Introduction

The subject of guns remains one of the most divisive topics in American politics today. Many Americans believe that more gun control is the only rational way forward. Many other Americans believe that the right to bear arms is both unassailable and essential. On one extreme of this spectrum are those who would make pointy sticks illegal, and on the other, those who would argue for a constitutional right to own a bazooka.

No matter where you stand on this issue, the purpose of this article is not to change your mind, but rather, to investigate the subject as objectively as possible. What is the data telling us? More importantly: where is that data coming from? What biases does it contain? What has been included? What has been omitted? Who has made these decisions?

Mark Twain once claimed:

There are three kinds of lies: lies, damn lies, and statistics.

Despite the cynicism, there is profound truth in this sentiment. Too often data scientists cling to data as the ultimate paragon of objective fact. This attitude conveniently ignores the reality that all humans have innate biases; even those working with the best intentions; even those who collect, aggregate and analyze data.

News in the Age of Memes

To better understand this phenomena, let us consider a specific statistic that gained a lot of traction following the Stoneman Douglas High School shooting that occured on February 14, 2018 in Parkland, Florida.

Jeff Greenfield, a political analyst and regular pundit on television news, tweeted the claim that “In the U.S., there have been 18 school shootings since January 1”. This statistic was promptly shared on other social media, becoming something of a meme, and sparking a debate regarding the true number of school shootings in 2018.

In the U.S., there have been 18 school shootings since January 1.
The original tweet has been deleted as of March 2018

PolitiFact investigated and rated the claim of “18 school shootings” as “mostly false”. Snopes also investigated, but offered a more nuanced answer. Ultimately the tweet in question was deleted. The source of this statistic was Everytown for Gun Safety, a non-profit organization which advocates for gun control. And herein lies our challenge. Most statistics regarding gun violence are being provided by pro-gun or anti-gun organizations, which can help to explain the confusing and often contradictory nature of these statistics we keep seeing.

So how many school shootings have we experienced in the USA in 2018 so far? No matter your opinion of guns, any further analysis is completely pointless if we cannot first agree on a statistic as simple as this.

Sadly, there is no easy answer, despite being such a simple question. Snopes took the 18 shootings as reported by Everytown and divided them into 7 categories as follows: 7 incidents of firearm attacks during school hours, 2 firearm attacks not during school hours, 2 cases of shots being fired during school hours for unknown reasons, 3 cases of unintentional gunfire during school hours, 1 suicide, and 2 cases of stray bullets hitting a school, one of which was during school hours.

When using the phrase “school shooting”, most Americans envision past tragedies, such as the Columbine High School massacre and Sandy Hook Elementary School shooting, cases in which large numbers of innocent students were killed or injured, cases in which infamous gunmen with unclear motives committed unspeakable acts of terrorism. Even the most ardent gun control advocate must agree that a suicide by handgun is a very different type of incident. Even the most ardent pro-gun advocate must agree that the preferred number of incidents, regardless of category, is zero.

A More Recent Example

We began researching this article following the shooting in Parkland. On March 2, 2018, roughly two weeks later, a student shot and killed his parents while visiting his dorm room at Central Michigan University. It is genuinely terrifying to think that we cannot go a month in America without another school shooting. It is also prudent to remember: had this student shot his parents anywhere else, it would not be considered a "school shooting" at all.

An Even More Recent Example

On March 7, 2018, while editing this article, yet another shooting occurred in Birmingham, Alabama. According to CNN: "At least two gunshots were fired, killing a 17-year-old female student and injuring a 17-year-old male student at Huffman High School, said Birmingham police Chief Orlando Wilson. He said police considered the shooting accidental, but did not elaborate." Is it reasonable to assume both Politifact and Snopes would consider this most recent event another "school shooting"? More to the point: who has the ultimate authority to decide?

Our Data

While attempting to find an objective source of data for this article we found a list of School Shootings in the United States on Wikipedia. In traditional academia, Wikipedia is considered an unreliable source. After all, anyone can write anything on a Wikipedia page. However, given the polarizing nature of this subject, the authors believe that the crowdsourced nature of Wikipedia may provide the most objective source of data available. If any reader finds flaws within the contents of this list, they are free to discuss the article with other Wikipedia editors, and suggest their own edits as needed. This is not to suggest that this data is without bias. As of March 9 2018, this list includes only 475 incidents in total, and has likely omitted many incidents which might qualify as “school shootings”.

