PHILADELPHIA >> Lawyers representing former NFL players estimated today that payouts from the concussion settlement with the league will top $1.4 billion, a $400 million jump because of thousands more players filing claims.

The number of players who filed to be a part of the settlement is outpacing all previous estimates and could keep growing, the lawyers said in a federal court filing based on estimates from an actuary. The estimate accounts for players who have filed claims and those who have officially given notice that they intend to file claims.

The actuary said participation rates are 21 percent higher than estimated when the settlement was reached. As of July 16, 499 claims totaling more than $485 million had been approved, according to the filing.

The massive increase in estimated payout came the same day a judge denied a request from the league to appoint a special investigator to look into what the league said are extensive fraudulent claims against the settlement fund.

Judge Anita Brody wrote in her federal court ruling that the league’s attorneys had demonstrated that there is “sufficient evidence of probable fraud to warrant serious concern.” But Brody said a special master and a claims administrator have effectively ferreted out those claims for now.

“The audit process is working effectively,” Brody wrote in her deferral ruling, saying if the claims administrator or special master notify the court an investigator is needed, “the Court will rule on the motion at that time.”

The league requested an investigator and cited in its May argument an independent study it said found more than 400 claims recommended for denial based on evidence of fraud by attorneys, doctors and former players attempting to cheat the program. The league has said those attempts to scam the $1 billion settlement fund have slowed down the awarding of valid claims.

The settlement, which took effect January 2017, resolved thousands of lawsuits that accused the NFL of hiding what it knew about the risks of repeated concussions.

It covers retired players who develop Lou Gehrig’s disease, dementia or other neurological problems believed to be caused by concussions suffered during their pro careers, with awards as high as $5 million for the most serious cases.

Attorneys for the league had cited practices such as doctors seeing players for evaluation not in clinical settings, but in hotel rooms, law offices or other places. They also cited a doctor who said she spent seven to 12 hours evaluating each patient, but approved sometimes as many as eight patients a day.

A lawyer for several plaintiffs said today that he and others representing the players supported Brody’s decision.

“Since the NFL filed its motion more than three months ago, the claims process has continued to accelerate and the current audit process is working effectively,” said Chris Seeger, co-lead counsel for the retired players. “We will not allow a small number of potentially fraudulent claims to be used as an excuse by the NFL to deny payment to legitimately injured former players.”

In their May arguments, Seeger and other attorneys noted that the instances of fraudulent claims would be cut dramatically after the most recent rules for claims went into effect, including a list of approved physicians to determine eligibility.

Brody warned in her ruling that she expects the process to ensure valid claims are promptly paid.

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