Terrorism Math

blackboard-mathBy any reasonable measure, we’re far too apprehensive about terrorism and expend far too many resources and sacrifice far too much liberty defending against its risks.  But there are smart ways and dumb ways to make that point.

Nate Silver, responding a few days ago to one of my posts, demonstrates the former:

Over the past decade, according to BTS, there have been 99,320,309 commercial airline departures that either originated or landed within the United States. Dividing by six, we get one terrorist incident per 16,553,385 departures.

These departures flew a collective 69,415,786,000 miles. That means there has been one terrorist incident per 11,569,297,667 mles flown. This distance is equivalent to 1,459,664 trips around the diameter of the Earth, 24,218 round trips to the Moon, or two round trips to Neptune.

Assuming an average airborne speed of 425 miles per hour, these airplanes were aloft for a total of 163,331,261 hours. Therefore, there has been one terrorist incident per 27,221,877 hours airborne. This can also be expressed as one incident per 1,134,245 days airborne, or one incident per 3,105 years airborne.

There were a total of 674 passengers, not counting crew or the terrorists themselves, on the flights on which these incidents occurred. By contrast, there have been 7,015,630,000 passenger enplanements over the past decade. Therefore, the odds of being on given departure which is the subject of a terrorist incident have been 1 in 10,408,947 over the past decade. By contrast, the odds of being struck by lightning in a given year are about 1 in 500,000. This means that you could board 20 flights per year and still be less likely to be the subject of an attempted terrorist attack than to be struck by lightning.

Bill Maher, chatting with Andrew Sullivan, demonstrates both, making the broader point well but then tacking on a silly example:

For those not inclined to view the video, one of Sully’s readers helpfully summarizes the latter:

In 2008 there were 34,017 deaths (and nearly 100,000 major injuries) related to automobile accidents in the United States.  Terrorists would have to blow up 113 Boeing 777-200s each year in order to kill that many people!  That is, they’d have to blow up all but six of the 777-200’s (which hold 301 people in a 3-tier international setup) currently owned by American Airlines, United Airlines and Continental Airlines (together they own 119 777-200s) and would have to do so every single year, which is probably faster than they can be built.

And yet there is hardly any talk of defending the American people from their Buick!

Yes, Americans willingly accept the risks that come with driving in order to accrue the substantial benefits.  But we drive far, far more often than we fly.  That’s why commercial airplane crashes always make the news whereas automobile accidents tend to make it on our radar screens only when they involve professional golfers being chased by supermodels wielding golf clubs.

Furthermore, it’s not entirely unreasonable to react differently to random acts of fate than willful acts of malice.  People willingly build houses near the ocean even though the probability of eventual damage from a hurricane is exceedingly high.  But they nonetheless lock their doors, buy alarm systems, and fund police forces to minimize the risk of burglary.

Still, as Matt Yglesias observed yesterday,

People understand that flying is way safer than driving, right? Making it more of a pain in the name of “safety” will kill people.

So, while factoring in the public’s justly having more concern about human-caused dangers than random ones is reasonable, there must be limits.

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James Joyner
About James Joyner
James Joyner is Professor and Department Head of Security Studies at Marine Corps University's Command and Staff College and a nonresident senior fellow at the Scowcroft Center for Strategy and Security at the Atlantic Council. He's a former Army officer and Desert Storm vet. Views expressed here are his own. Follow James on Twitter @DrJJoyner.

Comments

  1. yetanotherjohn says:

    Let’s see. There were 2350 deaths from the Japanese attack at Pearl Harbor out of a population of 133,402,471. So why did we bother going to war against the Japanese?

    What is not figured in is the number of deaths that would have occurred if we had done nothing. We know of attacks that were planned but thwarted. I would hope that even more attacks were thwarted that never reached the press.

