The Orlando Massacre And A Statistician’s View Of Gun Control





The horror of the carnage caused by a homophobic-terrorist in an Orlando night club has again stimulated the conversation for more laws to control gun violence in America.

Beyond the rational ideas of prohibiting gun purchases of a person on either the “no fly” or terror watch list or extending background checks on all gun show purchases, most critics of the status quo want a prohibition on the purchase of an AR-15 style assault rifle.

This rifle, made under several brands, is a near replica of the M-16 that has been used by the U.S. Military since the Vietnam War. It is a light and accurate high velocity weapon that can inflict significant damage even at 400 meters. The military version, however, has a switch that allows the shooter to change its operation from semi-automatic to full automatic. The civilian version is only available in a semi-automatic model with usually a magazine capacity of 20 – 30 rounds.

The use of this weapon in a crowded night club, even in semi-automatic mode would inflict incredible damage as demonstrated by the number of deaths and wounded patrons of the Pulse nightclub. That only 49 patrons were murdered during this three-hour assault is itself surprising.

The question for me, however, is whether the use of this devastating weapon is common in mass killings and, therefore, would banning the sale of it make a significant difference in the deaths of innocent people?

DISCLAIMER: Before anyone begins to wonder how I will treat this important subject, you should know that I personally have never owned a gun and never been a member of the NRA (or the Communist Party for that matter). However, I have used the M-16 assault rifle when in the service and even won a medal for marksmanship while on active duty.

I’ll start with some definitions since different media outlets use dissimilar criteria, often to prove their own point of view. A mass killing was defined by Congress in 2013 as the murder of three or more individuals (not including the shooter) during a single episode in a public place. Some experts would prefer (including the FBI) four or more but here I’ll use the legal definition.

The FBI also has a broader approach with the “active shooter” definition which they define as a situation in which a shooting incident is in progress and that some aspect of the crime affects the necessary protocols used in responding to it and how law enforcement reacts at the scene of the incident. In the Pulse shooting, these active shooter protocols were applied which may have delayed law enforcement’s use of extreme force for some hours.

Although mass shootings come under this protocol, most active shooter incidents end with far fewer or even no deaths and injuries than what is currently classified as a mass shooting. An example would be a husband whose wife told him she wanted a divorce and he reacted by shooting her and threatened to kill all their kids but a hostage negotiator talks him into surrendering.

In 2013, the FBI published a report detailing all active shooting incidents that occurred between 2000 and 2013 (“A Study of Active Shooter Incidents in the United States Between 2000 and 2013”). During this period 160 active shooter incidents occurred with a total of 1,043 casualties.

This report details each incident including the number killed, the age of each shooter and type of weapon or weapons used in these occurrences. Unfortunately, the FBI does not differentiate between a “rifle” and an assault rifle. (Why this is the case, I have no idea.)

By using media accounts of each mass murder incident, however, I have been able to identify which incidents where the shooter used an AR-15 type assault weapon and have extended the data through 2015. During this period, some 440 people were murdered in 72 separate occurrences. Figure 1 shows the number of people killed by weapon type.

Figure One -- Kane Piece

Most of the mass killings occurred when the shooter was using a handgun or handguns (almost all were semi-automatic), followed by AR-15 type assault weapons. Some 59% all deaths were caused by a handgun alone, while 22% occurred by a shooter with an assault rifle.

In the case of assault weapon incidents, the shooter was many times carrying a handgun or other type of weapon as well, but for my purposes here, we’ll assume that all the victims were killed by the assault rifle.

In addition, during this same period some 43 of mass killing incidents occurred when the shooter used only a handgun, nearly 60% of all mass shooting events. Only 11 events occurred when an assault weapon was used or 15% of all mass shootings incidents during this 14-year period. Consequently, the probability that a mass shooting will occur with the shooter using an assault weapon is only 15%.

Interestingly, the use of assault weapons in mass shooting incidents is preferred by younger men. All but one of the assault weapon shooters were 33 years or younger, with an average age 25. The oldest shooters used both a handgun and rifle, with an average age of 51 years. I guess there is a generational gun gap.

