Our Real Problem is not Gun Control

Today you will be treated to a guest post:

by: Tuxamation

What does some French guy born in the 1700s have to tell us about traffic accidents, shootings and other random events?

Suppose we had a highway in town that averaged only one accident per year. The accident is a random event, just because there was an accident last Tuesday, it does not affect the chances that there will be an accident today. It turns out that random events like the accidents on our hypothetical highway are described, in statistics, by something called the Poisson distribution. Siméon Denis Poisson (born 1781) showed that with one accident per year 90% of the years will have between 0 and 5 accidents. In fact, if we observed the intersection for 100 years the accidents we observe would look like this:


Even though we average one accident per year, it is not uncommon for us to have years with zero accidents. We have about 38 years with zero. It’s also not uncommon for us to have years with three accidents. We have 6 years with three, and 18 years with two. If we had a year with one accident followed by a year with three accidents, the news media could claim that things are getting worse. The accidents have increased by 300%. Poisson tells us that with such low numbers a 300% increase (while tragic for some of the travelers) does not mean things are getting worse.

Well, suppose your area had a completely different section of highway that had been carefully studied and it was shown that on average there were 17 accidents per year. Poisson tells us that 90% of the accidents per year will fall between 10.8 and 25.5. When a 25 accident year is preceded by a 10 accident year, the news media can claim there has been a 250% increase in accidents on the highway. Now, suppose you were told that over a 20 year period, the number of trips per year on the highway had increased from 226 million to 308 million. With the long term average remaining at 17 and the number of trips increasing you would have to conclude that things are actually getting a little better.

The graph below (from John Allen Fox) shows the number of mass shootings for the years 1980 to 1994. It can be found HERE.

Mass Killings

The blue line is the number of mass shootings (defined by the FBI as four or more victims in a short time interval) from 1980 to 2010. We have 20 observations. The long term average appears to be 17. Poisson tells us that 90% of the observations will be between 10.8 and 25.4. We would expect 2 out of 20 to be either above 25.5 or below 10.8. 1985 looks below 10.8 and 2002 is above 25.5. The blue line looks like a Poisson distribution with an average of 17. Notice that between 1994 and 2004 (the years of the “assault” rifle ban) there is no significant decrease in the blue line.

1992 looks to have had 25 incidents while 1985 was about 7. The news media can claim in 1992 that there has been over a 300% increase in mass shootings since 1985. They would be correct, but Poisson tells us that the 300% increase in context of this data is not meaningful.

The US population increased from 226 million to 308 million over this period. The average per capita incidents are actually down by 27% from 1980 to 2010. In 2010 we had one mass shooting for every 18 million people in the USA. Any plan to prevent mass shootings would have to be accurate enough and invasive enough to detect something that is one part in 18 million.

In response to the tragic Sandy Hook Connecticut shooting, Diane Feinstein in December of 2012 has promised to introduce a draconian “assault” rifle ban that will include semiautomatic pistols as well as semiautomatic rifles. She wants to prohibit the transfer of certain guns and confiscate these guns upon the death of their current owners. Feinstein says her desire for the ban is based on the crime data, but these tragedies of Connecticut and Colorado are being used to push a preexisting agenda. Feinstein said in 1995 (CBS 60 Minutes) that if she could get the votes, she would disarm all Americans.

The Poisson distribution, and the incidents of mass shootings, tell us that things are not escalating as Diane Feinstein and the news media would have us believe. The very same people who aren’t good enough with numbers to get a budget together are telling us they’re good enough with numbers to understand how their gun ban will make all safe. Well the dead French guy’s math says they don’t know the numbers, but despite the numbers there’s an even more important argument against Feinstein. That’s for the next installment.


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