Mass Shootings and TerrorismOur obsession with small probabilities and rare eventsIsaac FaberBlockedUnblockFollowFollowingJan 22I started considering this article last month around the anniversary of the death of my father.
Even with Christmas, the weeks leading up to and after the holiday are always a little somber.
Thoughts of death and mortality intermingle with my children’s innocent excitement for Santa’s arrival and the welcoming of the new year.
My dad passed away in 2001, a few months after September 11th.
He died after a short battle with gastrointestinal cancer.
During his treatments, we had a chance to muse about how the terrorists had changed the world.
The paradox was lost on me.
I and my father believed the greatest threat to the United States had just revealed itself.
However, at the time, I also firmly believed that his cancer was an anomaly.
Perhaps exposure from his youth was to blame; a freak occurrence.
Years later I’ve come to realize how simple my thinking was.
I am much more likely to have a battle with cancer than pass away from a terrorist attack.
I now understand how violence, like terrorism and mass shootings, plays a small role in our lives.
I make this statement having experienced my fair share of death.
For the past 16 years I have been a Soldier in the United States Army and can attest that at a 2:1 ratio, combat has not been the primary cause of military funerals.
In fact, I just attended yet another non-combat military funeral this past weekend.
Suicide, motorcycle accidents, car crashes, cancer, and heart attacks have removed more of my friends from this earth than patrols.
This obviously isn’t going to be every Soldier’s experience, but it is for most and it is consistent with the data.
The truth is, you are probably not going to die in a mass shooting or terrorist incident.
They are exceedingly rare events.
You likely have been told this before, but it stands in stark contrast with the amount of news coverage and political attention such events receive.
Over the last half-century, the average number of victims in the United States population is something close to the values listed below.
+ — — — — — — — — + — — — — — — — — — – — — — — — — +| Incident Type | Avg Annual Victims |+ — — — — — — — — + — — — — — — — — — – — — — — — — +| Mass Shootings | 2.
5 per 10 mil in population || Terrorism | 18.
8 per 10 mil in population |+ — — — — — — — — + — — — — — — — — — – — — — — — — +There are many reasons we fixate on these events.
Maybe because they fit so neatly into political narratives.
Or perhaps violence took center stage as the prime concern for our ancestors and our biological wiring does not change as quickly as civilization.
However, there are data-based reasons that justify the rare event obsession.
They (rare events) can be a precursor of something larger.
Sometimes the unexplained movement in the grass is a lion.
Perhaps infrequent events involving guns and terrorism are symptomatic of burgeoning epidemics and not just episodic societal background noise.
A data science view of this problem would be concerned with how non-linear the impacts of such events are.
In lay terms, do the events get exponentially worse or increase rapidly in frequency?I have almost always found it a mistake to dismiss human intuition.
Often, there are good reasons for people to hold specific beliefs.
In the case of mass shootings and terrorism, some of the characteristics of the data may explain our obsession.
Looking just at the United States here is a view of the total number of victims per incident.
Each of these incident types has a story to tell.
Typically with discrete rare events, a Poisson process is used for modeling and forecasting.
This is, for example, how earthquakes are commonly understood.
However, a Poisson process has the assumption of being memory-less with stable inter-arrival times (average time between events).
Visualizing the statistical inter-arrival times shows mass shootings becoming more common (currently as common as terrorism) with a drastic increase in frequency starting in the ’80s.
One silver lining is that the average total victims in mass shootings are stable year over year.
On the other hand, terrorism is stable with respect to inter-arrival but has a much larger variation in the total victims per incident.
Another way to look at the difference between these two types of rare events is comparing the average time between events with respect to the number of fatalities.
The number of fatalities for a mass shooting seems to be capped at around 100 regardless of the time between events.
However, with terrorism, the noticeable outliers tell a different story.
The (admittedly crude) trend line hints that the longer the time between events the greater the number of possible fatalities.
In fact, fatalities magnitude grows non-linearly.
So, for example, every time we add 10 years to the average time between events the expected number of fatalities grows by as much as 10x.
In this light a truly massive scale terrorism incident, killing between one hundred thousand and one million people, is not only possible but likely.
By the extreme boundary of this basic model, we can expect such an event as often as every 50 –100 years.
These types of rare event trends can be recognized by our psyches, even before we consciously realize it.
Mass shootings are accelerating in frequency and low impact terrorism is an indicator of a much larger event.
Both of these problems are at the forefront of our minds because our intuition is telling us to pay attention, and so is the data.
All of the data and code used to create this article can be found in this MatrixDS project.
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