Can We Predict Mass Shootings?

...And Can Dragon Slayers, Earthquakes And Forests Help Us To Find Future Mass Murderers?

What do you usually bring along you when you go to the cinema? Wallet, jacket, partner(s), children, friends, car keys? So far, so good. How about a bulletproof vest? Or a map outlining the probability of your favorite cinema being attacked by a mass shooter on that evening? Would you go if it showed, let‘s say, a twelve percent chance this will happen?

The bad news: we won‘t be able to predict precisely where the next mass shooting will happen. And perhaps we never will. There. I said it.

The good news: there is research underway that will allow the detection of factors that facilitate mass shootings. Partial and short-term predictions might be possible, after all.

Actually, software to predict certain types of crimes exists already.

Aren't they crunchy? / original image copyright of Nabisco.

Are Earthquakes Crimes?

Some years ago, I wrote a piece about crime prediction software that can point out crime hot spots on a map. It helps US and UK officers to be literally in the right spot at the right time. BEFORE a crime happens. The piece‘s title was „The Crime Prophets“. Since then, quite a few things have happened. The media have often compared the software to Steven Spielberg‘s sci-fi film Minority Report (careful, 11-year-delayed spoiler!). The chief scientist at that time, mathematician George Mohler of the University of Santa Clara, is now the CEO of a spinoff named PredPol (short for Predictive Policing).

However, that comparison is wrong in many ways.

PredPol does a good job at predicting the likelihood of burglaries, and it will be extended to predict also other crime types in the future. However, PredPol does not predict murders. Which is what Minority Report is about, right? Predicting murders. Moreover, the two approaches could not be more different: while Minority Report relies on three psychics (so-called precogs), Mohler‘s algorithm focuses on past burglaries and robberies‘ data (which is fed to the system by both the officers and the affected residents). PredPol then takes a model that derived from earthquake prediction models and calculates the burglary "aftershocks": crimes are modeled as clusters of points in space and time. Earthquake aftershocks tend to appear in the space-time „neighborhood“ of the original quake. The same holds for burglaries. Is Mohler‘s modeling approach applicable to murders, too?

I talked to Mohler, and he told me his model would never work for predicting mass shootings, since burglaries and killing sprees are very different in nature. The probability of a murder to happen in the "neighborhood" of a previous murder is not the same as for a burglary. In fact, mass murders are extremely rare cases of homicides. Anyway, Mohler is currently writing a paper on predicting gun crime, a to-be-implemented feature for (probably) the end of 2014. Sounds like this could be a starting point to predicting murders and potentially mass shootings.

The boxes show where the next burglaries most likely occur. / copyright: PredPol, Inc.

Now, this could be the point where I could throw in a couple of statistics. Show some numbers, like how many mass shootings have happened in the US and point out how grim those stats are. Which I am not going to do, and there is a reason for that:

It all depends on the definition of what a mass shooting is. How many victims have to be killed in order to make a „proper“ mass shooting? Four (the FBI‘s definition)? Twelve? As Paul Campos, professor of law at the University of Colorado points out in his piece for TIME magazine, trends depend on how this definition is made. Moreover, Campos seems not THAT enthusiastic about predicting crimes. He says:

„Criminology is very far from an exact science [...]“ - Paul Campos, University of Colorado

That is, there are still unknowns to be dealt with. Some researchers, however, have already begun dealing with these unknowns.

Studying Social Patterns

Adam Lankford, for example, is a criminal justice professor at the University of Alabama. He has researched the behavior of mass murderers and thinks analyzing numbers can actually predict some behaviors, at least up to a certain extent. He says, that by paying attention to the right data (for example the amount of victims, weapons used and attack location), officers could assess better what to expect at a crime scene - which would be some kind of short-term prediction. It wouldn‘t tell them when and where the next attack would happen. But it could help them to take the right decisions when they arrive at the crime scene.

In his piece for WIRED, Lankford writes that during the Columbine massacre the first police officers that arrived at the crime scene focused on securing the school’s perimeter, because they thought the attackers would still be alive. As a matter of fact, both of them were already dead at the time these officers arrived. And it gets worse: during this time, injured victims bled to death. Had the officers known there was a high chance the shooters had already committed suicide, would they have set their priorities differently? I think so.

Lankford conducted a study where he analyzed 81 mass shooting incidents between 1990 and 2010. He found patterns among their social behavior and says:

„Mass shooters often are struggling with some combination of mental health problems, family conflicts, work or school difficulties and social marginalization. They are almost always suicidal or indifferent to their own survival. They often have expressed complaints to those around them about feeling like victims themselves of persecution, oppression, or bullying.“ - Adam Lankford, University of Alabama

Moreover, he also investigated the likelihood of a mass shooter committing suicide (or, at least attempting to). He found that the likelihood of a mass shooter killing himself is increased by the following factors:

  • For each additional victim killed: +16%
  • For each additional weapon brought to the attack scene: +76%
  • Shooting in a public place? +419% (no typo!)

