(CNN) Ray Rice. Adrian Peterson. Greg Hardy. Ray McDonald. All of them are current or former NFL players that generated numerous headlines for their run-ins with the law.

In the last decade, the headlines and coverage generated from stories about NFL player arrests can make it sound like the NFL is full of criminals.

But is it? According to a new study, the numbers don't support that narrative.

"There's a perception that the NFL has this huge crime problem and that it's longstanding," said Dr. Alex Piquero, a professor of criminology at UT Dallas who was one of the authors of the study. "That's what everybody believes. The data show that it's not true."

The study, "The National Felon League? A Comparison of NFL Arrests to General Population Arrests," was compiled by Piquero and Wanda Leal and Dr. Marc Gertz of Florida State University. The authors compared arrest rates among 1,952 NFL players to arrest rates among males between ages 20-39 in the general population from 2000 to 2013. The general population data came from the FBI Uniform Crime Reports , which calculates arrests per 100,000 people.

Using the same FBI method, the authors calculated arrest rates for NFL players in that date range. The researchers measured arrest rates for total crime, property crime, violent crime and public order crime, which includes arrests for drug and alcohol-related offenses, prostitution and disorderly conduct. For most years, the total arrest rate for the general population was 1½ to 2 times as high as the total rate for NFL players.

"We have long recognized that arrest rates of NFL players are far below the general population," NFL Vice President of Player Engagement Charles Way said in a statement. "NFL players are highly visible members of their community who are all expected to conduct themselves properly. Everyone in the league -- coaches, players and executives -- is held to higher standards of responsible conduct because of what it means to be associated with the NFL. We have long-standing policies and programs designed to encourage responsible behavior, and have evolved them to ensure that everyone meets that standard and embodies our values."

However, the study does not show arrest rates for domestic violence, a topic that permeated the media's coverage on Rice, Hardy and McDonald. Researchers could not calculate the arrest rates for domestic violence because the FBI data does not specify it.

Also notable was that NFL players had a higher arrest rate for violent crimes than the general population during six of 14 years studied, including a spike in violent crime arrests of NFL players from 2004 to 2008. In that category, the numbers for the general public remained unchanged.