Although more deaths occurred by handguns during this period the average number of casualties per incident was greater among the assault weapon cases, as demonstrated by Figure 2.

Figure Two -- Kane Piece

The average number of deaths in an assault weapon mass shooting was 9 (rounded) while handguns killed on average of 6 innocent people per incident. To make sure that these differences are not random, I performed analysis of the variance (ANOVA) on this data and the differences were statistically significant at .02 level. In other words, the fire power of the AR-15 weapon was (I hate to use this term) more efficient.

Right now seven states and the District of Columbia ban the purchase or possession of assault type weapons, including California where 14 innocent people were murdered by an assault weapon in San Bernardino. The Supreme Court recently left in place a lower court ruling that states have the right to ban these weapons and high capacity magazines. But if the Congress would approve a ban on these weapons would it really stop the mayhem they cause?

If all of these mass murders during the 2001 through 2015 occurred without the use of an assault rifle, we would expect, based past data that an average of three individuals would have survived per incident, if the shooter was using a semi-automatic handgun instead.

During this period, a total of 11 mass killing events involved the use of an assault weapon. Using the average three lives saved by banning this weapon, we would expect, on average, an additional 33 people that would still be alive today. (When controlling for the age of the shooter this estimate drops to 31 people.)

Even though the probability of a mass shooting occurring with an assault weapon is low, but when we are talking about the loss of human life, 33 additional survivors are not insignificant. I know some of you are thinking that even with a ban, criminals will still get their hands on assault weapons and, certainly, that is true.

But all of this is moot, because the Congress is unlikely to prohibit the purchase of any firearm type. In the past five years, 100-gun control bills have been proposed and either never made it to the floor or failed. The exclusion of people from purchasing guns on either the “no fly” list or terror watch list did not pass even in the wake of the Orlando mass killings. I don’t know about you, but I would rather be able to fly than buy a gun.


21 Responses to “The Orlando Massacre And A Statistician’s View Of Gun Control”

  1. Islam's Law says:

    Jimbo, you loose some of your credibility in your first sentence by not identifying Omar as an Islamic terrorist. He certainly had no fear of homosexuals by his actions. That being said, he could have done the same damage with a rifle or a handgun. Glock has a great magazine that holds 33 rounds and fits almost all of their handguns and is much more concealable than an AR or Sig, the gun used in Orlando.

    What is not mentioned is the thing that most of these events have in common, a “gun free” zone.

    The bar in Orlando, Fort Hood, Columbine, Sandy Hook, and most of the other locations all were gun free zones so that not law abiding person was their to stop the carnage. That is why I try to avoid gun free zones.

    Any responsible person needs to consider buying an AR or other weapons to protect your life and property. And train your children, when the are of age to do the same. The notion to restrict capacity is silly. It is like asking a car owner to restrict their fuel tank to 5 gallons of gas because you are 20 times more likely to be killed by a car than a gun.

    The police are being put under pressure to no longer protect us to point where you are not being a good parent if you refuse to teach your children to protect themselves.

    Our most important civil right is the second amendment, it protects all of our other rights.

    And Jim, thank you for your service.

  2. Lee F Chudso says:

    The irratiinal illogical obession of people to use the Second Amendment to justify the lunacy of mostly unregulated sale of military fire arms inappropriate for target shooting (I have two NRA shooting medals) or hunting continues to ENDANGER THE PUBLIC

  3. Real Deal says:

    Intelligent gun control in a nation as committed to gun rights as ours, aiming to reduce murders including mass killings, requires us to make choices most likely to result in the least harm done to innocent others.

    It is not clear how many of the 259 hand gun deaths you report are suicides versus murders. I do know that your chances of surviving a handgun wound is better than surviving an assault fire bullet designed to tumble upon impact and tear the insides out of a victim.