The data for this study came from a 2010 NYPD police report of 179 NYC shootings where the identity of the shooter is known. Note: in 41% of the cases, attackers and victims had a professional relation.

Furthermore, the criminal justice professor thinks that controlling the legal purchase of guns in local stores or through the Internet might help to prevent mass shootings up to some degree. Given the fact that most mass shooters are socially awkward and therefore unable to settle face-to-face black market deals.

The raw numbers support Lankford‘s idea. The magazine Mother Jones has collected a data set on mass shootings between 1982 and 2012 and analyzed it here. Their findings: in 49 out of 62 cases, the weapons were obtained legally. That‘s almost 80%.

Based on that data, The Atlantic Wire‘s Philip Bump attempted to construct an actual prediction of when and where the next mass shootings will occur (while knowing this is not likely to happen in reality). This is what Bump found:

The next mass shooting will happen in Spokane, Washington on February 12, 2014. The attacker will be a 38 year-old white man with mental health issues. There will be 7 people murdered and another 6 injured. The gun will have been bought legally in that same state.

Of course, this will never happen. Probably. Unless someone purposely tries to prove Bump wrong.

To sum it up: There is a tendency of suicide among mass shooters that can be predicted (no matter if it’s a “real” suicide attempt or a suicide by cop). Moreover, precursors exist that are more than mere hints. Analyzing these signs can be used for predicting certain properties, but not a full mass shooting.

Will We Find Murderers In The Forest?

There is a more specific attempt to predict future murders, developed at the University of Pennsylvania by statistician and psychologist Richard Berk. Berk developed an algorithm that can predict the likelihood of a prisoner on parole committing a murder or being murdered. Berk‘s algorithm tries to tackle the biasedness of parameter selection and prioritization in a different way: the algorithm, rather than humans, determines hitherto unknown relationships in the data. The results help to plan for appropriate supervision measures. Or, as Berk puts it: „High-risk folks obviously get tighter supervision“. Currently, Berk‘s algorithm is being used in Philadelphia and Baltimore.

Berk uses a machine learning method called "random forests".

Here is how it works: The algorithm takes predictors (such as the number of firearm offenses, the numbers of days spent in the county prison, etc.) and forms a multitude of decision trees. Each tree is constructed from a random sample of data, and each of the branches is created choosing random predictors. What the trees do is assign each case to a class (will this case be a prospective murderer?). In the case of Philadelphia, the three classes are:

  • High Risk: offender predicted to commit at least one serious crime (murder, robbery, sexual crime)
  • Moderate Risk: offender predicted to commit only non-serious crimes
  • Low Risk: offender not predicted to commit any new crimes during a two-year period

By the way, decision trees are also one possible way of displaying algorithms, since they can be visualized like flow-charts.

For the assessment of Philadelphia’s cases, a total of 53 different predictors were used to classify individuals on parole. Errors remain a problem, just like with any other type of prediction. That is, false positives and false negatives. Geoffrey Barnes and Jordan Hyatt of the University of Pennsylvania have shown in a report that for forecasts of high-risk offenders, the false positives (i.e. offenders on parole falsely predicted to kill somebody) amount to almost 10%. Forecasting low-risk offenders, the researchers encountered about 4% of the predictions to be false negatives. For this application, the false negatives have a truly nasty effect: it would result in offenders on parole to be put under loose supervision, while in reality there is a high probability they will commit a serious crime.

In Minority Report, Tom Cruise alias John Anderton's case was a false positive (after all, he didn’t kill Crowe, unlike predicted). Badly predicted and wrongly accused of future murder. But who can blame the precogs? They didn't have any numbers to crunch.

A falsely predicted murder that in reality never happened - a.k.a. a false positive. / copyright: 20th Century Fox.

Dragon Slayers Versus Mass Shooters?

Lankford calls mass shootings “extreme aberrations”, "outliers". Which reminded me of research I had read about before: Didier Sornette of the ETH Zürich conducts research on extreme events like stock market collapses and how to avoid them. He calls these extreme events “dragon kings”. They are extreme outliers, which would be compatible with the definition Lankford gave to mass shootings. Sornette thinks there are precursors and signs that return periodically and build up slowly – until an extreme event occurs. Just like water heating up slowly until it reaches its boiling point. At that moment, it transforms into vapor. An extreme event, if you will. By measuring and analyzing the precursors, these dragon kings can be predicted.