As of March 7, this data includes 10 incidents of school shootings in 2018 so far, the most recent of which was the aforementioned shooting in Birgmingham, Alabama. The oldest incident listed in this data is the Enoch Brown School Massacre of July 26, 1764, roughly 12 years before the Declaration of Independence. This provides hundreds of years of data, and allows us to attempt to establish trends over time.

To further contextualize this data, we also considered the total population of each state and the homicide rate per 100,000 of each state. This data was pulled from Wikipedia on March 5, 2018. We used the most recent data available.

Giffords Law Center Annual Gun Law Scorecard

While researching this article we also considered Giffords Law Center Annual Gun Law Scorecard. This score reduces the relative gun control efforts of each state into an intuitive letter grade. This organization is strongly in favor of additional gun control. States with more gun control have earned higher grades according to Giffords.

All of this data, along with the R script used to create the following visualizations, are provided free for all via our GitHub account. We encourage all fellow data scientists to explore our repo, replicate our results, and notify us if any errors are discovered.

Simple Stats

We begin our article with some simple summary statistics.

School Shootings by Day of Week

Below we have visualized deaths and injuries per incident by the day of week. The dotted line shows the average combined deaths and injuries per incident.

Deaths and Injuries per Incident by Day of Week

The number of school shooting incidents drops during summer months, as we would expect:

School Shootings by Month

However, although less common, summer attacks are more violent than average:

Deaths and Injuries per Incident by Month

As of March 7, 2018, school shootings have already occurred in 47 of the 50 United States, leaving only Delaware, Maine, and Rhode Island remaining. Below we have visualized the number of incidents by state:

School Shootings by State

To better visualize incidents per state, here they are with deaths and injuries removed, and a dotted line showing the average number of incidents per state listed:

School Shooting Incidents by State

California, Florida, Illinois, New York, Ohio, Pennsylvania and Texas have all had more than 20 school shootings each.

When we visualize deaths and injuries per incident by state we find an extreme outlier in Wyoming:

Deaths and Injuries per Incident by State

This is due to the Cokeville Elementary School hostage crisis on May 16, 1986, during which 79 people were injured.

Deaths and Injuries per Incident by State

If we ignore Wyoming, we can see things more clearly.

In addition to Wyoming, Connecticut, Colorado, Mississippi, Oregon, Virginia and South Carolina are the only states to average more than 5 combined deaths or injuries per incident.

Trend Analysis

Are school shootings increasing in frequency?

Are these attacks becoming more vicious?

What are the rates of change?

To begin answering these questions, below we have visualized all available data from July 26, 1764 to March 7, 2017:

School Shooting Incidents by Decade

As we can see in the above graph, following the 1950s, school shootings began increasing at an alarming rate. Looking at data from 1950 and beyond, the average number of incidents per decade more doubles from roughly 25 to over 50:

School Shooting Incidents by Decade

However, when we visualize deaths and injuries per incident, the graph looks very different:

Death and Injuries per School Shooting Incident by Decade

School shootings, measured in terms of total incidents, deaths, or injuries, are increasing rapidly. However, when we measure school shootings in terms of deaths and injuries per incident, we see a decreasing trend. How can we explain this?

Consider the University of Texas tower shooting on August 1, 1966, which occurred when school shootings were less common overall. The most extreme tragedies are still rare events, even when compared to other school shootings. This, combined with the increasing frequency of school shootings overall, may help to explain this trend. Let's dig deeper.

A School Shooting Bubble?

To better visualize this data, let us consider these numbers the way a financial analyst might view an investment. That may sound rightly horrifying, but the authors of this article mean no offense. Our only objective is to better understand this problem.

Consider this: dividing these incidents by decade is arbitrary. In the world of finance, rather than grouping data into static time periods, investors prefer to look at "moving averages", sometimes called "rolling averages". To find this number, we simply sum a value over a given number of days, and divide by that same number of days.

For example, a financial analyst might compare the 50-day moving average to the 200-day moving average to better understand what a stock price is doing. Traditional logic dictates that when one of these indicators rises above the other, this usually implies that the market is about to move significantly.

Can this same type of analysis be applied here?

Below we have visualized the average number of school shootings per year with 5, 10 and 25 year moving averages:

Number of School Shooting Incidents, Moving Average

The upward trend is clear in all three averages. More alarming is the rapid spike we see starting around December 14, 2012, the date of the Sandy Hook Elementary School shooting. Before this point, the 25 year moving average (orange) shows a steady linear increase, which is already tragic enough. Following Sandy Hook, in terms of number of incidents, we entered an age of unprecedented violence.

There is no logical reason why this model should follow the same pattern as a stock price, and yet, in many ways, it does.

