’s pursuit of pioneering research to enhance the health of athletes past, present and future,” said NFL Commissioner Roger Goodell. “This research will extend beyond the NFL playing field and benefit athletes at all levels and others, including members of our military.”

Good for the NFL. More research is clearly needed. But we also ought to be thinking about whether we can justify risking this kind of brain damage in sports or in wars that are not clearly in defense of our homeland.

For years, we’ve known that military vets make up an abnormally large percentage of our prison population, but new studies are showing that prison inmates are seven times more likely than the general population to have suffered a brain injury.

According to Scientific American magazine, about 8.5 percent of all Americans have a history of traumatic brain injury, with about 2 percent being disabled as a result. But it said that 60 percent of the prison population has had at least one TBI, which can alter behavior, emotion and impulse control.

On average, each year that a brain-injured person spends behind bars costs taxpayers $29,000.  Then think of the lost productivity and the lost lives of more than 2 million Americans in our system of so-called “corrections.”

That’s a loss so huge that it boggles the mind.