So I left a note on Facebook this past weekend that got some likes and a ‘share’ even.  Being a Facebook post, it was long on emotion and a little shorter on precision, so I promised a friend a blog post that was a bit more structured with regard to gun control, mass shootings.  Here goes.

1) The problem of event likelihood versus event duration

There was a press release from the Libertarian Party on Dec. 16th that basically said we need to allow all people to arm themselves so they can defend themselves in the face of an attack.  The problem is twofold; any student of game theory knows that once an attack has started you’re already on the back foot (thus, arming yourself is unlikely to help, since you have inherently asymmetric information about when or where a mass shooting event will occur), and shortening duration is rather cold comfort for those who are killed in shorter duration attacks.  There’s also a third problem; their sample size is minuscule.  Eight attacks since 1997 is a very small number compared with the total number of attacks in the last three decades.  Let’s unpack.

While the goal should be a decrease in number of attacks, what the Libertarians are describing is attacks of shorter duration.  2.2 deaths per attack looks pretty good until you do the math across cases.  To have 2.2 deaths you’re still potentially having massive murder sprees depending on the number of events per year.  This is because a concealed-carrying citizen might not be at every event, or may be the first killed.

Let’s say out of 15 events someone with a concealed carry permit intervened successfully fourteen times, but the 15th time the concealed carrier’s gun jammed or they were shot first.  The average fatality rate across all 15 cases remained the rather benign 2.2 fatalities per event, but unfortunately this means in the 15th event 33 people were killed.  This is also the problem with using averages.  Fourteen cases with no fatalities out of fifteen is a pretty good record, and an average body count of 2.2 is unfortunate but not shocking…until you realize that in event fifteen, 33 people died (here’s the math: [0+0+0+0+0+0+0+0+0+0+0+0+0+0+33]/15 = 2.2).

The problem with framing this as a duration problem, as the Libertarians do, and using an average body count, is that it claims succes due to a small average body count, but we don’t think of mass shootings in terms of average because these events are inherently outliers.  No one cares that your method for preventing violence was awesome fourteen times; it’s the fifteenth time, when everything went profoundly wrong, that matters.  (It’s also worth noting that Jack Levin of Northeastern University, a noted expert on mass murder, pointed out that we’ve averaged the rather shocking number of about 20 mass shooting events per year over the last three decades…if the Libertarians only have eight rather dubiously analyzed cases [see next point] to stake their claim on, out of possibly 600 total cases, I’ll take my chances waiting for the police…or instituting reasonable gun control policies).

2) The problem of the dubious qualitative analysis 

A friend of mine posted this on Facebook; its some detail on one of the cases cited by the Libertarians in the above section (the last case, in the Oregon mall).  So let’s say I’m at the mall in Oregon when the shooting starts and I’m lucky enough to be in one of the 8 out of 600 (0.013 percent) cases in the last three decades where someone with a concealed carry permit intervenes.  Lucky me right?  Well, not from what I learned in this article…

Apparently the concealed carrier, Nick Meli, didn’t shoot the guy.  At best, the shooter may have shot himself knowing Mr. Meli had drawn his gun while taking cover in a store: “I’m not beating myself up cause I didn’t shoot him,” said Meli.  “I know after he saw me, I think the last shot he fired was the one he used on himself.”  From the wording, I’m lacking certainty about the causal relationship between Mr. Meli’s handgun and the shooter’s choice to off himself when he did.  But at least Mr. Meli didn’t fire, knowing he might have hit bystanders.  The same can’t be said for the commenters.  Here’s a gem:

“Always figured if you position your body down low, with the strong side knee on the ground (hopefully utilizing some solid ballistic cover), your shots will angle up and climb towards the threat. As a bonus, the back of your bicep can rest firmly on the weak side upright knee, affording a very solid aiming/shooting platform.

If the round misses, it will continue upward after passing the target. The closer the threat, the steeper the upward angle …. seems good in theory, and I’m prepared to try it if there are innocents in view right behind the threat.”

That’s from ‘armored member’ (first comment), who clearly didn’t pass the ballistics portion of AP physics.  Yes, those bullets will go up over the innocents “right in view behind the threat”…until gravity takes over.  Then they’ll hit someone who up to this point was safely in the distance, whilst the shooter carries on.  But hey, seems good in theory.

That anyone would count this as a “success” story baffles me on a variety of levels, but it points to a core analytic problem for the pro-gun community: the gun didn’t help.  As far as we can tell from reading, the shooter wasn’t slowed or affected by the concealed-carrier, unless you believe his story based solely on his recollection (recall bias probably renders Mr. Meli’s account void anyway).  In fact, from what we can tell, if Mr. Meli had used his weapon, he may have killed other bystanders.  This is not a ringing endorsement for the argument that more guns in private hands make us verifiably safer.

In conclusion

I’m getting snarky, so I should wrap up.  What did we learn?  1) Event likelihood is more important for policy making than event duration or average body count, since averages can hide massive murder sprees in aggregate data and 2) The “success stories” of citizen shooters preventing mass shootings are likely cases of attribution error cynically/dubiously reinterpreted to appear to be cases of success.  Basically, if you don’t want the kinds of events that happened in Sandy Hook, the only fool-proof way to get to that conclusion is to start working on public policy to regulate and/or prevent people from having easy access to these weapons in the first place.