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Saturday, March 10, 2018
Current Affairs ... Politics ... Public Policy ...

The tragic school shooting in Parkland, Florida which occurred two weeks ago has gotten a lot of people talking about gun policy. It has also inspired the numbers geeks to take another look at the numbers regarding “mass shooting incidents” and regarding “assault rifle weapons”. Both of these phrases are easy to say, but quite difficult to define precisely.

However, given that I consider myself a hobbyist numbers-geek, I thought I would search around and see what kind of stats I could come up with from public internet sources. I wanted to see if there are any apparent correlations between shootings and social trends in public communication, such as the rise of 24 hour cable news, the world wide web, and smartphones and social media. I was wondering if the rising “sensitivity” of our society to sensational events like mass shootings because of instantaneous media sources, widely-available sources of information that did not exist before 1980, had anything to do with the rising number of shootings in our country.

OK, so how to define “mass shootings”? There does not seem to be any one agreed-upon standard; one fairly common definition is taken from a July 2015 Congressional Research Service report. This report defined a mass shooting as “a multiple homicide incident in which four or more victims are murdered with firearms, within one event, and in one or more locations in close proximity.” An even stricter definition starts with this requirement, and further removes gang-related,
criminally inspired incidents (e.g. turf wars for illicit drug sales or revenge killings), family/household inspired shootings (e.g. son kills parents and two siblings), and religiously inspired terrorist incidents.

There are a variety of sources of data available, but I felt that the best study was done by the Washington Post. In this study, the Congressional Research definition (at least 4 deaths) was combined with the exclusion of gang, family and terrorist inspired incidents; what we are left with is the “what the hell” shootings where a disgruntled individual without any particularly strong political or religious motivation decided to open fire at a group of unsuspecting strangers in a public space. What was especially compelling about this study was that it went back to 1966, as to include the Charles Whitman clock-tower shooting at the University of Texas in Austin, where 17 people were killed. This was perhaps the first modern incident in the US where strangers in a public place were suddenly under attack, for no discernible reason. I could not find any other information source going back that far.

However, Mother Jones also complied a database of incidents starting from 1982, and its definition of mass shooting incident closely parallels the one used in the Washington Post (except that it includes some incidents with less than 4 deaths but significant injuries, from 2005 on). Unlike the Post, however, Mother Jones lets you download an Excel spreadsheet listing each incident, and this spreadsheet provides a wealth of detail for each shooting. The Mother Jones data is not fully consistent with the Washington Post info, as Mother Jones includes some cases in the later years that WaPo didn’t, and MotherJ missed a lot of otherwise qualifying cases that WaPo came across between 1982 and 2000. Still, between the two sources, I was able to compile my own modified Excel database, manually entering information on the cases in WaPo going back to 1966 and adding those which MotherJ missed after 1982.

I also excluded the MotherJ cases that would not qualify in the Washington Post study. Admittedly, this may not seem right; the WaPo standard of at least 4 deaths is arbitrary. If a shooter kills 2 people but injures 25 others, why is that less significant than an incident where 4 people die and no one else is injured? However, what I want to catch is the long-term trends going back to the late 1960’s, and thus I am stuck with the WaPo standard for sake of comparing apples to apples.

So, here are three charts that I produced from my hybrid WaPo/MotherJ database, for the 1966 to 2017 period. I have charted yearly number of defined “mass shooting” incidents; total number of people killed per year in these incidents; and total number of deaths and injuries from these shootings. Here are the three graphs that summarize my results:

Nominal Mass Shooting Stats 1986-2017

The blue, green, and orange lines show the number of incidents, deaths and death plus casualties per year, respectively. It is rather hard to see any trends from these plots; there is a lot of year-to-year variation. If you plotted an overall “least squares” regression line through each of these plots, you would obviously see an upward trend in each. However, I really wanted more than an overall flat line; I am looking to identify trend shifts within the 52 year period. One way of roughly capturing that is to plot out a 5-year rolling average, i.e. the average each year of the readings for that year plus the proceeding four years. This is far from a perfect “trend identifier”, and the 5-year averaging rule is admittedly arbitrary; you could use 3 years or 8 years, and the results might look quite different. But still, a 5 year rolling average smooths out the ups and downs somewhat and does help a bit to see where trends start and end.