From 1950 until the early 1960s the 5 year (blue) tests the 25 year (orange), breaking to a historic low right around the Gun Control Act of 1968. This is followed by a spike that ends around 1972, roughly the same time that the Bureau of Alcohol, Tobacco and Firearms was created. Through the early 1990s, the 5 year (blue) continues to periodically return to the 25 year (orange), but then diverges, reaching a new peak in the late 1990s. The 5 year (blue) decreases from here, tests the 25 year (orange) again around 2005, and finally breaks below around the same time as the Stock Market Crash of 2008. As before, after breaking below the 25 year (orange), the 5 year (blue) quickly spikes again, retracting slightly in the early 2010s, before skyrocketing to unprecedented levels.

In the world of finance, this sort of pattern is often referred to as a "bubble".

We have no theory to explain why the number of incidents of school shootings should behave like a financial instrument, aside from it being a really weird coincidence. There is no solid basis by which to infer that the rate of incidents will soon "crash". Only time will tell.

Waves of Extreme Violence

What about the relative viciousness of these attacks? To better visualize this we looked at more moving averages. Specifically, the average number of combined injuries and deaths per year, divided by the average number of incidents per year. Here are the results:

Deaths and Injuries per Incident, Moving Average

As predicted, the University of Texas tower shooting on August 1, 1966 skews our data radically. Texas aside, the most extreme violence appears to come in waves. The 5 year moving average is currently relatively low as of March 7, 2018. Does this mean that current attacks are relatively less vicious than those that came before? In terms of averages: yes. However, that is a potentially misleading talking point. Let's unpack it.

Below we have visualized the 27 worst school shootings since 1950, those with at least 10 combined deaths and injuries:

The 25 Worst School Shootings since 1950

Of these 27 worst incidents, 7 of them (roughly 26%) have occurred within the past 8 years. So why are the average number of deaths and injuries per incident so low right now?

Relative Frequency of Extreme School Shooting Events

The relative frequency of these extreme events is decreasing. For example, in the 1970s there were 30 school shootings, and of these, 4 caused at least 10 combined deaths and injuries (~13%). By comparison, so far in the 2010s there have been 147 school shootings, and of these, 7 caused at least 10 combined deaths and injuries (~4.8%).

In other words, although the number of school shooting incidents has skyrocketed, a decreasing percentage of these have caused the level of carnage seen in the most extreme attacks. This can be partially explained by the fact that more recent events, regardless of magnitude, are more likely to be listed on the wiki page from which this data is taken.

Gun Control

Many organizations, such as the Giffords Law Center, believe that more gun control is a rational response to this crisis. Skeptics fear that more gun control won't address the real issues here. What is the data telling us?

Giffords provides a gun score grade to each state; the better the gun control, the better the grade. We assigned a numeric value to each of these gun score grades as follows:

Letter Grade Numeric Value
A 96
A- 92
B+ 89
B 86
C+ 82
C 79
C- 72
D 66
D- 62
F 59

In the below visualization, we compared these gun score grades to the homicide rate of each state, to see if any correlation exists:

Giffords Gun Score v Homicide Rate

As we can see above, when the Giffords grade improves, the average homicide rate decreases, with a Pearson's correlation coefficient of -0.2381. It is important to remember that correlation does not imply causation. It is also important to note that the homicide rate includes murders that do not involve guns. The authors believe that the homicide rate serves as a good index of the relative violence level of each state, and thus, can serve as our baseline here.

Giffords Gun Score v Homicide Rate: Box and Whiskers

According to Giffords, 25 states earned F grades, 14 earned C's and D's, and 11 earned A's and B's. We have grouped them accordingly in the above box-and-whiskers plot. Measured in terms of mean or 3rd quartile, the top graded states have a lower homicide rate than poorly graded states. Is this proof that more gun control is the answer?

What About School Shootings?

It stands to reason that contemporary gun control laws had no effect on crimes committed before they were enacted. Therefore, we only included school shootings that occurred after January 1, 2000 in the following analysis. The homicide rate above is measured per 100,000 population. In order to make a fair comparison, we looked at the number of school shooting incidents per 100,000 people based on total state populations according to 2017 estimates. We then plotted the result for each state against their Giffords gun score grade. How does that correlation compare?

Giffords Gun Score v Incidents of School Shooting

As the Giffords gun score grade improves, the number of school shooting incidents per 100,000 decreases. However, this correlation is not as significant as before, with a Pearson's correlation coefficient of -0.0974 versus a -0.2381 correlation with homicide rate.