    The argument on plane miles is a good one for why you should not stop flying (stopping because the hassle is to much is another issue). It is not a good one for why we should do nothing. The argument on traffic fatalities ignores that we get a positive good out of travel and no balancing good out of terrorist attacks. We chose to impose safety restrictions (e.g seat belts) to minimize the risk. Talking about going to war against objects (e.g. cars) shows a fundamental lack of understanding about what war is.

    We have 6 options. We can ignore the threat and suffer the losses, we can defend against the threat, we can change the motivation of the attackers, we can eliminate those who would attack us, we can disrupt the ability to attack us and/or we can fundamentally change the playing field (e.g. star trek transporters). We have done a little bit of all 6 and not as much as we could in all 6 areas. But at the end of the day, the only ones that will succeed in the long run are to change the motivation or eliminate the attackers. Which leaves changing the motivation. A westernized Iraq as an alternative to radical Islam, helping moderate Islam and hurting radical Islam and showing that we are the ‘strong horse’ are the best ways I can see for changing the motivation. In the mean time, we defend and disrupt as much as we can.

    As to the security precautions, they seem to be a series of post-horse leaving barn door closings. And the most effective has been the change in passenger attitudes.

  2. Dave Schuler says:

    You might want to check my post on this subject, James. Nate is using a tool that’s appropriate for determining the likelihood random or semi-random events to analyze what is, mathematically speaking, a game. That’s an inappropriate use of the tool and he certainly knows better than that.

  3. Drew says:

    This sort of “what, me worry” analysis fails on two points: 1) unintended accidents are one thing, being hunted for slaughter is another, 2) there may be a paradigm shift in terrorsit capabilities and tactics. That should be fully vetted.

    All the “don’t worry, its safe” statistics could have been made prior to 9/11. Then, they didn’t work…….

  4. PD Shaw says:

    I’ll second Dave’s post on the topic:

    I have no idea why somebody as smart and knowledgeable as Nate Silver is using simple probability, a tool handy for determining the likelihood of the occurrence of random events, in analyzing the likelihood of acts of terrorism onboard commercial airlines. It’s an activity about as suited to the task as doodling cars on the back of a napkin is to winning the Indianapolis 500.

    Terrorist attacks aren’t random and don’t behave according to the laws of simple probability. Mathematically speaking, they are games with players, strategies, costs, rewards, and multiple moves, each of which is dependent on previous moves.

    More at the link.

  5. anjin-san says:

    A westernized Iraq as an alternative to radical Islam,

    Guess you have still not learned the lesson we seem to have to learn over & over & over…

    We cannot simply remake other societies to suit our needs. We are dealing with a culture far more ancient than our own, one which we have a poor understanding of. It has a life and dynamic of its own, and a vast amount of historical inertia behind it. Crack some history books and see how much luck the Romans had trying to do a makeover on Parthia to suit their needs.

    It is true that a pro-American Iraq would benefit our interests. But I am thinking that starting a war that killed tens of thousands of perfectly innocent people in Iraq is probably a poor way to accomplish that goal. All we have done is move them closer to Iran.

  6. Wayne says:

    I have issues with some of the sleight of hand use of numbers. The number of flight hours is misleading. It takes one minute for an airplane to blow up. Saying “yeah but it was an eight hour flight so your chances are 1 in 480 of being blown up on that flight” or anything similar is B.S.

    The use of the parameters “airline departures that either originated or landed within the United States” is bull. Most attacks don’t fall in those parameters and if they do get attack will not actually land in the U.S. or at all. Most attacks are originated overseas and then get diverted.

    Re” This means that you could board 20 flights per year and still be less likely to be the subject of an “”attempted terrorist attack”” than to be struck by lightning”

    News flash, not all terrorist attacks are done on flights. The fact is most don’t, they just get a good deal of press.

    Then there is the information left out such as only 1 in 7 die from lightning strikes and being classifies as being struck by lightning doesn’t mean a direct hit. Electricity tends to travels around objects. Granted not all die from terrorist attacks either but a relevant point no less. Also 2/3 of lightning strikes are due to work or rec\sports activities.

