There is an interesting debate going on in the comments of this NPR article on the legal trouble some NFL players have been getting themselves into recently. Are NFL players getting more or less in trouble than "the average person"? The article states: "[The] data found that the percentage of players arrested in the NFL last year was 1.9 percent, compared with the 4.9 percent of American adults arrested in 2010," and goes on to suggesting that "football's popularity creates the perception that the problem is worse than the numbers suggest," but perhaps it is only a perception problem.
Commenters to the article make the great point that it really depends on who the NFL athletes are compared to. What should be the baseline here: "males only, ages 20-40 mainly", or "other people making $100,000+ salaries," or "[other people] arrested in the "normal" population [who] kept their jobs"?
Unsurprisingly, this is an issue that has preoccupied researchers before, and for a thorough statistical analysis of the topic, I recommend Criminal Violence of NFL Players Compared to the General Population by Alfred Blumstein and Jeff Benedict. The paper dates from 1999, so it would definitely benefit from an update, but it is interesting nonetheless. The authors use as their benchmark the young male population, adjusting for race. (They don't consider income because crime data depending on income levels is not readily available.) Their conclusion is that the NFL rates are well below those of the general population. In their words, the NFL players, who are winning games based on their physical strength on the field, might actually be exhibiting restraint - in the sense that they get less in trouble with the law than their peer group - off the field.