Sornette applied his theory to model the tank pressure of the space rocket Ariane 5 (which exploded in 1996). The precursors analyzed were acoustic emissions that came from stressed rocket parts. This same modeling works for biology and medicine as well. For example, Sornette applied it to predict parturitions, where pre-birth contractions can be used as precursors. Moreover, he has used them to predict the success of movies, landslides and glacier collapses. You can watch his inspiring TEDGlobal talk here:

When I asked him whether his model could be applied to predict mass shootings, Sornette said no, but added:

“But we should certainly be able to identify and diagnose probabilistically the growth of the facilitation factors and of the social climate that catalyze the emergence of mass shooting, probably down to the time scale of days.” - Didier Sornette, ETH Zürich

Sounds promising.

As Lankford correctly suggests, crunching the numbers might provide clues to at least partially predicting mass shooters’ next steps. We are nowhere near a one-stop solution for predicting a single event with all associated details. Crunching numbers works fine as long as you have numbers. But many mass shooters have no criminal record. They just snap out of the blue. Seemingly. If we tried to analyze facilitating factors ahead of mass shootings, we would need to analyze data such as medical records. This could generate a whole new debate on data privacy and security. Especially when considering that the authorities often use a false security tradeoff to break all sorts of laws: "if you want to be safe from terrorists, we need to collect all your data" or some such thing.

Think about it: If we wanted to constantly monitor all the people, they would have to agree to undergo regular mental screenings (EEGs, fMRIs, you name it) as well as give away additional privacy-related data. Have you just gone through a divorce? Do you live in an unstable home? Have you gone bankrupt recently? These might all be factors that would need to be assessed, since they could affect your mental health.

Maybe we should ditch non-measurable and unproven speculations like „he loved horror movies“, or „he played (insert a random computer game here) all day long“ – “so computer games and horror movies must be bad”. There are no studies proving correlation, let alone causality. We need to focus on facts and data and recognizing patterns within these facts.

For me, also gun registrations count towards these measurable signs. Someone without a gun cannot become a mass shooter. And while it is certainly true that there are other ways of obtaining guns, these ways are not always viable for future mass murderers.

The pattern that I can recognize from these research projects is that we should pay close attention to early signs, or precursors, and especially to mental health issues. This is a typical big data challenge: selecting the right data and extracting meaningful, hidden information from it.

As long as Lankford and Sornette are optimistic about the future of at least predicting facilitating factors of mass shootings, I am too.

What’s your take on this? Would you give away private data and undergo regular mental screenings if it benefited society?

I’d be more than happy to discuss this with you on Twitter @martinangler!


“Self-Exciting Point Process Modeling of Crime”, Journal of the American Statistical Association, Vol. 106, No. 493. (January 2011), pp. 100-108 by G. O. Mohler, M. B. Short, P. J. Brantingham, F. P. Schoenberg, G. E. Tita,

“Statistical Procedures for Forecasting Criminal Behavior: A Comparative Assessment”, R Berk, J Bleich.

"Predictability and Suppression of Extreme Events in a Chaotic System," Hugo L.D. de S. Cavalcante, Marcos Oriá, Didier Sornette, Edwart Ott, Daniel J. Gauthier. Physical Review Letters, Oct. 21, 2013.

“How we can predict the next financial crisis”. Didier Sornette, TEDGlobal Edinburgh, 2013.

3 Responses to “Can We Predict Mass Shootings?”

  1. Alec Reply | Permalink

    84,000,000+ million legal gun owners killed no one today.

  2. cheryl Reply | Permalink

    well it's not just the presence of mental illness or a history of prior criminal activity which predicts certain types of crime, it's also dependent upon... personal beliefs. A man who thinks women are autonomous beings who are entitled to say no to the offer of sex, normally doesn't rape; while a man with an agressive personality who views women as masturbatory objects deliberating thwarting his satisfaction, would. (I learned a long time ago to look for those signs as a way for me to predict who I can be safe around and who is more likely to cause me problems when alone with them.)

    In the same way, someone who thinks violence is the way to solve certain kinds of frustrating problems is much more likely to use violence than someone who doesn't. I must admit, I'm all for researching how to detect psychopaths and narcissists at an early age -- and then preventing them from obtaining positions of authority or influence over others.

    So to answer your question, yes I'm okay with giving up certain kinds of information about myself -- let's just make sure it's the right kind of useful information. Oh and also, I can see how a program designed to ferret out psyopaths and narcissists might have to operate in secret: firstly, those harmful personality types would learn how to fake the signs of a normal person during testing, and secondly they would campagin heavily against such a test since they would be trying to protect their right to abuse others without detection. It's easier to spot them when they don't know you're looking for them.

    Interesting article, thanks!

    • Martin W. Angler Reply | Permalink

      Hi cheryl,

      Thanks for your comment! It's an interesting thought that people who know they are being monitored could try to "fake the signs" and "campaign heavily against such a test". I completely agree with that. I just hope it wouldn't be too easy to fake fMRIs and EEGs. Regular mandatory mental screenings sound pretty Orwellian to me, though.

      Who knows, maybe in the future, as a consequence, there will be a whole new industry selling "how-to-appear-mentally-healthy" products?


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