    Comparing natural events to unnatural events is problematic in itself. A more fair comparison would be how many flights (in flight or not) in the world are attack to the total of such then compare it to then number of lightning strikes that hit someone compare to number of lightning strikes in the world with per capita and time frame figure in.

    To simply take the odd of being hit by lightning in year and compare it to being involved in terrorist attack on a plane is simply a faulty comparison.

    It is a “little” like Jack saying he slipped and fell 5 times in his lifetime while walking and was hurt. He also played Russian roulette twice and never got hurt. Therefore it is much safer to play Russian roulette then walking. Doesn’t past the smell test.

  7. Wayne says:

    That said I would be more worried about getting struck by lightning than being involve in terrorist attack “within” U.S. but believe we do need to spend money and effort to counter terrorist. Hopefully we can keep the vast majority of terrorism off our shores.

  8. sam says:

    Terrorist attacks aren’t random and don’t behave according to the laws of simple probability. Mathematically speaking, they are games with players, strategies, costs, rewards, and multiple moves, each of which is dependent on previous moves.

    OK, Dave, but then what? What are the odds of you, or me, or any particular person being on an airplane targeted by a terrorist? And even if Nate did go a bit overboard–or astray, if you want–I think it was in the service of a counter to an anticipated overreaction on the part of the TSA and Congresscriters. And, Drew, none of this, I repeat, none of this is in any way an argument for relaxing our guard or for not doing everything possible to thwart terrorist designs. It’s just that we ought not go around loosing our bowels over every terrorist attempt on us. Vigilance, yes. Termination with extreme prejudice, if called for, yes. Crapping our drawers, no.

  9. Andy says:

    OK, Dave, but then what? What are the odds of you, or me, or any particular person being on an airplane targeted by a terrorist?

    The point is that you can’t calculate the odds with any degree of accuracy. Six data points over a decade is not enough to be able to draw any conclusions – it’s like conducting a poll with only six people. And, using Nate’s math, there was a zero percent chance of a 9/11 before 9/11. In short Dave is exactly right that quantitative probability does not work for things like terrorism.

    I’d also point out that people are not completely utilitarian. What I mean is that people don’t view death from a car accident and death from a terrorist attack as equal outcomes.

  10. It’s just that we ought not go around loosing our bowels over every terrorist attempt on us. Vigilance, yes. Termination with extreme prejudice, if called for, yes. Crapping our drawers, no.

    Exactly. A guy burns his balls off on a plane and suddenly people — especially on the Right who are evidently a species prone to hysteria — start demanding we find someone to torture and freaking out because the POTUS didn’t rush to the nearest microphone to “reassure” them.

    These people would have been a barrel of fun in London during the Blitz or Northern Ireland during the troubles or Israel pretty much any time in the last 60 years.

  11. Gerry W. says:

    An accident is one thing and murder is another. And since my wife and I was on a similar flight a year and a half ago, means nothing unless it happened to you. And yes, we were in Rome, and flew to Amsterdam and then on to Detroit.

    There is lots our government can do. Every airport that has flights to the U.S. and even in the U.S. has to have the sniffer machines. We need better intelligence and the cooperation of intelligence as in this case the info never got to the TSA. And the TSA is the last line of defense. You also need profiling from people from troubled areas of the world. And that includes England as they have a population of muslims. And finally, it should be instructed that you greet your “neighbor” on the airplane. You greet the people in front of you, in back of you, and beside you.

  12. GreyWolf says:

    Good God!! If the federal still cannot fix the leveys in N. Orleans, how can we expect them to fight intl. terrorism? A fat govt. against a small, well organized group of radicals is a losing battle. The failure is upon the govt.

    Finally, someone just wrote a book about a small town in America who stands up to federal tyranny & ends up starting the 2nd American Revolution.