So, the fatter purple line in each graph is the rolling 5 year average. What was I hoping to correlate with (and maybe held explain) its movements? In a rough “eyeball” sense, of course; I am not prepared to apply any sophisticated statistical analysis here. OK, first there was the rise of popular 24 hour cable news channels in the early 1980s, following CNN’s birth in 1980. Before then, a mass shooting might appear on the front pages of local newspapers and be noted on local radio and TV new shows, but usually would not make the national news broadcasts on CBS, NBC and ABC, nor make the pages of widely-read newspapers like the NY Times and Boston Globe. But with 24 hours news, any sensational incident anywhere in the nation could be covered nationally, almost instantly. A troubled man (almost all mass shooters are men) could now be assured of instant (if fleeting) fame for his seeking the revenge or justice that he images regarding his bloody rampage.

By 1995, the World Wide Web kicked news-transmission rates up a notch, with greater speed and wider distribution for anything “sensational”. Then around 2005, the spread of smartphones and social media turbocharged the instant audience effect from the Internet and cable. These are all factors that did not exist in 1966 when Whitman took to the bell tower, nor in the following 15 years, when the number of incidents, deaths and casualties per year were relatively low (although an upward trend starts to emerge around 1975).

Before we proceed with an analysis of my graphs, let me admit to an obvious problem. The population of America grew by about 2/3 between 1966 and 2017. As such, you might expect a larger number of incidents and casualties in 2017 versus 1966 just because of population growth, all other things equal. To account for this, I adjusted the numbers to eliminate the effect of population growth, i.e. I estimated what they would be for the same base population level that existed in 1966. Here are the revised graphs with that adjustment:

Nominal Mass Shooting Stats 1986-2017

So, now we are seeing the effects of everything except population growth on mass shootings, at least in theory. Let’s go through my hypotheses — first that the rise of popular 24 hour cable news stations in 1985 encouraged more mass shootings. Unfortunately, the data does not support that conclusion. In 1984, the 5-year moving average of incidents and casualties took a significant upward bump, but from 1985 through 1990, these numbers steadily declined back to the level of about 1983. And prior to 1984, when cable news was not very influential, there had been a slow but steady rise in incidents and casualties, a trend which appears to have started in 1975. I am not sure what in 1975 would have started this trend, but we cannot say from this graph that the spread of cable news was a significant factor. This is not to say that cable news had NO effect; but the “noise” in these numbers prevents us from reaching any conclusion or strong suspicion about it.

So we move on to my next hypothesis, that the rise of personal computers and the world wide web from 1995 forward also encouraged more mass shooting incidents. The 5 year moving average of incidents and casualties went up and down after 1995, but until 2007 stayed lower than it had been in 1995. [Note that the averages for 1995 are not that much different from 1994 and 1993, thus the 1995 averages are probably not driven by “freak events”.] So, we really can’t detect any effect on these graphs from more widespread internet use by the public. Again, this does not prove that expanding internet use and access to news had no effect at all, but we cannot detect any effect from these numbers.

It looks roughly as if mass shooting incidents and casualties had at least leveled off between 1995 through 2006, even if there continued to be significant year-by-year variation. What might have caused that? We will get back to this question, but first let’s consider my final hypothesis, regarding the rise of smartphones and social media.

I would expect that the effect of ubiquitous pocket computers tied with the burgeoning popularity of social media web sites would start being felt around 2005. As with most of my analysis, this is a rough guideline, not based on rigorous review of usage statistics. But with that said, let’s take a look at what did happen from 2005 forward. It seems pretty clear that from 2005 forward, a steady upward trend occurs in the 5 year average of incidents, with a more dramatic rise in number of deaths, and an even more pronounced upward slope when you add in injuries. (The huge jump in 2017 deaths plus injuries, for both nominal value and rolling 5-year average, is obviously attributable to the October, 2017 Los Vegas strip massacre, where 59 died and 422 were injured; that is the highest number of deaths and the highest injury tally in the entire analysis).

