Update: The gun violence lottery

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The most-viewed post in the short history of this blog was a February post entitled “The gun violence lottery”. In the wake of the Las Vegas mass shooting, I posited a rather cold math question: What if there is no single “cause” of mass shootings in the U.S. beyond “an unsecured gun was available, and we have millions of unsecured guns available every day”?

In other words, what if we view each gun as a “lottery ticket” in a gruesome daily lottery? Think of a lottery that averages just under one winner per day. Because of natural randomness, however, some days might see no winners at all, or just one, while other days might see, in decreasing probability, two, three, or more winners.

It turns out that there is some basic math for predicting the timing and number of daily winners in a lottery like that. And, unfortunately, that math tracks American mass shootings (defined as 4 or more casualties) all too well. In response to the June 28 shooting at a newspaper office in Annapolis Maryland, I have updated my math for the period through June 28, 2018, and it matches prior years all too well. [1]

The statistical technique used here looks at lotteries and mass shootings, where the “winners” are the tragic victims, as Poisson processes (pronounced “pwa-san”). [2] Poisson processes are those events that “just happen” at some consistent, or slowly-changing, random rate. It turns out that stuff that “just happens” randomly quickly begins to form a pattern that we can mathematically estimate and predict into the future.

So far in 2018, we have averaged 0.86 mass shooting incidents per day, from 154 recorded incidents over 179 days. This rate is slightly down from 0.95 per day for all of 2017, but within expected statistical variation. At the 2017 rate, we might have expected 170 mass shooting so far this year, but even in 2017, the rate varied throughout the year by a small amount.

In 87 of those 2018 days, no mass shooting was recorded. 53 days saw one mass shooting, 26 days saw two, and the count goes rapidly down from there (see the data below). [3] The Poisson calculation says that if the average (called the lambda) were 0.86 shootings per day, the random event would have no “winners” in 76 of those days, with one “winner” in 65 of the days. If we were to graph out the predicted versus actual for the number of incidents per day, it could come out like this:

Mass shootings 2018

Just like in 2017, the Poisson formula was quite close in predicting the actual daily counts, but under-predicting the number of “zero-incident” day count and over-predicting the “one-incident” days. Interestingly, and just like 2017, the sum of the zero and one days, was almost exactly as predicted (140 actual versus 141 predicted) and the number of “two incident” days was also very close (26 versus 28). The number of “three incident” days was exactly on the money at 8.

Indeed, the orange “actual” line is so smooth that it suggests that our 24-hour-day cut-off may be just too arbitrary. Time is, in reality, continuous, more like our orange line. Think of it this way: a night-time shooting could easily be on either side of the arbitrary “midnight” line.

What is the data telling us?

Unfortunately, but not unexpectedly, the 2018 year-to-date data is consistent with the 2017 predictions using the Poisson randomness criteria. It is important to note that this is not proof of “Poisson randomness,” but it does suggest that we do have this phenomenon in the U.S., where we can tell, within an eerie accuracy, “How many?” mass murder incidents we will have today. We just can’t get a handle on “Who, specifically?” If the averages hold, we can expect anywhere between 160 and 176 more mass shootings in the remainder of 2018.

We have had four incidents so far in the first half of 2018 with ten or more casualties, including the tragic Parkland school shooting (and I’ll bet you can’t name the other three). In all of 2017, there were 11 of these “10+” incidents, so we are, unfortunately again, not far off track.

Another way to express this mathematical phenomenon is that guns “exist” to “go off” at some point. The more guns, the more statistically will “go off,” and we have far more guns per capita than anyone else in the developed world. Further, the bigger the ammunition capacity of the gun, the more bullets spray the surrounding area, with thus more casualties.

Rattner graph on gun availability

Source: Steven Rattner – MSNBC

So, what is the role of the shooter in this “lottery”? My take here is that there are millions of people in the United States at any given time who have any given reason to erupt in violence. The purported shooter in Annapolis is just one of these. If just a tiny one-third of one percent of the U.S. population is “on the edge” of violence at any point in time, that would mean 1 million people.

Pick your favorite cause for somebody being “on the end of their rope” (religion, politics, video games, the rude driver in the other lane), but it is really “all of them,” and maybe you yourself sometimes have this trouble. Some of these people have ready access to weapons, but most don’t, and most, fortunately, manage to “put a cork” in their anger today. Or alternatively, they take it out on themselves (see my earlier post on suicide, which, when “successful,” is also mostly due to basic availability of a weapon).

In short, it’s the damn guns, folks. That’s the math. We have sold far too many “tickets” for this sick lottery, and millions of them are in statistically-risky hands.

The good news is that, while we can’t completely get rid of these “lottery winners,” we can change the statistical terms of the lottery and reduce that number significantly. Will we? [5]


You can subscribe to this blog using the email box to the left, or click on the Facebook or Twitter icons to get notification on new posts. Come back to this site on Sunday to read an important post about how Donald Trump used a very old “deal” technique to co-opt American Christianity into silence on moral issues.


Notes:

  1. The data through June 28 come from the Gun Violence Archive.
  2. For a more complete discussion of “Poisson events” see this earlier post.
  3. Here is the data through June 28, 2018:
    Mass shootings data 2018
  4. 2017 predicted vs. actual:
    2017 Mass Shootings
  5. See my earlier takes on what makes the U.S. different on guns and what actions might change the statistics.

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