    Big govt. is a complete failure to any task so why do people think govt. can do anything. Anyway, it’s a good book for 2010 & what else is in store for us in 2010.
    http://www.booksbyoliver.

  13. JACK ARMY says:

    Guess you have still not learned the lesson we seem to have to learn over & over & over…

    We cannot simply remake other societies to suit our needs. We are dealing with a culture far more ancient than our own, one which we have a poor understanding of.

    I think that Japan and Germany are good examples of “societies remade to suit our needs.” Both had cultures much older than our own and now they are close allies.

    It seems naive to me to think that just because we don’t fully understand a culture means that we cannot possibly change it. I don’t think that fanatic Islamists truly understand our culture yet undoubtedly they’ve managed to change it.

  14. just me says:

    Dave Schuler is wise-I think his points are very good ones.

    In the end I think much of the TSA security measures are smoke and mirrors and often end up harrassing the average traveler more than they foil any plot to bring down a plane, but I don’t think the likelihood of weather we should have any security at all based on the probability of being on one of those planes makes any sense either.

  15. Dave Schuler says:

    OK, Dave, but then what? What are the odds of you, or me, or any particular person being on an airplane targeted by a terrorist?

    What are the odds of checkmate in chess? The question is gibberish.

    The questions that we should be asking are are we in a better or a worse position?

    If we resign or pass, we’ll be in a worse position. We must adapt what we do to what our opponents are doing, attempt to increase our opponents’ costs and reduce their rewards while reducing our own costs and maintaining or increasing our prospective rewards.

    I’m not defending the status quo. I’m merely saying that simple combinatorial probability is meaningless in evaluating our position. Terrorist attacks are not like trying to determine the likelihood of pulling a black token from an urn with so many black tokens and so many white ones in successive moves.

  16. Mr. Prosser says:

    Good post and pretty good discussion of the difference between probability and game theory. Game theory can be useful in intelligence and I hope our government is using it. Game theory and intelligence require removing emotion from the situations. Most individuals have been in or seen auto accidents and can adjust their fear, but the fear of falling out of the sky does tend to raise emotion. Of course the political reactions and TSA reactions to this specific incident are for the most part, silly. They remind me of Mel Brooks as Governor Lepetomaine meeting with his cronies in “Blazing Saddles” – “We’ve got to save our phony-baloney jobs, gentlemen!”

  17. anjin-san says:

    I think that Japan and Germany are good examples of “societies remade to suit our needs.”

    Well, if we were kids in a high school history class, that would be a pretty good answer.

    Lets look at WW2. How were we able to remake the societies of Germany & Japan? Simple. We dropped bombs on them until they became malleable. After enough destruction, after enough people had been incinerated or blown to bits, and enough human misery caused, they said “We will do anything, just stop bombing us”.

    Now keep in mind, Japan attacked us and Germany declared war on us without any hostile act on our part. That is certainly no the case with Iraq, a country we attacked based on a provocation that turned out to be, well, utter crap. “We know they have them and we know were they are”. In WW2, we clearly had the moral high ground. In this case, no.

    So if you want to say that we are an empire, and we will just use death and destruction as our means to an end when it suits us, why come out and say it.

    It seems naive to me to think that just because we don’t fully understand a culture means that we cannot possibly change it.

    That is true, but it is not responsive to my statement, and it is kind of lame too. Of course we can change other cultures. What I said was “change them to suit our needs”. You should study the law on unintended consequences. Like when we supported Bin Laden and his ilk against the Soviets. Did not work our exactly as we had planned.

  18. anjin-san says:

    If we resign or pass, we’ll be in a worse position. We must adapt what we do to what our opponents are doing, attempt to increase our opponents’ costs and reduce their rewards while reducing our own costs and maintaining or increasing our prospective rewards

    Well said.

  19. anjin-san says:

    Big govt. is a complete failure to any task so why do people think govt. can do anything.