    Many legitimately use hand guns for protection. It is the most commonly owned type of firearm for that or any purpose. So while 259 looks like a large number, as a percentage of total handguns owned, hand guns likely do the least harm to others. On the other hand, if we take the much smaller number of assault weapons owned and compare it to the number of deaths these generate, there is likely a striking conclusion not reported in this study.

    Nobody needs an assault rifle for personal protection. Hand guns are better for this purpose whereas the purpose of an assault rifle is to kill many people at once. So if we want to reduce gun deaths while preserving our right to own guns, getting rid of the assault weapons makes a lot of sense. If the suggestion is being attempted that hand guns are less safe than assault weapons, this analysis fails to achieve the objective.

  4. SAM FIELDS says:

    I could not disagree with Jim more in his conclusion that getting rid of assault rifles will diminish the number of mass shootings. It would not reduce that number by even one.

    I can’t imagine that any of the sick bastards that have committed these heinous acts would have been stymied if they were denied access to an AR 15 or one of its clones.

    To be sure that weapon has an accuracy range of 400 meters. How often do you read about a mass killing from that distance? The only one I can think of is Charles Whitman in 1966 who was shooting from a tower at The University of Texas with a Remington 700 that held 4-5 bullets.

    The overwhelming number of mass killings are in close quarters making the range difference between a handgun and an AR 15 irrelevant.

    The only argument that one might have made is the advantage of higher ammunition capacity with a rifle. But even that is not what one might imagine. For at least the last twenty years large clips for handguns have offered 30+ rounds. When you exhaust that clip it can be ejected and replaced within 3-4 seconds all the while firing the other handgun.

    While I was researching this comment I came across the Beta C-Mag which has a drum capacity of 100 rounds and will fit nicely with certain handguns made by Glock!

    The acquisition and use of military type guns has little to do with their efficacy in mass killing and everything to do with: compensating sexual insecurity/confused sexual identity/ poor performance by Mr. Winky, etc…and reading too many Sergeant Rock comic books.

  5. Chaz Stevens says:

    >> Any responsible person needs to consider buying an AR or other weapons to protect your life and property.

    Nice job. Hand my that BFG-9000 — they’re trying to jack my ottoman!

    You’re 22x more like to experience a gun related incident, by the way…

  6. Stormwatch says:

    The problem is two-fold.
    First thing we need to do is change the culture of glorifying guns. It started back in the 30s with all the mobster movies and the cute nicknames given to gangsters and hoodlums. It got so bad early on that J. Edgar Hoover asked Hollywood if they’d start making movies about the good guys. Nowadays, most network dramas are cop shows where there’s a lot of gunfire. Turn on a music video or go to the movies and its all shoot em up stuff. So we need to stop glorifying gun violence.
    The second problem we have is that America is a nation that never sees the light until we’re all the way at the end of the tunnel. It doesnt matter if it’s war, disease, infrastructure, social issues or guns. We’re not far enough down the tunnel yet. Anyone who needs an AR-15 and a few magazine rounds is probably someone I dont wanna live near or hang out with. Not until a politicains wife and or kid get taken out by some Islam hijacking nut job or other crazy person using an AR-15 or AK-47 will anything change. Then and only then will they see the light.


    Glorifying gangsters started long before the 1930s. What about Jesse James, Butch Cassidy and other assorted figures from the old West?

    Interestingly enough, one of the first laws passed by towns springing up in the West was to restrict guns to limit the possibility of shootouts and murders.

  7. Stormwatch says:

    You’re correct. It did start long before the 30s. Once radio and movies came along, it all went nationwide. Yes, many sheriffs made it a point to make folks check their guns at the saloon door. Some didnt even allow them in town.

  8. Sam The Sham says:

    I sure wish our fore-fathers didn’t have any of those nasty and scary guns they had back in 1776. We wouldn’t be in the predicament we are in today otherwise. There is just too much of that freedom thing going on around here.

