A couple of years ago, when the weight of evidence had tipped to the point that no reasonable party could any longer deny the seriousness of brain injuries that American football players inflicted upon each other, I made a semi-serious prediction: Within a generation, the National Football League (NFL) would become the National Flag Football League (NFFL). Only such a radical change to the rules of the game could reduce the concussion problem to a tolerable rate and save the league from its own violence.

We did not suddenly discover then that football was often harmful to the long-term well-being of its practitioners. Retired players, many in failing physical and mental health, had for years been appealing to the league to provide better care and coverage for injuries sustained. However, as an entertained public, we conveniently ignored the crisis until several players, including a presumptive future Hall of Famer, killed themselves for reasons apparently connected to degenerative brain disease.

Nor are recent stories about violence of football players toward nonplayers — particularly, punching women and giving children a whooping — the first signs of such trouble. Once again, it's the players' stature, recency bias, frequency effect and vivid narratives — on film, in photographs and in other media — that have shocked us into the inability to deny the inhumane violence of America's most popular professional sports league. Should it surprise us that exceptionally large, strong and fast men — who have been trained, exhorted and rewarded since childhood to annihilate one another on the field — have difficulty restraining these impulses off the field? In retrospect, my NFFL prediction unfortunately neglected a larger problem of violence among football players toward others, not just toward one another.

"Wait a moment," you might object. "Don't judge the sport and the rest of its upstanding citizen-players by the actions of a few." And rightly so: According to New York Times analysis of a USA Today "database of arrests, charges and citations of NFL players for anything more serious than a traffic citation," on average fully 39 out of 40 players have had clean records in any given year since 2000. (Anecdotal evidence suggests that were traffic citations included, the offense rate would accelerate faster than the exotic sports cars in which many players have been caught speeding, but that could be unfair speculation.) Ironically, 2014 has been a good year, on track to be the cleanest since the data have been collected.

Still, over time, it's hard to defend a 2.5 percent annual arrest rate (even higher for the Minnesota Vikings), and it's also not easy to determine how low that rate must go to be tolerable. Experience suggests that the number of those caught is probably small relative to those committing similar offenses who have gotten away with them. Expertise suggests the need to shine a light on leadership, the ones responsible for league discipline who are also doing the training, exhorting and rewarding — who seem to reverse course faster than the league's best running back when the team needs him, or when allegedly nonexistent evidence resurfaces.

There remain divided opinions as to whether the commissioner was justified in suspending coaches who permitted a "bounty" program aimed at taking out opposing teams' critical players. What else have those leaders done to restrict hitting to clean, safe, on-field contact? Even as they have put new rules in place increasing protections for so-called "defenseless" players, regulators seem unable to keep pace with the speed and strength of the modern player.

Of greater concern is that they have not even begun systematically to examine holistically whether the on-field behaviors they champion translate into off-field recklessness. If NFL leadership fails to make that connection and render changes to the sport's culture of violence, then the banner of flag football may get the call to save the league even sooner than I once predicted.

Christopher Michaelson is an associate professor of ethics and business law at the University of St. Thomas.