The NFL and lawyers for thousands of retired players have reached an agreement to end the use of a race-based method to evaluate dementia claims in the league’s landmark concussion settlement programme.

It follows public outrage over the use of “race-norming” – a practice that critics said made it difficult for black retired players to qualify for payouts, and which came to light after former players Najeh Davenport and Kevin Henry filed a civil rights lawsuit over it last year.

The method assumes black players start with lower cognitive function than white players, which makes it more difficult for them to show they suffer from a mental impairment linked to their playing days.

Critics say it may have prevented hundreds of black players suffering from dementia to win awards that average $500,000 or more.

The vast majority of the league’s players – 70% of active players and more than 60% of those who are currently retired – are black.

The revised testing plan means former black players will now have the chance to have their tests reassessed, and in some cases, seek a new round of cognitive testing, according to the settlement.

Details of the deal filed on Wednesday in a federal court were first reported in The New York Times.

“No race norms or race demographic estimates – whether black or white – shall be used in the settlement programme going forward,” the proposal said.

It still needs to be approved by a judge, but follows months of closed-door negotiations between the NFL and lawyers for the retired players, plus those representing Davenport and Henry.

“We look forward to the court’s prompt approval of the agreement, which provides for a race-neutral evaluation process that will ensure diagnostic accuracy and fairness in the concussion settlement,” NFL lawyer Brad Karp said in a statement.

Cyril Smith, a lawyer for Davenport and Henry, told ABC news the agreement was “a huge win” for black players, while Christopher Seeger, the counsel representing all former players and their families, hailed the deal as a “hard fought” victory.

The concussion fund has to date paid out $821m for several types of brain injuries, including early and advanced dementia, Parkinson’s disease and Lou Gehrig’s disease, also known as ALS.

The binary scoring system used in dementia testing was developed by neurologists in the 1990s as a way to factor in a patient’s socioeconomic background.

Lawyers representing the black players suspect white players were qualifying for awards at two or three times the rate of black players since the payouts began in 2017.

It’s unclear whether a racial breakdown of payouts will ever be carried out – or made public – but some players have asked the Civil Rights Division of the Justice Department to investigate the matter.

Nearly 20,000 NFL retirees have registered for the settlement programme, which offers monitoring, testing and, for some, compensation.