  9. Mike Marchetti says:

    For those who throw the word freedom around when it comes to gun control need to get a grip on reality. Would we we be less free, certainly. Just as we are less free to walk on a construction site without a hard hat, or get in our car without putting on a seat belt or even better get in our car drunk and drive. Think about that for a minute we don’t have the freedom to do what we want in the privacy of our own car. What were lawmakers thinking?

    We don’t have that freedom because we are not a nation of one we are a nation of many. The freedoms we have as individuals need to be managed for the safety of those who live, work and play among us. Our lawmakers had the courage to take away our freedoms in our own cars yet wither at the thought of gun control. That is pathetic by any measurement. Do people still get killed or injured by drunk drivers, of course. The argument that if you pass a law all will be made right has never been a standard for improving the safety and quality of life for the many.

    In the end our lawmakers are trading some lives for votes, there is no other viable explanation or argument for their lack of action. The president is correct not making a decision on gun control is making a decision. A decision that puts more lives in danger, that is just a fact.

  10. Sam The Sham says:

    those who would give up essential liberty to purchase a little temporary safety deserve neither liberty nor safety.

  11. Mike Marchetti says:

    Well not sure what temporary safety means but it sounds a lot like carelessness. So I guess we are being to careful having to take our shoes off and go through a security check point to board a plane. Or be searched entering a football game. I wonder if any lives have been saved doing that. Oh wait we know they have. But then we already know the world revolves around the entitled who think they can afford to be careless to suit themselves.

  12. Lock and Load says:

    Mike, it is a fact, the more we restrict law abiding citizens from owning guns, the more dangerous it is. You miss the whole point and you somehow think that less guns make us safer. That has been proven wrong over and over.

    In your world you would have us dialing 911 and cowering waiting for help.

    Help that comes too late, over and over again. That is something we should have learned from Orlando and Sandy hook.

    I will lock and load and protect my family thank you. And that is a freedom you can’t take away without amending the constitution.

  13. Sober As a Judge says:

    #10 That qoute from Benjamin Franklin is constantly used out of context. It arose during the French and Indian war. Franklin was then in the Pennsylvania Assembly, and the legislature needed to tax land to provide aid to the war effort. The Governor, who owed his job to land owners, vetoed the bill asking the Assembly to instead fund their needs in some other way.

    The “essential liberty” Franklin was referring to was the loss implied to the jurisdiction of the legislature to tax. He was not referring to a civil right. And the security he was referring to was the state’s security against invasion, not individual security.

    The fact of the matter is we give up some of our freedoms to achieve a state of “liberty” which is a subset of freedom, in which we prize public order above some freedoms that would do public harm for the specific purpose of being able to live together in a state where we can enjoy our remaining freedoms. Only liberty does this in a free society.

  14. Dear Mr. Marchetti says:

    Driving is a privilege, controlled by Statute. It is not a Constitutional Right.
    Wearing a hard hat on a construction site private property is NOT a Constitutional right.
    Last time I checked attendance at a football game is not a constitutional right, although maybe it should be..
    We do have background checks, we do not allow felons to have weapons or those committing domestic violence. Also you cannot carry into a place like Pulse, which is unfortunate because not one person in that club was able to defend themself from the terrorist.
    Are you really willing to start changing and amending the Constitution. The First Amendment? No longer able to voice your opinion? We know you would like to amend the Second. How about the Fourth? Fifth?…


    You are so right. If we start changing our existing rights in the Constitution, we open up a can of worms.

  15. Count LF Chodkiewicz Chudzikiewicz says:

    Mr Marchetti’s comments are correct m Counsellor ignores 200 years of experience where societies that regulate arms have dramatically lower murder rates and yes depriving people of rapid firing guns does save lives without trashing the Second Amendment.
    Sadly the movement of alien non Europeans into urban Western areas has created mass murders which have been caused by both bombs and assault rapid firing guns.
    Every group in our country advocating gun anarchy is right wing old limited educated Whites with onky exceptions in the Far West where looser gun laws could be appropriate. The mindless statements about Chicago n Paris having tough laws but having mass murders or high murder rates ignores the fact Belgium next to France n the States around Illinois are awash with barely regulated guns.
    Anyone who travels between Bruxelles n Paris by train or car knows guns are freely purchased in Belgium and brought into the French cities.