    Guess you have not heard about our armed forces. Rumor is they are just about the best there is…

  20. PD Shaw says:

    Besides the irrelevance of the statistics, what bothers me about the analysis is it’s focus on the individuals that might be killed.

    The goal of terrorism is to attack the society, and I don’t believe American society is tolerant enough to handle a certain level of deaths attributed to Muslims. I don’t know what that level is, don’t want to find out, but it’s not in Nate’s calculations.

  21. sam says:

    Besides the irrelevance of the statistics, what bothers me about the analysis is it’s focus on the individuals that might be killed.

    Look, I think that you and Dave are arguing at cross-purposes with me. I didn’t take Nate’s stats as being offered as foundational to some policy, to some strategy. He offered them without editorial comment, and I took them to be, in a sense, rhetorical, as being offered to shape an attitude. Or rather, perhaps, to counter an attitude. That attitude being be best expressed by, “Jesus, they’re gonna get us and they’re damn near unstoppable. So let’s just scare the shit out of ourselves and ratchet up our security procedures to the nth degree and make travelling by air as miserable an experience as possible.”

  22. JACK ARMY says:

    Oy, excuse my lowly high-school education.

    Lets look at WW2. How were we able to remake the societies of Germany & Japan? Simple. We dropped bombs on them until they became malleable. After enough destruction, after enough people had been incinerated or blown to bits, and enough human misery caused, they said “We will do anything, just stop bombing us”.

    I was trying to point out the post WWII period in which Japan and Germany (and most of Europe for that matter) relied on the US to support their reconstruction. It was during THAT period that we were able to affect their cultures. I agree wholeheartedly that dropping bombs doesn’t change the culture, merely the will to continue fighting. It is after the fight that the opportunity to reshape culture is offered.

    I’m fully aware of the law of unintended consequences. As a veteran of 22 years, I’ve watched our foreign policy sway back and forth depending on the threat, or perceived threat, at that time. That is a political football, though, as what is politically (and often times militarily) expedient at the moment may not have positive or controllable effects in the future. But then, our current administration and Congress are more than willing to mortgage the future for political gain/control now. Will policies enacted now have unintended consequences in the future? Of course. Does that mean we don’t do anything for fear of the unintended? Of course not.

    Hopefully that wasn’t too lame for you. If it was, it was certainly an unintended consequence.

  23. Dave wrote:

    I’m not defending the status quo. I’m merely saying that simple combinatorial probability is meaningless in evaluating our position. Terrorist attacks are not like trying to determine the likelihood of pulling a black token from an urn with so many black tokens and so many white ones in successive moves.

    There are many factors, but ratio of bombers to good passengers (red to black tokens) certainly is one.

    It is in fact a little like the ratio of good gun owners to mall shooters, though it might take a few deep breaths for some of you to see it that way.

    And interestingly the limiting factor in both cases seems to be that among hundreds of millions of human beings, very few actually want to be plane bombers or mall shooters. Human nature is actually remarkably good (on the order of 100,000,000 to 1 or so)

    (Apparently the fantasy is that we can afford effective screening devices for every aircraft loading ramp in the US. Ludicrous.)

  24. tom p says:

    You might want to check my post on this subject, James. Nate is using a tool that’s appropriate for determining the likelihood random or semi-random events to analyze what is, mathematically speaking, a game. That’s an inappropriate use of the tool and he certainly knows better than that. DS

    Dave, with all due respect, you (and all the others here) are wrong. It IS a game. To pretend otherwise is to lose the game. This is exactly the right tool to use to figure our possible (probable) losses. The problem most people have is an inability to see the rules by which our opponents are playing the game.

    We have a tendency to see these things in terms of “life and death” (where life has a value of infinite possibility and death is the negation thereof) while our opponents see these things as “so what“? (where life is… a means to an end? beside the point?)

    Consider what has happened in Iraq in the last 8 yrs. Now imagine the same thing here. Not possible, is it?

