### What was the probability Zimmerman was right? (Part 2)

7/18/2013 04:06:00 PM
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This post is an updated version of my previous post of the same title.

Some commenters over at Matt Yglesias's post noted that the data I used in my previous post--police commissioner Ray Kelly's claim that 75 percent of violent crimes are committed by black people--was woefully inaccurate. Indeed, from the FBI's table 43(a), the national average for 2011 was actually just 38.3 percent. Though New York City does have a higher-than-average rate, it turns out that Kelly exaggerated that number for the media, since his own report  actually puts the figure at 66 percent for New York City.

Bear in mind that these are from arrest data, so they are likely to overstate the actual percentage of crimes committed by black people because police disproportionately target black suspects. Just looking at NYC, 54.8 percent of all victims of police "stop-and-frisk" are black, even though black people comprise only 22.8 percent of the population there. The error of this circular logic should be obvious: you can't point to the fact that police are arresting a disproportionate number of black people as evidence that police need to arrest a disproportionate percent of black people. (Question for criminologists: got any studies out there that disentangle these selection bias effects?)

Ok, couple points. First, someone edited wikipedia to claim that Sanford, Florida has a higher violent crime rate than the US national average. FBI data show that this is false: rate for Sanford is 329 per 100,000, compared to the national rate of 386.3. The Florida Department of Law Enforcement has 2012 state-wide data on arrests by race, which is the closest I can get to the local racial demographics of violent crime for Sanford, Florida, where the shooting of Trayvon Martin occurred. That data shows that across Florida, about 45.2 percent of violent crime arrests are black.

So the violent crime rate for Sanford, Florida is 329, while black people comprise 30.5% of the population there. Plugging these figures into the Bayes' Theorem explained in my previous post shows that the probability of an observed black person in Sanford, Florida being a violent criminal was $$Pr \left(B|A\right)=\frac{Pr\left(B\right)Pr \left(A|B\right)}{Pr\left(A\right)}=\frac{0.00329\left(0.452\right)}{0.305}=0.0049$$

So, to all the critics of my previous post: actually, Zimmerman shot Trayvon over a 0.49 percent chance he would commit some type of violent crime.

One commenter suggested that I use burglary data instead of violent crime. I don't think so. Break-ins involving the actual threat of violence against a home's occupants aren't classified as burglaries in these data--they show up as robberies, murders, or assaults instead. The classification of burglary in the URC data involves only crimes where there was a break-in, a trespassing, and a larceny, but no actual threat of violence against a person. That's an important distinction, because without the risk of personal injury, the damages from burglaries are fully recoverable through civil lawsuit. The point is, the threat of violence against a person is the only defensible reason to allow the shooting of a human being. And that means that we need to look at violent crimes and not burglaries.

Also, one extremely critical point I made earlier that no one seemed to appreciate is that the number of crimes is strictly larger than the number of criminals, because there are repeat offenders. More over, as I mentioned earlier, the data is based on arrests, and since police disproportionately target black people, this means there is selection bias in our data that overstates the proportion of crimes committed by black people Together, these points imply that there is a huge upward bias in my 0.49 percent figure, and the actual probability of a black person being a criminal is much, much lower. I can't stress this enough: my computation essentially gives an upper bound on the true probability.