NFL players are likely to suffer chronic brain injury at a "significantly higher" rate than the general population and also show neurocognitive impairment at a much younger age, according to documents filed on behalf of the league in federal court Friday.

Former players between 50 and 59 years old develop Alzheimer's disease and dementia at rates 14 to 23 times higher than the general population of the same age range, according to the documents. The rates for players between 60-64 are as much as 35 times the rate of the general population, the documents reported.

The figures, compiled by actuarials hired by the NFL, appeared to be the first public admission by the league that retired players incur brain damage more frequently than the general public. The report did not specify why the rates for retired players are significantly higher.

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The NFL's report, along with one filed by the plaintiffs, was prepared for U.S. District Judge Anita B. Brody, who is presiding over the lawsuit in Philadelphia that accuses the NFL of hiding information that linked concussions to brain injuries. Brody sought the documents as evidence that a settlement the two sides reached in the case is sound.

"These results validate that our assumptions are reasonable and conservative because when compared to prevalence rates among the general population, they are significantly higher," wrote The Segal Group in the documents prepared for and presented by the NFL. "Moreover, as anticipated, the model determines that players will first be diagnosed with qualifying diagnoses at a younger age than the general population, which is consistent with plaintiffs' allegations."

Nearly three in 10 former NFL players will develop at least moderate neurocognitive problems and qualify for payments under the proposed concussion settlement, according to documents filed by the league and the players.

The Segal Group estimates that 3,488 former players will make nearly 6,700 claims for payments related to brain injuries caused by playing football, according to the documents. Of those 3,488 claims, 94 percent would be for Alzheimer's, Parkinson's disease or moderate dementia, but the NFL's documents show that many, if not the majority of, players will be ineligible for compensation before reaching age 80.

The settlement has come under intense criticism from several lawyers involved in the case, although it remains unclear whether that opposition could derail it. For months, many of those attorneys have been requesting the underlying actuarial data that negotiators relied upon to close the deal.

After reviewing the documents, one prominent lawyer who represents several former players said the data refuted the claims of lead negotiators that the settlement provides adequate compensation for players with chronic brain damage.

"They're going around saying what a great settlement it is, when the average Parkinson's player gets $320,000; that's utter nonsense," said the lawyer, who asked not to be identified for fear of upsetting Brody. "The average Alzheimer's guy gets $340,000. That's just utter nonsense."

Roger Goodell and the NFL agreed this summer to pay out more than the $675 million for player awards agreed to in the concussion settlement. Allison Joyce/Getty Images

The players' actuary estimated that former players were at twice the risk for Alzheimer's, Parkinson's, Lou Gehrig's disease and dementia as the general population between the ages of 20-60 years old. After that, they estimated the ex-players' risk would be closer to normal.

The NFL's actuary reported significantly higher rates of Alzheimer's and dementia for all age groups. Players younger than 50 were at least eight times more likely to develop those diseases, for example.

In 2009, the NFL funded a University of Michigan study that showed that former players between 30-49 were 19 times more likely to have Alzheimer's and other mental disorders than men of the same age. But the league disavowed the study, saying that it did not specifically study dementia and was based on unreliable phone surveys.

The documents released Friday have been sought for months by attorneys and media to understand how negotiators arrived at the settlement. The two sides announced in August 2013 that the NFL would pay $765 million -- $675 million designated to retired players with neurological impairment.

One actuary who reviewed both reports for ESPN said he was struck by how similar the findings were.

"It is common to have experts employed by each side wind up with substantially different conclusions," said Scott Witt, owner of Witt Actuarials and a frequent expert in damage calculations. "In this case, I was struck that both experts' reports are fairly harmonious."

Numerous retired players and attorneys have questioned whether the money was sufficient to cover the growing number of players with confirmed brain damage. At the time the proposed settlement was first announced, Christopher Seeger, a lead co-counsel who negotiated the deal for the players, promised that "analysis from economists, actuaries and medical experts" would prove that the settlement will cover "all eligible retired players."

But Seeger and the NFL refused to produce the information. Some attorneys speculated that the NFL was withholding the data because it contained potentially damaging information: the league's own estimates of how many players are likely to suffer brain damage.

That information goes to the heart of questions about the long-term health effects of tackle football. Despite mounting evidence about the link between football and brain damage, scientists have not yet established the prevalence of diseases such as chronic traumatic encephalopathy, or CTE, which has been discovered in dozens of NFL players following their deaths.

In January, Brody refused to provide preliminary approval for the deal. She ordered negotiators to turn over all documentation used to support the settlement, including the analysis by actuaries and economists, noting her concerns that not all qualifying players would be paid.

The plan would pay up to $5 million for players with amyotrophic lateral sclerosis, also known as Lou Gehrig's disease; $4 million for deaths involving CTE; $3.5 million for Alzheimer's disease; and $3 million for moderate dementia and other neurocognitive problems.

However, only men younger than 45 who spent at least five years in the league would get those maximum payouts. The awards are reduced, on a sliding scale, if they played fewer years or were diagnosed at a more advanced age.

The players' data therefore predicts the average payouts, in today's dollars, to be $2.1 million for ALS, $1.4 million for a death involving CTE, and $190,000 for Alzheimer's disease or moderate dementia. The average ex-player being diagnosed with moderate dementia is expected to be 77 with four years in the NFL.

About 28 percent of all retired players are expected to be diagnosed with a neurocognitive injury that is eligible for compensation under the plan. But only 60 percent of them are expected to seek awards, based on prior class-action litigation.