Actually the percentage of their players that are running afoul of the law is tiny. This year was an unusually large crop with close to a dozen, meanwhile the NFL's starting roster at the beginning of the year (we won't count players that came in to replace the injured) was 1696 (32 teams times a 53 man roster). A dozen out of nearly 1700 is negligible, but the press loves bad news so that dozen gets tons of copy and air time.
I admit that it's not a large percentage, but I can say with some confidence that the number of people living within a .5 mile radius of my home (about 1500-2000 people) who are entangled in the criminal justice system is zero or close to it.
So yes they receive plenty of press but the crime will always precede the publicity. No crime, no publicity.
According to the brainless probably racist picked last in gym class type that portray Pro athletes as thugs cities are overrun by pro athletes beating and killing and raping all day and everyone in a city with at least one team shouldn't leave their houses.
Actually when they're not playing with a few exceptions Chicago's pro athletes if you see them out in public they are most likely raising money for charity or signing an autograph.
Just saw a bunch of Cubs people at a restaurant before going to a local appearance as they head into their fan convention.