The significance of the New England Patriots’ use of under-inflated footballs last season was unclear, and the results of the investigation into the behavior were debated. But the National Football League’s punishments of the Patriots and their quarterback Tom Brady on Monday were severe.

The NFL suspended Brady without pay for the first four games of the upcoming season and fined the Patriots a record $1 million while stripping them of their first-round draft pick in 2016 and fourth-round selection in 2017. The NFL said Brady was suspended for conduct detrimental to the integrity of the league and the Patriots were punished for violating the playing rules and failing to cooperate with the investigation. The fine is the largest ever leveled against an NFL team.

“We reached these decisions after extensive discussion with Troy Vincent [the league’s executive vice president of football operations] and many others,” NFL Commissioner Roger Goodell said in a written statement. “We relied on the critical importance of protecting the integrity of the game and the thoroughness and independence of the Wells report.”

The penalties bring closure — inevitable appeals notwithstanding — to a bizarre narrative that centered on one of the NFL’s most successful teams and its biggest stars being charged with violating an equipment regulation most fans didn’t know existed.

In the wake of their AFC championship game victory over the Indianapolis Colts, the Patriots were accused of using footballs filled with air pressure below the league’s minimum. The so-called DeflateGate controversy became the dominant sports story over the next two weeks, even as the Patriots were pursuing their fourth Super Bowl championship.

The four-time Super Bowl-winning quarterback becomes the highest-profile player ever suspended by the NFL. He is one of the biggest stars in all of sports, the golden-boy quarterback who fought his way from sixth-round draft choice to all-time great. But the Patriots’ latest controversy has rekindled a debate over the extent to which their Super Bowl triumphs have been tarnished. The Patriots were previously punished for videotaping opposing coaching signals in violation of league rules.

Brady’s suspension is without pay. He was suspended for conduct detrimental to the integrity of the NFL, the league announced.

Attorney Ted Wells, appointed by the NFL to investigate the matter, wrote in his report released last week that the team probably violated league rules deliberately and Brady probably was at least generally aware of the activities. Wells cited the actions of John Jastremski, an equipment assistant for the team, and Jim McNally, the Patriots employee who serves as the attendant to the officials’ locker room at home games.

According to the league’s announcement on Monday, Patriots owner Robert Kraft told Goodell last week that the team had suspended Jastremski and McNally indefinitely without pay. The NFL said Monday that neither can be reinstated without Vincent’s approval, and even if they are reinstated, there will be limitations on their activities at least through the conclusion of the 2015 season.

“It is impossible to determine whether this activity had an effect on the outcome of games or what that effect was,” Vincent wrote to the Patriots, according to the league’s announcement. “There seems little question that the outcome of the AFC Championship Game was not affected. But this has never been a significant factor in assessing discipline. There are many factors which affect the outcome of a game.

“It is an inherently speculative exercise to try to assign specific weight to any one factor. The key consideration in any case like this is that the playing rules exist for a reason, and all clubs are entitled to expect that the playing rules will be followed by participating teams. Violations that diminish the league’s reputation for integrity and fair play cannot be excused simply because the precise impact on the final score cannot be determined.”

Some supporters of Brady and the Patriots criticized Wells’s phrasing in his report that investigators found it “more probable than not” that the team circumvented the rules and Brady knew about it, calling that an insufficient basis for substantial penalties. But such a preponderance of the evidence is the standard of proof that the NFL utilizes in such cases about the sport’s competitive rules.

The league punished the Patriots as repeat offenders under the sport’s competitive rules. In 2007, Goodell fined Coach Bill Belichick and the Patriots a total of $750,000 and stripped the team of a first-round draft pick in the ‘Spygate’ scandal. That time, the Patriots were found guilty of videotaping opposing coaching signals in violation of league rules.

This time, Vincent wrote to the Patriots that their “prior record” was a factor in the penalties, citing the 2007 sanctions.

Goodell had vowed tougher penalties league-wide for future violations of the sport’s competitive rules in a 2008 memo to the NFL’s competition committee in the aftermath of Spygate.

Patriots owner Robert Kraft said in a written statement released by the team Monday night: “Despite our conviction that there was no tampering with footballs, it was our intention to accept any discipline levied by the league. Today’s punishment, however, far exceeded any reasonable expectation. It was based completely on circumstantial rather than hard or conclusive evidence.”

Kraft called the league’s investigation “one-sided” and also said: “Tom Brady has our unconditional support. Our belief in him has not wavered.”

Vincent’s letter also cited a lack of cooperation by the Patriots and Brady with Wells’s investigation. Wells wrote last week that the Patriots cooperated. But he also wrote that the team’s attorney refused to schedule a follow-up interview with McNally. Kraft said in a written statement last week that McNally already had participated in a series of interviews with investigators and the Patriots considered that request excessive.

