Stochastic terrorism part 2 – the mass shooting lottery

In the aftermath of each new tragedy of mass gun violence, people always look for a cause. There are likely many “causes” of mass gun violence, but the math points to a clear, correlated “temperature” that summarizes all of the causes and spits out violent acts that are at the same time random, yet probabilistically predictable.

In the prior post in this series, I looked at the concept of stochastic terrorism using the model of the “sand pile effect,” which suggests that we can see incidents of mass gun violence as the random, yet probabilistically predictable, “collapse” of a built-up “sand pile” of unresolved tension created by political rhetoric, the easy availability of “high-lethality” weapons, and unstable holders of these weapons. In this post, I will update a related concept that I first explored earlier in the year, which is that incidents of mass gun violence follow a random mathematical pattern all too similar to predicting the number of winners in a lottery on any given draw.

Recall that the assertion behind stochastic terrorism is that it is possible for people with bad intentions to use the internet and other mass media to incite random, unknown-to-you perpetrators to carry out violent acts against your targets. In effect, while there is no clear “pulling of the trigger” tied to any given piece of incendiary rhetoric, nonetheless a clear pattern emerges out of the seeming-randomness of gun violence if you raise the temperature and “flick the spark.”

The Gun Violence Archive documents and maintains a database of each reported incident of gun violence in the United States, and highlights any incident as a “mass shooting” if the number of killed plus the number of injured totals to four or more people. Based on that data, there is a statistical predictability in terms of when incidents of mass violence will occur, although the who and the where are much less predictable. Past posts have looked at this data for 2016 and 2017, with an update through the first half of 2018.

How many lottery winners will there be today?

The nationwide Powerball and Mega Millions lotteries have been in the news recently as lottery managers have been “tweaking the odds” to push toward bigger payouts. Much of the mathematics that lottery managers use to manage the results of their lotteries while still maintaining randomness (hopefully) was developed by the 19th century French mathematician Siméon Denis Poisson (pronounced “pwa-sahn”).

For instance, if we set up our lottery to average just one winner per draw, the actual results are counter-intuitive. Out of 100 games set up this way, about 37 draws will produce zero winners, and another 37 will produce just one winner. The remaining 100 draws will have quickly-declining probabilities of two winners (about 18 times) and three winners (about six times) with larger numbers of winners still possible but increasingly unlikely. Here are the probabilities graphed:

Lottery Winners

Number of lottery winners over 100 draws
at mean = 1 winner per draw

Be assured, lottery managers know very well the math of the “Poisson distribution,” and have at their disposal a number of ways to maintain, over time, their desired number of average winners per draw versus the number of non-winning “contributors” required to keep their lottery profitable.

How does this apply to gun violence?

And so, here is the creepy part (if statistics can indeed be “creepy”). When you apply this same Poisson math to the reported Gun Violence Archive data, the timing of the incidents fits this “random” pattern all too well. For the last three years, the number of reported “mass shooting” incidents (defined by the Archive as four or more killed plus injured) has been averaging about one incident per day, sometimes slightly more and sometimes slightly less. Through October 31, 2018, for instance, the average number of incidents per day for 2018 has been 0.99. And by the way, no other developed country in the world has a rate anywhere close to this number.

And so, what if each of these crazed acts are the “random collapses of the sand pile”? Just like the lottery draws shown above, this does not mean that every day would exactly one incident, even if that average were exactly 1.0 rather than 0.99. In the 304 days of 2018 through October 31, there were 129 days with zero reported mass shooting incidents in the United States. There were 94 days in which one incident was reported and 54 days with two reported. There have been days with up to six mass shooting incidents reported, all of these incidents summing to that 0.99 average number of incidents per day.

Here are the 2018 actual reported incidents versus what Poisson’s “lottery math” would have predicted (note that “lambda” is the Poisson “average”):

2018 mass shootings thru Oct

Mass shootings thru Oct. 2018 vs. Predicted

If we overlay this on the “lottery winner” graph above (substituting days for “draws”), we get this:

2018 mass shootings thru Oct

2018 mass shootings thru Oct. vs. Predicted

While the actual number of “zero-day” incidents overshoots the “random” prediction and the “one-day” incidents undershoot, note that the total of the two, at 223 days, is very close to the predicted 225 days between the two. Also note how close the “two-day” and “three-day” actuals are compared to the prediction.

This pattern is very similar to the 2017 and 2016 results, previously reported here. One possible explanation for the “zero plus one” closeness to the prediction is that, while lottery draws occur at the same time on discrete days, gun violence is more “continuous,” indeed especially at night, making a midnight cut-off a bit arbitrary. The orange gun violence line in the graph above shows this “continuous” nature well.

And so, is this “stochastic terrorism”?

As noted in Part One of this series, it is impossible by the nature of “stochastic terrorism” to tie particular incidents of violence to any given expression or actions, and most of these “mass violence” incidents may not meet some criteria of “terrorism.”

The data does support the idea, however, of the “sand pile effect” noted in the earlier post. If there are thousands of people “on the edge” at any given time, and at the same time “loaded for bear” with high-lethality weapons, there is “something” setting these people off into a violent spree that appears to be eerily random, but at a consistent rate over the last three years.

It is quite appropriate, I suggest, to see this one-per day “average” of mass gun violence as a “temperature” of sorts. In 2014, this “temperature” was a significantly-less 0.74 incidents per day. The increase in “temperature” since 2014 translates into about 3,000 additional deaths, and over 8,000 additional injuries per year. Let me suggest that all of these people are the “victims of terror.”

Back in May I suggested three ways in which the “temperature,” the statistical death and injury rates from gun violence, could realistically be reduced. There are other good suggestions out there begging for real research and data, which the government is not allowed to do by act of Congress.

On Tuesday, November 6 we can, however, change the Congress. Come back to this site on Tuesday for a handy tool for determining if your favorite candidates can still win as their races come down to the wire, or click on the Facebook or Twitter icons to get notified of new posts.

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