So, perhaps our society’s evolving habit of being tied for just about every waking hour to a media network that provides instant notice and detail of sensational news events is encouraging more and bigger shooting incidents. However, the jump that started after 2006 has to be seen in the context of the “pause” or “level off” trends that arguably occurred between 1994 and 2005. To some degree, the fast increase after 2006 might be driven at least in part by something that ended just before then, some factor that had been retarding and discouraging mass shooting incidents since 1994.

What might that factor have been? The most obvious candidate that comes to mind is the federal assault weapons ban, which had been enacted in late 1994 and was lifted in late 2004. I am not the first person to have had that thought after reviewing the data; Louis Klarevas, a professor at the University of Massachusetts at Boston, published a book in 2016 named “Rampage Nation: Security America From Mass Shootings“, where he claims that the federal weapons ban prevented at least some mass shootings and thus saved at least some lives (Klarevas claims that the law caused a 37% decline in mass shooting fatalities during its tenure). Also, according to Wikipedia,

In a 2013 report from the Australian Institute of Criminology, Samantha Bricknell, Frederic Lemieux and Tim Prenzler compared mass shootings between America and Australia and found the “1996 NFA coincided within the cessation of mass shooting events” in Australia, and that there were reductions in America that were evident during the 1994–2004 US Federal Assault Weapon Ban.

According to the Australian report, these reductions were “small”, although any reduction of unnecessary deaths and injuries is noteworthy. Interestingly, this report used the 4 dead victims or more standard that the Washington Post (and I) used, and utilized the same Mother Jones database that I used (supplemented by other sources).

Of course, there are critics of these studies and their conclusions. In a recent article in the LA Times, Jon Stokes, a contributing editor to and founding editor of, makes the point that the “pause” in the increase of mass shooting incidents during the federal weapons assault ban could not have been driven by decreased access to assault weapons, because semi-automatic assault-style rifle firearms are hardly used by mass shooters. He also criticizes Klarevas’ work because Klarevas uses a more stringent standard of “mass shooting” than the usual 4 dead victims standard; i.e., Klarevas used 6 victims, and thus found a decrease in incidents and deaths. Had he stuck to the usual 4, there would not have been a decrease, just a “level off” (as I observed).

Again, my numbers use the 4-death standard, and thus there is no significant DECREASE. However, it is pretty clear that there an upward trend had started around 1975, and it did level out around 1995. And then from 2006 on, this upward trend appears (roughly) to re-start and accelerate, rising at a faster rate than before the 10-year ban.

As to his point regarding the weapons used by mass shooters, Stokes looks at the Mother Jones database (what else?) and finds that during the 10 year ban, there were three shootings using assault weapons (I also counted three, using AK47s and a HiPoint 995 carbine). My WaPo-MotherJ combined database lists 32 mass shootings and 322 deaths and injuries during this period, so the percentage of shooters using assault weapons during the ban is around 9.4%. Stokes then says that in the decade prior to the ban, two shootings involved “civilian versions of military rifles”. Actually, I found three incidents on the MotherJ database between 1985 and late 1994 where an assault rifle was used (two Chinese AK47s and an AK47 variant, the MAK90), sometimes along with handguns or shotguns. I count 26 total incidents and 349 total deaths and injuries in this period, so the assault rifle percentage for that period is around 11.5%. Stokes claims that “these numbers are far too small for any sort of statistical inference, especially if you’re trying to build a case for banning tens of millions of legally owned rifles”.

OK, Mr. Stokes has a point — the base number of incidents and weapons used are not very high, in the range of 1 to 8 per year. Even when lumped into 10 year chunks, it is difficult to attain 95% statistical significance (assuming a bell curve distribution of “noise” factors) without a great number of observations of such highly variable data. The overall percentage of incidents involving assault rifles goes down somewhat during the ban, and the total number of deaths plus injuries goes down despite more incidents; but these movements are probably not enough for statistical significance. It is fairly clear that before and during the assault weapons ban, assault-style rifle weapons were not the weapon of choice of mass shooters; a majority of incidents involve semi-automatic handguns.