    We are playing the same game… only by different rules. And make no mistake, to them it is a game, and they can not lose. Look at the mileage they have gotten out of a “failed” terrorist attack. Now imagine what they would have gotten out of a successful attack.

    It seems naive to me to think that just because we don’t fully understand a culture means that we cannot possibly change it. JA

    Jack, despite your addendum, your original positition still seems incredibly naive. Again, they don’t care if they live or die. That is their culture, not ours. And the Japanese didn’t either… until we proved we could eliminate their culture from the face of the earth. But we are not going to do that or even threaten to do that now. You know it. I know it. So do they.

    The questions that we should be asking are are we in a better or a worse position? DS

    Which is exactly the question Nate is asking.

    I’m merely saying that simple combinatorial probability is meaningless in evaluating our position. DS

    Must disagree Dave. It is not meaningless in our present situation. It is entirely appropriate. In order to gauge risk we must have a system by which we can judge the varying degrees of probability of our own demise in a terrorist attack versus other means of death.

    In my own case, I figure somewhere between 0 and .025% (I do travel overseas)(and I work at a “high value” target)(but live in a very small town in middle America that most would have a hard time finding on a map)

    An accident is one thing and murder is another. And since my wife and I was on a similar flight a year and a half ago, means nothing unless it happened to you. And yes, we were in Rome, and flew to Amsterdam and then on to Detroit.

    I was in Madrid the day after ETA blew up a parking garage at the Madrid airport a couple years ago. So???????? Tell me my death would have changed the course of history… Let us get real… I am nothing. You are little more.

    And they may be 2 different things… but only in your own mind… not in the laws of probability. Gerry, no offense, but do you really think the security policies of our nation should rest on your personal continued existence? Or that we should rest our foreign policy (or security policies) on wether you die in a terrorist attack, a car accident, or a tornado?

    Besides the irrelevance of the statistics, what bothers me about the analysis is it’s focus on the individuals that might be killed. PD

    PD: Nate does not focus on the individuals, you do. You think he means “us” when he actually means any one of “us”.

    I don’t believe American society is tolerant enough to handle a certain level of deaths attributed to Muslims. PD

    On this we can agree: Americans are pussies.

  25. anjin-san says:

    It is after the fight that the opportunity to reshape culture is offered.

    Even if we accept this hypothesis, Bush screwed up the opportunity so royally in Iraq that we are just out of luck. They rushed in with no real plan beyond deposing Saddam. We have been paying for this stupidity ever since, and will continue to do so.

    You also need to look at “reshaping” on a case by case basis. One size does not fit all. We utterly crushed Germany and Japan. Like I said, their cultures became malleable. We were able to effect change. The fact that we had geniuses like George Marshall and Gen. MacArthur on the job did not hurt. They were able to overcome cultural differences to a great extent.

    How exactly do you propose we “reshape” Iraq? Sorry, that horse is out of the barn. We spend a lot of money there, and most of the reconstruction efforts are a joke. It was basically a giveaway to Halliburton and Bechtel.

    If we were to follow the WW2 model, we would have to start saturation bombing of their population centers. Perhaps after we kill half a million people or so they will be more open to change. Perhaps not. Like I said earlier, are we willing to be the kind of people who will not hesitate to use death and destruction to further our aims? Do you want to be the shining city on the hill, or just the strongest beast in the jungle. Myself, I would like us to be more like a Zen Monk/warrior. Compassionate and wise, but able to kick ass when ALL other options are exhausted.

    Perhaps you could go into a bit more detail about how Obama is “mortgaging the future”. The multiple train wrecks left by the Bush admin are now his fault?

  26. anjin-san says:

    do you really think the security policies of our nation should rest on your personal continued existence?

    Seems to be what a lot of conservatives think. “Oh God, oh please. oh please, save me from Bin Laden”. They seem perfectly willing to make the move twoards a police state if that will keep them comfy and watching TV in their living rooms. Look at the renewed calls for torture after a pretty lame attempt to blow up a plane.