Wells wrote that Brady participated in an interview with investigators but failed to comply with requests that he turn over electronic information and devices.

“Your actions as set forth in the report clearly constitute conduct detrimental to the integrity of and public confidence in the game of professional football,” Vincent wrote to Brady, according to the league’s announcement. “The integrity of the game is of paramount importance to everyone in our league, and requires unshakable commitment to fairness and compliance with the playing rules. Each player, no matter how accomplished and otherwise respected, has an obligation to comply with the rules and must be held accountable for his actions when those rules are violated and the public’s confidence in the game is called into question.”

Brady’s suspension enables him to participate in offseason activities with the Patriots, training camp and preseason games. He must sit out the first four regular season games, beginning with the NFL’s season-opening game Sept. 10 against the Pittsburgh Steelers in Foxborough, Mass.

Brady will appeal his suspension, according to his agent, Don Yee.

“The discipline is ridiculous and has no legitimate basis,” Yee said in a written statement. “In my opinion, this outcome was pre-determined; there was no fairness in the Wells investigation whatsoever. There is no evidence that Tom directed footballs be set at pressures below the allowable limits. In fact, the evidence shows Tom clearly emphasized that footballs be set at pressures within the rules. Tom also cooperated with the investigation and answered every question presented to him.”

Yee repeated his criticism, first voiced last week, that the league failed to act before the game after the Colts privately raised concerns about the Patriots’ potential use of deflated footballs. A person familiar with the league’s deliberations said last week that the NFL is satisfied that its representatives involved in the matter followed proper procedures.

“We will appeal, and if the hearing officer is completely independent and neutral, I am very confident the Wells Report will be exposed as an incredibly frail exercise in fact-finding and logic,” Yee said. “The NFL has a well-documented history of making poor disciplinary decisions that often are overturned when truly independent and neutral judges or arbitrators preside, and a former federal judge has found the commissioner has abused his discretion in the past, so this outcome does not surprise me. Sadly, today’s decision diminishes the NFL as it tells its fans, players and coaches that the games on the field don’t count as much as the games played on Park Avenue.”

Former federal judge Barbara S. Jones overturned the league’s indefinite suspension of Ray Rice when put in charge by Goodell of resolving Rice’s appeal.

If Brady’s suspension is not reduced on appeal, the first game he would be eligible to play would be an Oct. 18 meeting with the Colts in Indianapolis. That is a rematch of the AFC title game that produced the DeflateGate allegations.

Brady, for his part, said in a public appearance last week that his satisfaction with the Patriots’ Super Bowl victory over the Seattle Seahawks to cap last season had not been diminished by the controversy.

Kraft said in a written statement last week that he was disappointed by Wells’s report. He and the Patriots have maintained since soon after the allegations surfaced that the under-inflation of the footballs they used while on offense in the AFC title game resulted from environmental conditions in a cool-weather game. Under NFL rules, each team supplies the footballs that it uses while on offense.

Wells’s report found no wrongdoing on the part of Kraft, Belichick or the team’s assistant coaches.

“As you know, we regard violations of competitive rules as significant and deserving of a strong sanction, both to punish the actual violation and to deter misconduct in the future,” Vincent wrote in his letter to the Patriots. “In this case, the footballs were intentionally deflated in an effort to provide a competitive advantage to Tom Brady after having been certified by the game officials as being in compliance with the playing rules. While we cannot be certain when the activity began, the evidence suggests that January 18th was not the first and only occasion when this occurred, particularly in light of the evidence referring to deflation of footballs going back to before the beginning of the 2014 season.”

The fine against the Patriots is the largest ever imposed on a team by the NFL, surpassing a $968,000 fine of the Denver Broncos in 2001 for salary cap violations.

The NFL treated the Patriots far more harshly than it treated two other teams, the Atlanta Falcons and Cleveland Browns, punished earlier this year for violations of the competitive rules.

The Falcons were fined $350,000 and stripped of a fifth-round pick after being found guilty of using artificial crowd noise at home games. Team president Rich McKay was suspended from the NFL’s competition committee, and the employee directly responsible for the violation would have been suspended for eight games if he’d remained with the organization.

The Browns were fined $250,000 and their general manager, Ray Famer, was suspended for four games for improper in-game texting. The Browns did not lose a draft choice.

Goodell or a person appointed by him would be empowered to hear an appeal by Brady. If Brady’s suspension is not reduced, he would lose about $1.88 million of his $8 million salary for the season; He would not be paid for the bye week that occurs during the suspension but would be reimbursed for that later. Brady’s second-year backup, Jimmy Garoppolo, would be in line to take over as the team’s starting quarterback during his absence.

Brady last missed a game in the 2008 season. He suffered a season-ending knee injury in the opening game that season. The Patriots, with then-backup Matt Cassel at quarterback, went 11-5 but missed the playoffs.

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