Which is the odd one out from the 3 figures shown below? All are the average number of Americans to die each year from these causes.
- A – 69 from Lawnmowers
- B – 31 from Lightning
- C – 9 from Islamic Terrorists
Do think about your answer before you read on!
Well done! You got the right answer! I know this because all 3 can be the odd one out depending on what criteria you are using.
Lawnmowers is the odd one out because this is an AVOIDABLE risk. You can simply decide not to use or go near a lawnmower. Lightning and Terrorists on the other hand are hard to avoid. Whilst some areas will be more prone to lightning and terrorism than other areas, the fact remains that both can strike anywhere in the world.
Lightning is the odd one out because this is a NATURAL risk. Terrorists and Lawnmowers are man-made but lightning is nature expressing its power.
Islamic Terrorism is the odd one out because the government is trying to REDUCE this risk. As far as I am aware, no attempt is being made to reduce the risk of death from lightning or lawnmowers whereas the US government has spent billions and billions on reducing and eliminating this risk including controversial moves such as President Trump’s so-called “muslim ban” on immigration.
Islamic Terrorism is the odd one out because this risk is FAT TAILED. Lawnmowers and Lightning are not fat-tailed but what do I mean by Fat Tails?
With two reasons for Islamic Terrorism, C was the answer I was actually looking for so that I can talk about Fat Tails in data. I am sure you want to know where Kim Kardashian comes into this but you will have to wait!
What are Fat Tails?
The term “fat tail” has been popularised (but not invented) by the author Nassim Taleb. He recently came up with a great way of distinguishing between data that is fat tailed and data that isn’t. Suppose you took two people totally at random from the UK and you worked out the following two statistics.
- The sum of their heights is 13 feet.
- The sum of their net wealth is £20 million.
Immediately you are probably thinking that these two individuals must somewhat exceptional since the average height of a person is under 6 feet and the average net wealth is more like 5 figures rather than 8 figures. Putting that to one side, suppose all you were told are the two totals given above and not the individual values. If you had to guess what the probable values were for each individual, what you would come up with?
I strongly suspect you would come up with something like these scenarios.
- Both individuals are probably 6 foot 6 inches in height.
- One individual is a multi millionaire, say net wealth of £20m and the other has a net wealth of zero.
Both scenarios are far more plausible than these scenarios.
- One individual is 1 foot tall and the other is 12 foot tall.
- Both individuals have a net wealth of £10 million.
Remember both individuals were chosen at random from the total population of the UK. We have clearly been lucky (or unlucky) in getting two exceptional individuals but even with that in mind we would come up with very different scenarios for height and wealth.
With height, we know there is an effective maximum to the possible height of a human. Obviously babies can be 1 foot tall but no adult of 9 feet has ever lived. 7 foot basketball players are reasonably common in basketball leagues such as the NBA but not otherwise. So it is no surprise that we would divide the total height of 13 feet by two and come up with two individuals close to 6 and a half feet.
With wealth though, there is effectively no maximum. We know that millionaires and billionaires exist but there are not that many. The vast majority of people have little or no net wealth so it seems very unlikely we could choose two millionaires at random. It is far more likely that we have selected one millionaire and one commoner.
Wealth is fat-tailed, heights are not fat-tailed. Both Taleb and I contend that lawnmowers and lightning are not fat-tailed but Islamic terrorists are fat-tailed.
Why Terrorism has a Fat Tail
If you apply Taleb’s trick to lawnmowers and lightning, what this implies is that from year to year, the number of deaths due to these causes will fluctuate but the variation from year to year has some limits. As a result, the long run average of 31 deaths from lightning and 69 deaths from lawnmowers is quite stable. A stable long run average is a good base rate to use as a prediction for next year. You might not expect your prediction to be right but using the long run average is often the best way to minimise errors in your prediction.
A fat-tailed data set does not have a stable long run average. It is totally dominated by the extreme values and the fluctuation from year to year can be considerable. Indeed when I told you that on average 9 Americans a year are killed by Islamic Terrorists, you should have smelt a rat straightaway. When I saw that statistic, my mind immediately thought of the twin towers and 9/11. I know that just under 3,000 people were killed directly in just that one event. When you consider that Islamic Terrorism (as opposed to other types of terrorists) has targeted the United States for 30 years at most, immediately you would think that the average number of Americans killed by Islamic Terrorists has to be at least a 100 per year so where did this figure of 9 come from?
Enter Kim Kardashian
Last year, Kim Kardashian tweeted the numbers listed at the start of this post along with other causes of death. You should read that tweet to see where the numbers came from. Where did she go wrong?
Strictly speaking, it wasn’t Kim’s fault. She simply picked up on figures quoted by others. As you can see, these figures are for the 2005 to 2014 period and thus 9/11 is excluded. This is a near perfect demonstration of fat-tailed data. By including and excluding certain years, the long run average changes dramatically. Had the period 2000 to 2014 been used, the average would have been around 200 not 9. Fat-tailed data such as deaths from Islamic Terrorists results in unstable long run averages.
If the long run average is unstable, can we use it as a base rate for predicting the number of Americans killed next year by Islamic Terrorists? Clearly not since we don’t know what the long run average is. This is where Kim went wrong with her tweet. She wanted to use these figures to influence the debate over the so-called “muslim ban” by basically saying “you’re overreacting, you are more likely to be killed by a lawnmower”. But she was not comparing like with like. As I stated earlier, you can avoid the risk of lawnmowers but not terrorists, the government is doing a lot to reduce the risk of terrorism but not lawnmowers which is why the death rate is so low.
Ah but you might say since 9/11 prompted the US government to take Islamic Terrorism so seriously, the current low rate of 9 is a testament to that effort and is therefore a better long run average than 200. Are you sure about that? Would you be willing to bet your life on that? I wouldn’t. One nuclear bomb in New York in the next 10 years and we will be looking at a minimum death rate of 1100 per year (assuming best case scenario of 30,000 deaths which is a lot less than Hiroshima). A nuke is very unlikely but it is not impossible and a long run average of 9 deaths is only possible if you are going to say that a repeat of 9/11 or worse is impossible this century.
It is a fact that when it comes to man-made systems such as the financial markets or terrorism, we greatly overestimate our ability to measure risk because we fail to realise such risks are fat-tailed. The financial crash of 2008 was a vivid demonstration of this as was 9/11. At some point in the future, another terrorist attack on a massive scale is going to take place and you can bet that following that people will be asking “why did we underestimate the risk of that happening?”
So if Kim was wrong, does that mean her implied criticism of a “muslim ban” was wrong? My opinion is the question is not one where statistics can give you an answer. Terrorism is a man-made phenomena and is really the realm of game theory rather than statistics. It is about the balance of attack and defence and attackers will always seek ways to get around defensive measures and defenders will always have to ask themselves whether their defensive measures will be effective in reducing risk and are justified on political and moral grounds. After all, France could have won the world cup last week by poisoning the Croatians just before the game which would have been effective but does somewhat miss the point!