Numbers don't support NFL's punishment for Saints players This spring, the football world was rocked by news of the organized bounty system operated by the New Orleans Saints over the last three seasons. The program allegedly involved cash payments for hits against targeted players on the opposing team. NFL Commissioner Roger Goodell has been aggressive with his punishments. Coaches and management were suspended - head coach Sean Payton for the entire 2012 season; former defensive coordinator Gregg Williams indefinitely; linebacker coach Joe Vitt for six games; and General Manager Mickey Loomis for half the season. The NFL also handed out punishments to four current or former Saints: Jonathan Vilma, Anthony Hargrove, Will Smith and Scott Fujita, with linebacker Vilma receiving the harshest verdict - suspension for the entire 2012 season. The punishments given to the players stem from such allegations as contributing funds to the bounty program, lying about it or obstructing the investigation. These allegations are being contested - Vilma, for one, recently stated, "I have been linked to a bounty, and it is simply not true." But even if they are true, there is a relatively benign explanation for the players' off-field involvement in the bounty program. That explanation rests on dueling facets of any coach-player relationship: Players don't always want to do what their coaches ask them to, but coaches don't ever want to be ignored. PHOTOS: New Orleans Saints bounty scandal When a coach asks a player to act maliciously or illegally, this tension is bound to arise. And so, while there is strong evidence that the Saints' coaches encouraged misbehavior, what if the players ignored their coaches' exhortations to violence on the field, while providing token participation - and appeasement - off the field? As the commissioner's rulings are appealed, there's one important question that must be answered: Did the Saints actually cause more injuries than the average team? The NFL's penalties for the coaches are easy to justify. Their misbehavior has been well documented. But such harsh penalties for the players should require some evidence that the bounty system affected their on-field behavior, evidence that the Saints injured more players than the typical team. As Hargrove's agent, Phil Williams, pleaded to the league: "If these men have committed such grievous crimes that you have determined that their careers should be in danger and / or their names sullied, why be so secretive about the 'evidence' that you use to condemn them.... Do you actually have any concrete evidence that any player from another team was injured as a result of a 'bounty' and that a player from the Saints was therefore paid accordingly?" The NFL has still provided no such evidence. Looking at all of the NFL's evidence, we know that the bounty system existed, but we don't know whether it influenced the players' on-field behavior. Ultimately, the latter is an empirical question. We collected data on player injuries for the 2009, 2010 and 2011 football seasons, those in question for the bounty scandal. Each week, teams publicly list a pregame injury report that catalogs every player who might have his performance affected by injury in that weekend's game. Collecting all of those reports provides fairly complete information regarding the timing and severity of player injuries. With these lists, one can roughly pinpoint when a player was injured by identifying when he is added to an injury report. Though injuries might occur innocently and not technically be "caused" by one's opposition, a team that tends to injure more opponents should stick out in injury reports. If the Saints tended to injure more players, then teams that played them would tend to list more injuries the following week. To test whether the Saints injured more players than a typical team, one need only compare the number of players added to injury reports after a Saints game to the league-wide average. Did the New Orleans Saints injure more players? The data-driven answer is a resounding "no." The Saints appear to have injured far fewer players over the 2009, 2010 and 2011 seasons. The numbers are striking. From 2009 to 2011, the Saints injured, on average, 3.2 opposing players each game. The rest of the teams in the league caused, on average, 3.8 injuries per game. This difference is highly statistically significant, or in other words, it would hold up in a court of law or a fancy academic journal. In each year of the bounty program, the Saints injured fewer players than the average for the league. In 2009, the Saints injured 2.8 players a game, and other teams injured on average 3.8. In 2010, it was 3.5 and 3.6, and in 2011 it was 3.3 and 3.8. The Saints' behavior on the field was certainly aberrant, but positively so. Only one other team, the San Diego Chargers, injured fewer opponents per game over this entire time frame (3.1 injuries). Of the 32 teams, the Saints injured the third fewest in the 2009 season, the 15th fewest in 2010 and the third fewest in 2011. Might this record be linked to the Saints' being too weak or cowardly to respond to the bounties? Certainly not. Lily-livered players don't win Super Bowls. However, the bounty system was run by the defense. Perhaps the offense was unusually kind to its opponents, offsetting the statistical misbehavior of the defense. That too is easily disproved with the data. Even if one focuses only on injuries to opposing offensive players, the Saints don't stand out as particularly vicious. In 2009, the Saints injured far fewer offensive players than did other teams, at 0.9 per game as opposed to an average of 1.9 for other teams. But in 2010 and 2011, the Saints were statistically average, injuring slightly more offensive players in these seasons but no more than chance might allow. Over the three years, the Saints injured fewer offensive players than average. The NFL's case against the players should require documentation that the Saints injured significantly more players than average. They did not. The evidence, then, suggests that the Saints' story is consistent with a scenario in which the Saints players admirably ignored their coaches on bounty hits. Because no NFL player ever wins an argument with a coach, one can understand why the players might not have protested. But the data show that the bounty system is unlikely to have influenced their play. Kevin Hassett is director of economic policy studies at the American Enterprise Institute, where Stan Veuger is an economist and research fellow. Neither is a Saints fan.