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The fat tail of terrorism and why the graphs shared by Bill Gates mislead

The low number of deaths due to terrorism is more attributable to better vigilance and advances in prevention mechanisms. However, that does not automatically mean a reduction in its potential for fatalities.

Recently, Bill Gates shared an infographic showing causes of death in the US, what people most commonly search for and what media reports on. The graphic showed that while only 0.01% of people actually died of terrorism, it constituted over 7% of the google searches and media devoted over a third of its time reporting on it. Gates commented that he was amazed at what we see in the news and the reality of the world around us. He exhorted upon us to fight the fear instinct that distorts our perspective.

Should we, really?

This note is meant for the layperson with almost no background in statistics and one who is convinced (rightly) that 1) Gates is a smart man and 2) Gates means well. If you do not qualify one of these criteria then you may stop reading.

Not to be left behind, “data journalism” handle IndiaSpend tweeted an article showing terrorism accounted for 0.007% deaths in India while over 2/3rd were due to non-communicable diseases like heart attack and diabetes. And yet India’s defence budget is larger than its health budget. A few of us would also remember similar data put out by Steven Pinker that showed that more people die in car accidents every year than terrorism.

Does it mean the fear of terrorism is greatly overestimated? That it is a bogeyman created by immoral politicians and TRP hungry media?

Well, not exactly and let’s see why.

Motor accidents (or deaths due to toaster malfunction or death due to falling off ladders or heart attack) can be represented by what is known as normal or Gaussian distribution. At the risk of oversimplifying- what it means is if there are 10,000 deaths in 10 years due to any of the above, then simply dividing the total number of deaths by the number of years will still give you a fair estimation of how many people actually die of it every year. Even further simplified it means that removing one observation from the sample is unlikely to change the shape of the curve or the average.

Terrorism doesn’t work like that. There were 3,042 deaths due to acts of terror in the USA in 30 separate incident between 2000 and 2009. However, just one incident; 9/11 accounted for 2,996 i.e. a staggering 98.48% of the total fatalities. If terrorism was a normally distributed event then we could make a fair assessment of its risk by dividing the number of deaths by the number of years and arrive at the conclusion that the potential number of fatalities due to terrorism would not exceed 30.42 (3042/10) in a year.

However as 9/11 proved, the actual fatalities exceed the estimate by 100 times. Further, taking one observation out of the sample would change the curve totally. If you take 9/11 out of the above data, the average number of deaths per year would fall to 5, thus further distorting your estimation of the threat terrorism poses. This is why you cannot use the yardstick to measure deaths due to illness or accident to assess the threat posed by terrorism.

Here’s another way to look at it- If somehow the US was able to prevent 9/11, the fatalities would have been reduced by close to 98%. That right there is the reason for vigilance against terrorism. Vigilance prevents. And while better prevention in normal distribution would only mean marginal gains (think how better diagnostic would not reduce deaths due to heart attacks beyond a point), in case of terrorism the rewards are exponential.

Lastly- the low number of deaths due to terrorism are more attributable to better vigilance and advances in prevention mechanisms. However, that does not automatically mean a reduction in its potential for fatalities. As Taleb shows here– while deaths due to Ebola (another example of fat-tailed distribution) in 2016 were far less than even deaths due to bedsheet tangling, tomorrow if we read in the newspaper that 2 billion people have died suddenly Ebola is far likelier to be the cause than death due to bedsheet tangling. Worrying about bedsheet tangling will only have marginal payoffs. Worrying about Ebola might prevent the disaster of the magnitude of an Armageddon.

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