SIDENOTE: in the 10 years prior to the ban, the average number of deaths plus injuries per incident was 13.43. For the three incidents in that period involving assault weapons, the average was 28. During the 10 year ban, the average number of deaths plus injuries per incident was 10.06. For the three assault weapon incidents during the ban, the average was 17. It seems pretty clear that when assault weapons are involved, mass shootings are worse.

As to Stokes and his problem with the statistical significance of available data — even if 95% significance cannot be obtained, isn’t some data better than none when human lives are at stake? Sure, “banning tens of millions of legally owned rifles” is something you don’t do lightly. But what if 15 lives could be saved every decade? What about 5? What about 1? I am trying to make the point that human life, like gun rights, is also precious. Perhaps 95% statistical significance or lack thereof is not a clinching argument when lives are probably at stake.

I also find it interesting that Stokes did not talk about what has happened since 2005 (late 2004, technically), when the ban had lapsed. I took a look at MotherJ’s database, and here’s what I found in that regard. Stokes uses 10 year periods, so let’s look at 2005 to 2014. During that time, there were 45 incidents and a total of 596 deaths and injuries. The average deaths plus injuries per incident was 13.24. During this period, I count 7 qualifying incidents involving what are labeled assault rifles, which is about 15.6% of all incidents. Those seven assault rifle incidents involved a total of 161 deaths plus injuries, for an average of 23 per incident.

What is scary is that from 2015 to February 2018, 3 years and 2 months, there were 8 qualifying incidents where assault rifles or “semiautomatic rifles” were used (the MotherJ database appears to use the two classifications interchangeably, as it labeled AK-47 and AR-15 weapons as “semiautomatic rifles”). That is more than in the previous 10 years. Also, these incidents involved a total of 840 deaths and injuries (yes, this number includes the recent Los Vegas strip massacre and the Parkland high school massacre). So if you calculate an average including Las Vegas, the result is 105 per incident; if you take Las Vegas out, the average for the remaining 7 assault weapon incidents is still 33.7 total deaths and injuries, a good bit higher than for the 2005-2014 decade.

I’m going to stop here. Perhaps I failed to make the case that the trend towards instantaneous nationwide news coverage of terrible killing events encourages their occurrence (although the argument that social media and ubiquitous pocket smart phones have influenced mass killers may be hinted at). I did not set out to address the question of assault weapons and whether more stringent controls on their sales and ownership would have any effect on mass shootings. However, the data seems to point to this idea, and a better look seems to affirm that notion. Personally, I used to be a strong gun control advocate, but I am now more “on the fence” about it. Not that the goals of gun control advocates are unworthy, but that the methods of enacting and enforcing gun control are often quite clumsy and inexact, and thus can easily effect a lot of people who want to own guns and who are responsible in their use, who fully respect the potential of guns for injury and death.

There is the problem, which most gun control advocates don’t seem to acknowledge, that in order to stop one bad person from getting and using a gun, you may need to impinge or deprive the rights of a thousand good people who would make safe and responsible use of such guns. Gun-rights people make the point that automobiles and alcohol use continue to be responsible for much injury and death, and yet there is little push for significantly more government regulation and restriction of those items. The question of increased gun control measures is not at all a “no-brainer”, as control advocates often seem to imply, nor is it necessarily a specious exercise of government control akin to what authoritarian movements sometimes did in gaining control over a people (gun rights advocates usually point out that one of Hitler’s moves after becoming German Chancellor in 1933 was to restrict and control gun ownership — although they fail to mention that the preceding Weimar Republic already had strict gun laws).

