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Anyone who watches football knows that NFL players — particularly running backs, linebackers, and defensive linemen — are going to absorb some punishing hits to the head.

But a new study shows just how devastating that toll can be on brain functioning and mental health, even 20 years after a player took his last hit on the field.

Harvard researchers surveyed 3,500 former NFL players and found that they were six times more likely than the general public to report serious cognitive problems such as confusion and memory loss.

The study found that the longer their professional careers, the more likely the players were to experience cognitive difficulties as well as signs of depression and anxiety.

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Running backs, linebackers, and defensive linemen were most likely to report serious cognitive problems. Those problems include having to read something several times to understand it, trouble keeping track of what they’re doing when interrupted, and difficulty remembering new information like simple instructions.

Depression, anxiety, and cognitive impairments persisted in players even 20 years after they retired, the study said, underscoring the long-lasting effects of head injuries.

Harvard researchers said the study was the first to document what many players have long suspected: that lengthy careers and hard-hitting positions can lead to brain trauma and mental health problems in retirement.

“These guys are such fantastic athletes, but a significant percentage of them are doing serious damage to themselves,” said Andrea L. Roberts, a research scientist at the Harvard T.H. Chan School of Public Health, and the lead investigator on the study, which was published Friday in the American Journal of Sports Medicine.

Roberts said the findings underscore the importance of preventing concussions, closely monitoring players who sustain blows to the head, and finding ways to lessen the impact of those injuries.

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A spokesman for the NFL declined to comment on the study, as did a representative for the National Football League Players Association.

The survey was conducted as part of the Football Players Health Study at Harvard University, a $56 million initiative examining the health effects of professional football, funded by the players union.

The results add to a growing body of research about the dangers of head injuries in professional football. Recent studies by Boston University researchers on the brains of deceased players, including Aaron Hernandez, have found evidence of chronic traumatic encephalopathy, the degenerative brain disease also known as CTE.

Just days ago, Andrew Luck, the Indianapolis Colts quarterback, retired at age 29, saying he could no longer live the life he wanted and felt no joy in the game after seven injury-plagued years in the league.

Rob Gronkowski, the Patriots star who retired in March at age 29, recently started hawking CBD oil, claiming it alleviated the pain he felt from hit after hit over nine seasons in the NFL.

“We really glorify professional football players and people don’t keep in mind what these guys are dealing with in terms of physical pain and injury because they hide it,” Roberts said.

Michael Alosco, an assistant professor of neurology and an investigator in Boston University’s CTE Center, said the Harvard study was important because “it’s probably one of the largest looking at the long-term consequences of playing football, particularly at the professional level.”

“That in itself is a tremendous accomplishment and a huge advancement in the literature,” Alosco said. “It really provides a strong link and a direct association between the amount someone plays professional football and later-in-life cognitive or neuropsychiatric difficulties.”

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Under pressure to respond to such problems, the NFL has in recent years made dozens of rule changes designed to lessen the risk of head injuries, such as penalizing runners or tacklers who initiate contact with their helmets.

The Harvard study, which was based on self-reported survey results from former players, found that 12 percent reported serious cognitive problems, compared to 2 percent of the general population. Nearly one in four players reported symptoms of anxiety and depression.

Roberts said she was disturbed to find that even 13 percent of former players under age 45 and 11 percent of former players under age 35 reported cognitive problems such as memory loss and confusion typically associated with old age.

“Those are numbers that make you feel sad,” she said.

Cognitive problems, depression, and anxiety were twice as likely to be reported by players who spent 10 seasons or more in the NFL, compared with those who played a single season. The risks for those veteran players were high even if they were kickers, punters, and quarterbacks, considered relatively low-impact positions.

“That points the finger right at NFL play,” Roberts said. “You can see, ‘Wow, the guys who played for 10 years are doing a lot worse than guys who played only a year and, for the most part, they played the same amount in high school and college.’ ”

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The study found, however, that even running backs and linebackers who spent only one season in the NFL reported serious cognitive problems. That finding, Roberts said, suggests that players in those high-impact positions suffered later in life from head injuries sustained while playing in high school and college.

Dr. Jamshid Ghajar, director of the Stanford Brain Performance Center, said the findings should prompt further investigation of ways to prevent and treat concussions in football as well as in other sports such as biking and wrestling where head injuries are common.

“In general, it points to the fact that we need better diagnoses and treatment of concussions so people don’t end up with these large, long-term problems,” he said.


Michael Levenson can be reached at mlevenson@globe.com. Follow him on Twitter @mlevenson.