Because my previous responses were so long, I never got to address the issue of economics, which I should, because @aussieninja does bring up a perfectly valid point, and that's the connection between crime and poverty. Economic downturn is the single largest correlating factor when looking at violent crime data. This is just as true for Russia as it is for the US. I don't have any data for violent crime in Russia prior to 1990, but I'm told it was relatively low until 1986... from civilians, anyway, whereas state-perpetrated violent crime was extremely high, just ask my maternal grandfather. Oh, wait, you can't, because he "fell off a train." Sure, comrade trashca- I mean commissar, was that before or after you shot him in the back of the head?

Anyway, the high murder rate in Russia in 1990 correlates to the economic situation, which was bad. Very bad. Between 1989 and 1990, the inflation rate was a whopping 2600%. The 1990s were no better, and the economic situation didn't begin to improve until Vladimir Putin implemented his own economic reforms and the country finally started to rebuild. The economic situation has continually improved, and the violent crime has continually dropped. I've seen it firsthand, because the last time I visited my hometown of St. Petersburg was in 2007, and other than the well-maintained tourist attractions such as Peterhof Palace, much of the city looked like it hadn't been touched since the siege was lifted in 1944. Okay, slight exaggeration, point being it was a wreck. However, @tatdt lives there, and she routinely shares pictures of the city. I recognise some of the locations, and they look nothing like when I was there. The city has changed a lot in the past 16 years, and everything I've seen so far looks like it's for the better.

Furthermore, where the crime is committed and who is committing it is the same in Russia as it is in the US: the inner cities. In Russia, this is gopnik territory, which most people avoid as much as possible. It's a fair assumption that drugs are also involved, and drug laws are just as ineffective there as they are almost everywhere else.

The bottom line is that the data shows a strong connection between economic prosperity and low violent crime. Since we know that free markets are more prosperous than command economies, I don't think it's much of a stretch to conclude that freeing the market would eliminate most violent crime.