In the end, as with everything else in a society where individuals have differing interests and opinions, it is a question of balance. The effect of the availability of rapid-fire military-like rifle guns on mass killing incidents in our country is indeed a legitimate and necessary input into setting this balance. However, in finding an acceptable balance, it must be remembered that only a tiny fraction of all available assault-style weapons are used in mass killings, and that mass killings are still relatively rare (as with terrorist incidents, the probability of dying in a mass shooting event is still very small, down there with lightening strikes). Most gun-related crime in America does not involve assault-style rifle weapons. And by contrast, a lot of responsible gun hobbyists own and make safe use of such weapons. For now, I don’t have an answer as to what the final balance should be regarding assault-style weapon availability; perhaps it should be harder to get and keep them, but they should not be made inaccessible to responsible gun enthusiasts. Overall, I want here to contribute a little bit of data (or data interpretation, however “half-assed”) regarding mass killings and assault weapons, which I believe needs to be a part of the dialectic on guns, especially assault-style weapons.

◊   posted by Jim G @ 11:05 pm      

  1. Jim, I think you do a good job of analyzing the number of mass shootings and the trend in their increasing due to the “‘sensitivity’ of our society to sensational events like [other] mass shootings.” In other words I think you are saying here, mass shootings can/have become the “trending” thing. (Correct me if I’m wrong.)

    The definition of a “mass shooting” is narrow (seems to me) and defining such is well done in your study. It’s important to narrow down the definition of what constitutes a mass shooting.

    Your search is to find out whether the “rise of 24 hour cable news, the world wide web, and smartphones and social media” have any correlation to mass shootings; and it’s here I tend to disagree with you.

    You found, if I read you correctly, that the two did not correlate and thus social media in general did not have an influence on mass shootings; and thus, you found that your own opinion regarding guns had changed. I know I’m simplifying this, but I think I’ve got the gist of what your hypothesis and conclusion are. (Again, correct me if I am wrong.)

    I think the correlation you are looking at is too broad and needs either some narrowing down or something added to more precisely define the role of social media in mass shootings. While I admit that in what follows I may be wrong and have a disagreement over nothing; yet I think it’s important.

    It occurs to me that perhaps it’s not so much social media as such that has an effect on mass shootings as what is ON social media (and other things close to what may be defined as social media) that carries the import of the effect of social media on society and mass killings.

    It seems to me that vast the proliferation of violence, and violence that is supposed to be funny, likely makes such violence, if not attractive to people, easy to tolerate, look at, and even enjoy, in short people become desensitized to seeing blood and gore as entertainment. Furthermore, the longer that violence is accepted as something everybody, or perhaps better defined as a large number of people likes, the easier it is for people to accept.

    It occurs to me that words (such as the ubiquitous “f***” and “s***” are often forbidden on social media, particularly TV, but any kind of mayhem, torture, bloody gore, etc., is more or less easily tolerated and accepted. I would wonder what the correlation is between mass killings and the proliferation of accepted violence in entertainment in movies and TV programs, video games, the acceptance of the concept of fear as related to violence, and the general desensitization of people’s reaction to such things would be.

    The more acceptable such violence becomes, the more desensitized people become, which then makes it easier for people to accept violence as normal when the right conditions arise.

    As to the gun ownership question: If the effect of the proliferation and acceptance of gory violence were included in this study, I would wonder what the results would show regarding the need for “concealed carry” and guns in general are.

    In general it does seem to me that there are some conditions, times, areas where guns are needed, for instance, when people hike in the woods and bears may be a problem, a gun would be important to have. In rural areas in general when animals are on farms and wild life might roam freely and come in contact with humans, again, I can see a need for fire arms in such rural areas.

    However, I find little occasion for use of any kind of fire arm, especially military type fire arms, in urban areas. It seems to me, in a very general sense, that if “guns” in general were against the law in urban areas, the population in general would be safer. I do admit that a careful defining of who might carry guns and what kind of guns they carry would require some strict defining. Yet, in general I can find little use for such in urban areas except their use in killing people.

    Your study is very thoroughly and carefully done, but it seems to me, with all due respect to the importance of your study, that it’s the content of social media that needs the study more than just the presence of social media as such. MCS

    Comment by Mary S — March 15, 2018 @ 6:49 pm

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