Giffords Gun Score v Incidents of School Shooting: Box and Whiskers

When we group by grade, the results are even less impressive. The A-B group has the least number of incidents, but the F group has a lower mean than the C-D group, and a similar 3rd quantile. In other words, even if we assume that better Giffords grades can explain the lower homicide rate above, these same gun control measures appear to be less effective at preventing school shootings than general homicides.

In the United States, 40 out of 50 states have suffered at least one school shooting since January 1, 2000. When it comes to the 10 states remaining: Alaska (F), Delaware (B), Idaho (F), Kansas (F), Maine (F), Montana (F), New Hampshire (F), North Dakota (F), Rhode Island (B+), and Wyoming (F) all have 0 incidents as of March 7, 2018.

The 5 states with the most incidents since January 1, 2000 include: California (A, 25 incidents), Florida (F, 18 incidents), Georgia (F, 10 incidents), Illinois (B+, 10 incidents) and North Carolina (D-, 10 incidents). The high number of incidents in California and Illinois, combined with the high number of states with F grades and 0 incidents, helps explain the weakness of the above correlation.

Does Gun Control Increase Deaths and Injuries?

When we use this same methodology to analyze combined deaths and injuries, we find something very strange:

Giffords Gun Score v Deaths and Injuries from School Shootings

As the Giffords gun score increases, the average number of deaths and injuries per 100,000 also increases, with a Pearson's correlation coefficient of 0.1096. This is the opposite of what we would expect to see, assuming gun control was effective at mitigating these deaths and injuries.

Giffords Gun Score v Deaths and Injuries from School Shootings: Box and Whiskers

All three grade groups have outliers, but judging by the mean or the 3rd quartile, the F group actually beats the A-B and C-D groups in terms of deaths and injuries from school shootings per 100,000 population. In other words, adjusted for population, states with poor Giffords grades are more likely to suffer incidents of school shootings, but those incidents are less violent, in terms of average combined deaths and injuries.

The 5 states with the most combined deaths and injuries per 100,000 are Connecticut (A-, ~0.86), Virginia (D, ~0.81), Vermont (F, ~0.80), Oregon (C, ~0.65) and Kentucky (F, ~0.54). We can clearly see these outliers in the above graph. These states have relatively low populations, and have been the location of some of the most deadly incidents. Connecticut was home to the Sandy Hook Elementary School shooting. Virginia was home to the Virgina Tech shooting. Oregon was home to the Umpqua Community College shooting. Kentucky was home to the Marshall County High School shooting.

Vermont had only one incident (August 24, 2006) with 5 combined deaths and injuries, but because it has a small population (only slightly larger than Wyoming) this level of violence per 100,000 population is significant.

The authors wish to remind you that correlation does not imply causation.

Digging Deeper

Below we have grouped all 50 states into 5 quantiles (10 states each) based on the number of school shooting incidents per 100,000 in each. We also calculated the average gun score grade for each group.

Giffords Gun Score v School Shooting Incidents by Quantile

The first group, comprised of the 10 states with 0 incidents since January 2000, has an average grade of 64.7% (D). The 10 states with the most incidents per 100,000 have an average grade of 65% (D). The best graded quantile earned 75.2% (C) and is the 2nd best group in terms of actual number of incidents.

Giffords Gun Score v School Shooting Deaths & Injuries by Quantile

When it comes to combined deaths and injuries per 100,000, we find that the quantiles with D grades outperform those with C grades. The best graded quantile earned 71.8% (C-) and is the 2nd worst group in terms of number of deaths and injuries.

Giffords Gun Score v School Shooting Deaths & Injuries by Quantile

When we use this same methodology to look at homicide rate per 100,000, we see that the states with better grades are clearly outperforming the others. Assuming better gun control is effective at reducing homicides, this is exactly what we would expect to see. However, this also presents a troubling question: why do these same gun control measures appear to be less effective when it comes to mitigating school shootings specifically?

Conclusion

No matter where you stand on the issue of gun control, no matter how we measure the above data, the children of America's schools are subject to unwarranted levels of violence. Only by working together, left, right, and middle, can we hope to resolve this issue. The results of our analysis are far from conclusive, and the authors do not claim to have all the answers. We invite you to explore the data for yourself. We also encourage you to consider the following thought experiment.

The Second Amendment of the United States Constitution reads as follows:

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

Imagine for a moment that you serve on the Supreme Court. According to your interpretation, what is the most powerful weapon an American citizen is legally entitled to have?

Use the slider below to adjust your decision:

Use the textbox below to explain your ruling (optional):

Submissions are anonymous. This data may be used for a future article.

Submit My Ruling

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