The Saints were second in the NFL with 17 regular-season defensive flags for violating rules intended to protect players from being hurt, just behind the Oakland Raiders' 18. The league averaged nine per team.
The Raiders have a long, proud tradition of aggressive rule-breaking.
"The Oakland Raiders have always been a very physical team," said Jim Tunney, a 31-year veteran NFL referee.
"I think it has a lot to do with team discipline and the way the coach wants to approach the game," he said.
Unlike the Raiders, though, the Saints did not otherwise commit a large number of penalties. As a result, violent penalties accounted for a league-high 37 per cent of all the Saints' defensive penalties. The Raiders, with the top number of 88 penalties overall, had a violent-penalty rate of only 20 per cent. The league averaged 21 per cent.
The Saints also led the league with 1.6 violent penalties per 100 defensive plays and the Raiders were second with 1.57 violent penalties per 100 such plays. The 32 NFL teams averaged just 0.84 on that basis.
When viewed together, the pattern of Saints' penalties suggests the bounty system may have encouraged defensive players to be selectively more violent.
"The data are consistent with the notion that violent plays are being rewarded or pushed," said Scott Berry, an expert on sports statistics at Berry Consultants in Austin, Texas, who reviewed Reuters' analysis.
The controversy over the level of violence comes at a time when the NFL, which is facing lawsuits from hundreds of former players who suffered concussions, has made player safety a top priority.
Reuters used data from Football Outsiders, an NFL statistics website that keeps detailed logs of each penalty. Violent penalties were defined as unnecessary roughness, roughing the passer, disqualification and personal fouls. All other defensive penalties, such as unsportsmanlike conduct, were considered non-violent in the analysis. Data regarding the number of defensive plays came from the FootballDB website. The NFL declined to provide detailed penalty or injury data.
Officials with the NFL declined to comment. The Saints and the Raiders did not respond to repeated requests for comment on the analysis.
Last week, the NFL handed down stiff penalties against the Saints after finding that defensive coach Gregg Williams ran a scheme that awarded Saints defensive players $1,500 for a "knockout" and $1,000 for "cart-off" injuries to opposing players during the 2009 to 2011 seasons.
The league suspended Saints head coach Sean Payton for an entire season. Williams - who had left the Saints for the St. Louis Rams - was suspended indefinitely, and Saints general manager Mickey Loomis must step aside for the first eight games of the 2012 season. The Saints will also pay $500,000 and forfeit selections for the second round of the 2012 and 2013 drafts, a significant handicap.
By Friday, every NFL team must certify it does not have a similar bounty program.
Retired Dallas Cowboys quarterback Danny White is sure there are others. "If I was a betting man, I'd go to Vegas with every penny I've got that there were other teams doing it ... I know when I played there was a bounty on me."
The analysis suggests other teams in the league may have systems, an ethos, or playing styles that encouraged violent rule-breaking. And it all comes amid a 70 per cent surge in violent penalties in the NFL since 2008.
The Tennessee Titans' defensive players, for example, were called for 14 violent penalties in 2011, third in the league.
Their violent rate of 32.6 per cent of defensive penalties was just shy of the Saints' rate and they were fourth in the league with 1.25 violent penalties per 100 defensive plays.
The Titans also have a history of being among the league leaders in violent fouls. In three seasons since 2006, the team has topped the league both in total numbers of violent penalties and in violent penalties per 100 plays.
Refereeing crews could in theory call violent penalties at different rates. But referees had a negligible impact on the teams' rates of violent penalties over the past six seasons, said C. Shane Reese, professor of statistics at Brigham Young University in Provo, Utah, who also reviewed Reuters' analysis.
And in recent weeks, several players and coaches have acknowledged some teams have for years had informal incentives for players who make big plays, including hitting players so hard they have to leave the game.
In early March, former Indianapolis Colts Coach Tony Dungy, now a football analyst with NBC Sports, said he knew the Titans have had bounties in the past, including to nail former Colts quarterback Peyton Manning.
He made the comment to NBC's ProFootballTalk blog. Reuters could not reach Dungy for comment. Titans officials declined to comment.
Retired hard-hitting Titans defensive player and sports radio host Blaine Bishop defended his former team. He played for the Titans from 1993 until 2002.
"When I was with the Titans, we never had a bounty system, period," he said.
In recent weeks, the Titans' hometown newspaper, the Tennessean, has reported that some players admitted to an informal system that rewarded big plays but they denied anyone was rewarded just for taking out an opponent.
Williams was defensive coordinator for the Titans from 1997 to 2000. From 2001 to 2003, he was head coach of the Buffalo Bills, and then from 2004-2007 he was defensive coordinator for the Washington Redskins. In 2008 he had that position for the Jacksonville Jaguars, before joining the Saints.
Reuters did not have the data to analyse the period when Williams coached the Titans, the Bills and the first two years of his Redskins career. The teams he coached between 2006 and 2009 did not have unusually high levels of violent penalties.
When Williams joined the Saints in 2009, however, the team joined the Titans among the league leaders in violent penalties.
Whatever the numbers say, players have their suspicions.
Consider a play during the Saints-Giants game at the Superdome in New Orleans last November.
About a minute into the second half, Giants quarterback Eli Manning threw a pass across the middle to Hakeem Nicks, who appeared to catch the ball for a moment. Then Saints defensive player Isa Abdul-Quddus drove his helmet into Nicks' helmet from the side, forcing him to drop the ball, crumple onto the field and briefly leave the game.
After an official threw a flag and Nicks lay on the ground, Abdul-Quddus celebrated along with several other Saints players - behaviour that, in hindsight, made Nicks question whether it had been motivated by a bounty.
"Uh, the way he was celebrating, you would probably think that," Nicks was quoted as saying by the Newark Star-Ledger earlier this month. Nicks later returned to the game, but sat out the next two practices due to a rib injury and concussion-like symptoms, Giants spokesman Pat Hanlon said.
Abdul-Quddus could not be reached for comment.
Nicks' agent Peter Schaffer said Abdul-Quddus violated a football code: "He tried to injure a player instead of tackling a player, and that's where the line is drawn."
Action is needed, Schaffer said. "If there are outside influences that are abnormally encouraging players to go past where the line is drawn, then we have to do everything we can to stop that."