    New Jersey had good gun laws in my youth but crimminals would get guns in Georgia n the Carolinas making it difficult to end gun violence in Newark Camden Elisabeth later Plainfield n Passaic or Paterson n Atlantic City.

    The US Constitution is not a suicide pact despite the 2nd Amendment lunatic fringe to make it so.

  16. Mike Marchetti says:

    @ #12/14 I do not and never found it necessary to own a gun. That is my right and choice as it is your right and choice to own and or carry a gun. While you are correct there are no formal statistics that less guns is more safe there certainly are no statistics that more guns make us more safe.

    I did carry and qualify as an expert with an M-16 while in the service as a Vietnam veteran. From my own personal experience it can be fun shooting at and killing pop up targets. I can also assure you that pointing and shooting at live targets is no fun at all and for some quite traumatic.

    The point I was trying to make without getting into wordsmithing every term is that absolute freedom when living in a society does not exist. I do not advocate taking away all guns. I feel that people often get defensive over the term gun control and feel it means taking away the right to have or carry any and all guns. That is not what I consider gun control.

    Our fore fathers set us on a path with certain rights and laws based on the world as they knew it then. Certainly as a society we have evolved. Evolved enough to allow women to become equal enough in the eyes of our laws to vote and no longer permit one human being to own another. I would like to think that as a society we are able to analyze the current situation and react appropriately. Just as our lawmakers did with our driving privileges.

    As a whole does our society really need assault and other heavy military style weapons circulating almost without regard to the qualifications of the individual to handle those weapons either mentally or physically? I happen to think not. I do believe the matter should not be decided by special interests who have a stake in the game financially and politically. I believe the matter needs serious analysis and then rigorous debate. I don’t believe maintaining the status quo is the right or prudent path and don’t believe for one minute our fore fathers would either. You should know that if our rights to bear arms were to come into jeopardy in its entirety I would gladly pick up a rifle again and defend our rights and beliefs. Until then if locked and loaded really makes you feel safer that is your prerogative, I feel fine without.

  17. Mr. marchetti says:

    Thank you for your service.
    We will agree to disagree and I will stand by the constitution and continue to defend.

  18. Read our forefathers lips says:


    The whole point of the second amendment is not about hunting or self defense, though self defense is important. The second amendment is about protecting us from our government and keeping our government in check. That is why those OD us who love freedom will never give up our AR-15s and other weapons.

    Oh, and Mike, thank you for your service.

  19. Count LF Chodkiewicz Chudzikiewicz says:

    No Constitutiional Right is exempt from logical regulation so we forbid polygamy and AND SHOUKD FORBID AK 15s And multiple clips of ammunition

  20. Mike Marchetti says:

    @ #18

    Your very welcome. I agree with you that the second amendment was as much about providing citizens the ability to defend themselves from potential government tyranny as any other logic. But again that was in a time when there was no difference in weaponry from what the government militia carried and what an individual citizen could own.

    God forbid if our society and government (military) were to fall into such a state as to require the citizenry to defend themselves against our military today. Pretty sure that AR-15 is no match for B-1 bombers, F-16 fighter jets, M-1 tanks, and laser guided missiles (let’s just leave nukes out all together).

    I don’t believe for one minute that the current rush to arm ourselves has anything to do with protecting us from our government. If that is the thought process then one should rethink that strategy. I do believe it has everything to do with protecting yourself from other citizens. In today’s world arming ourselves to the teeth with hand guns and automatic weapons only makes sense if we were to turn on each other absent military intervention. Again, God forbid.

    I was watching the Blue Angels and Thurderbirds workout prior to and during the recent air show. I told my son as they went screaming by you really should be proud of those guys and be very thankful that they are on our side.

  21. Chaz Stevens says:

    There are 300 million fucking weapons in the US.

    There are 90 million cats and dogs…

    300 million weapons … do you feel safe?