If you’re an NFL player, you must want to punch Aaron Hernandez in his dumb-sullen jaw for making his face into the face of the league. If you have any kind of pride in your profession, you must want to shove him in the tattooed chest, with the florid stupidities etched on it, and tell him to quit spilling his ink all over you and your teammates.

Appearances matter, not as a moral issue but from a purely practical standpoint. That’s the lesson to take from Hernandez’s self-portrait as a pop-style killer with a dead jailhouse gaze, one dangerously in love with his muscled-up arms. If he’s innocent, good luck proving it to the masses and a jury. It would be nice to say Hernandez’s appearance in court is his problem and his alone, but it isn’t. It has become the problem of every guy he played with or against because Hernandez has convinced many people, Geraldo Rivera and Rush Limbaugh among them, that the NFL wittingly harbors gang executioners.

Hernandez’s example has become Exhibit A for braying commentators who have painted the entire league in stigmas as crude as snake and dagger tattoos. Rivera denounced the league’s “jungle ethos” and — incredibly — described NFL players as “fatherless” products recruited from the “inner city” in need of “minders.” Actually, Hernandez was not fatherless, and he’s from middle-class Connecticut suburbs, not the inner city, and we all know what that 1970s euphemism means. It means poor and non-white and therefore brutal. Rivera was followed closely by Limbaugh, who said, “This has the potential to blow the lid open on the NFL and gangs and the whole concept.”

Here is a fact that you may find hard to believe after listening to them: NFL players commit crimes at a much lower rate than their peers in the general population. Around 2,700 players pass through NFL training camps every season, and 1,696 make rosters. Yes, some of them get arrested — about 2 to 3 percent a year. The national arrest rate for males aged 22 to 34? It’s 10.8 percent, according to FBI crime statistics for 2009.

There have been a grand total of 34 arrests of NFL players since the Super Bowl, according to a crime database compiled by the San Diego Tribune. If that number sounds high, juxtapose it next to the 1,600-plus men who did not get arrested and who did exactly nothing to deserve the phrase “jungle ethos.”

Now let’s take a look at some of those arrests, break them down and see what kind of crimes they were.

Seven of the arrests were for DUIs. This is not a great statistic, yet it’s hardly surprising, given that men between the ages of 21 and 25 are the worst offenders when it comes to drunken driving. One study in Illinois showed that the age group has a DUI arrest rate of about 17 per 1,000 licensed drivers.

Two of the arrests were for public intoxication. Three were for marijuana possession. Three more belong in the category of risky or feckless but comparatively benign behavior: Cardinals running back Javarris James failed to appear for a court proceeding, Eagles tackle Jason Peters got caught drag racing and Broncos safety Quinton Carter tried to cheat in a casino.

One was an arrest for minor weapons charges, when a player forgot he had a legally registered handgun in his luggage and took it to an airport.

At least six arrests were for violence-related crimes and were matters of the deepest concern. One was Browns linebacker Ausar Walcott, who almost killed a man with a punch in a bar fight.

Jets running back Mike Goodson faces an assortment of charges for riding in a car found to contain a loaded semi-automatic weapon with hollow point bullets, as well as drug paraphernalia. Browns defensive lineman Desmond Bryant was arrested for criminal mischief when he tried to break down the door of a stranger’s home. And Colts safety Joe Lefeged was charged with carrying an unlicensed gun and fleeing police after a Washington traffic stop.

Then there is Hernandez, who is in another category altogether, charged with one murder and under investigation for two more and who has pleaded innocent despite the growing number of people who seem to get shot around him. Whose self-portrait holding a Glock will haunt every sap in the league who gets arrested for too many cocktails or for pulling on a bong or who happens to have tats crawling up his arms. Right now the Limbaughs and Riveras are looking at them all as if they need to be manacled and perp walked.

As the previous recitation shows, the NFL has its share of legal and social problems. And there is no minimizing the three notorious murder cases in the last 15 years among Rae Carruth (2001), Jovan Belcher last year and now Hernandez. Clearly it’s not always easy to tell the difference between men who are talented at a violent game and men who are simply violent.

But the NFL is not the only organization that unwittingly harbors criminals. The military had 26,000 cases of sexual assault last year. And for sheer volume of criminal activity, don’t look at the NFL; look at financial institutions, which in 2011 accounted for 1,719 FBI cases. The statistics suggest the men who play football are, on the whole, less criminally violent than soldiers and more ethically respectable than looters with Harvard MBAs who commit acts of grand larceny with “financial instruments.” Or the middle management creeps employed by Cleveland Browns owner Jim Haslam at Pilot Oil, who have pleaded guilty to bilking long-haul truckers.

The league constantly deals with stereotype. It fights an ongoing war against portrayals of players as gun brandishing, wife-beating, uneducated, morally bankrupt, assaulting criminals. In fact, 80 percent of retired NFL players over the age of 50 have college degrees, compared with 30 percent of the general population, according to a University of Michigan study. That same survey said 64 percent of NFL retirees between the ages of 30 and 49 found are still married to their first wife. As a group they are more committed and disciplined than most employees, evince deep loyalty to their bosses and colleagues and sacrifice their long-term health for their families. In return for which they get ranted at by fans for being overpaid and stigmatized as thugs by foaming commentators in need of story lines.

So the next time Hernandez appears in court, don’t identify him as an NFL player. He’s not one anymore. And he never was a particularly representative one.

For Sally Jenkins’s previous columns, visit washingtonpost.com/jenkins.