Should You Fly or Should You Drive?Marin Vlastelica PogančićBlockedUnblockFollowFollowingMar 23The thought of a plane crash gives me the creeps because I need to fly regularly home to visit my family.

Recently there was a tragic accident by an Ethiopian airline where all passengers died.

If you are interested in details about the plane crash, you can get them here:Ethiopian Airlines crash: Six charts on what we knowBoeing has grounded its entire global fleet of 737 Max aircraft after new evidence was uncovered at the scene of a…www.

bbc.

comIf such a crash happens, apparently it is highly unlikely that anyone survives the ordeal.

I want to warn you upfront, this article may contain some alarming statistics regarding flying, so if you are prone to anxiety, I would advise against reading the whole article.

But, there are some positive things also to be said about flying that may ease the tension.

So, recently, I was flying from Croatia to Germany.

It was tranquil sunny weather of course at departure coupled with some nasty winds.

Before boarding my flight I already started thinking about the Ethiopian Airlines plane crash, really not the mindset to get into when boarding an international flight.

What I was thinking concretely was Bayes’s theorem with regards to airplane fatality rate, in other words, what is the probability that you are going to die by boarding a plane vs.

by driving a car?Photo by Paweł Puszkarski on UnsplashThe reason I thought about this is the classical assumption that flying is safer than driving, statistically.

Let me tell you, it sure doesn’t feel like it.

You look out the window of your plane, you see those wings basically flapping, not looking robust at all — of course, this was well thought through by some mechanical engineers taking into account the forces on the wings, their flexibility makes them more robust and less prone to breaking.

So, flexible not-robust looking wings are a good thing.

I need not state the obvious but I’ll state it anyway, I am not a mechanical engineer.

But I am equipped with the ability to use Google and, luckily, had learned some physics at the university.

But, despite all that, I can’t get rid of the bias in my brain — robust stuff shouldn’t move like that!A car ride is relatively smooth sailing, there is not much going on most of the time.

A plane ride is blessed on the other hand with a fun thing called turbulence.

Chances are you experienced some turbulence sometime in your life if you fly regularly, then you know it is not really a good feeling.

Statistics to the RescueStill nestled safely on the ground, I thought about the classical example of cancer tests in Bayesian statistics.

I won’t explain Bayesian statistics in detail here, but in a nutshell, it deals with conditional probabilities i.

e.

what is the probability of something happening given that something else has happened.

What makes the cancer test example so interesting is that, based on the confidence of the test, the probability that you will get cancer drops considerably, a more detailed explanation of Bayesian statistics with the cancer example can be found here:An Intuitive (and Short) Explanation of Bayes' TheoremBayes' theorem was the subject of a detailed article.

The essay is good, but over 15,000 words long – here's the…betterexplained.

comWhat I was concretely interested in is the probability that I am going to die by taking a plane vs.

probability that I am going to die by driving a car (excuse me for sounding a bit grim):Fortunately, I was thinking about this while I was experiencing one of the biggest turbulences in my life, thank you Dalmatia for the Bora(strong north wind on the Adriatic sea).

To solve the problem I looked up some statistics on crashes, fatalities for both planes and cars, I am not allowed to use the graphs but I will share the relevant statistics through links.

To make it a bit easier because this is a fast exercise of thought and by no means a full risk evaluation for flying vs.

driving, I decided just to look at the statistics for 2018.

So, first thing is the number of global airplane fatalities that happened in 2018, statistics are available here:Worldwide air traffic – fatalities 2018 | StatisticThe graph depicts worldwide air traffic fatalities from 2006 through 2018.

In 2018, 561 people died in air crashes…www.

statista.

comSince we are looking at 2018, the number of fatalities is 561.

On a positive note, I want you to remember the following:The fatality rate i.

e.

number of fatalities divided by number of flights is decreasingHow do I know this?.Well, here is the statistic for the number of flights per year:Airline industry worldwide – number of flights 2019 | StatisticThe statistic gives the number of flights performed globally by the airline industry from 2004 through 2019.

Passenger…www.

statista.

comNotice that the number of flights in a year is steadily increasing.

Comparing to the previous fatality graph — we can’t really claim that the yearly number of fatalities is steadily decreasing.

But, since the yearly number of flights is increasing, the fatality rate is effectively decreasing.

The wiggly nature of the number of fatalities is understandable since a plane crash is a rare event.

On one more positive note:Not all plane crashes result in fatalitiesFor 2018 we found out that the number of flights was approximately 39.

8 million.

I think it is a safe assumption to make that the average flight carries 300 passengers (this is of course not exact, but is making things simpler to calculate and probably is not that far from the truth).

So the number of passengers on all of those flights is the following:So, what is the probability of you being a casualty by taking 1 flight?.Well, it is this by a rough estimate:Quite small no?.Don’t get your hopes up just yet.

Let us take a look at the number of car rides based on the following source:Road Safety Facts – Association for Safe International Road TravelView the WHO's infographics on road safety facts.

Nearly 1.

25 million people die in road crashes each year, on average…www.

asirt.

orgApproximately 1.

25 million car accident deaths per year, this is quite a lot… Another statistic shows that there are 1.

2 billion cars on the roads in the world today… 1.

2 billion!.On a side note, just imagine the pollution that that causes.

Just that is worthy of a statistical analysis by itself.

Again, for some math simplicity, let us assume that there are 2 passengers per car on average.

Also, let us assume that on average, a car is used twice a day since most people commute with them to work and back.

This is a very strong and probably wrong assumption, I would assume that the average is below 2 since many people use cars only when they travel great distances.

Anyway, so the number that we are looking for is the number of persons that participated in car rides within a year:Now we can derive the probability that you would be a casualty in a car ride:How does this compare to flights?.Well, you can notice it is somewhat lower, approximately it is 16 times more probable that you would die in a car accident as in a plane crash.

16 times sounds quite scary when you would just hear this number and nothing else.

This ratio can change considerably based on the correct expected values for passengers.

If the expected number of passengers is higher than 2, then the ratio becomes lower also.

Concretely, if the expected number of passengers is 4, then the ratio becomes 8.

But disregard the ratio, what you are supposed to see is that both probabilities are marginally low, there is no reason to be scared of neither planes nor cars.

Of course, the more you use your car the higher the probability that you will have a tragic accident.

Needless to say, the probability depends also on other factors such as where you are driving your car, your driving experience, the length of the journey and the car quality itself.

Nevertheless, let us state another interesting question.

Based on probability, how many car rides or plane rides do you need such that the probability converges to 1 that you will die?.We can see this as the probability of surviving converging to 0.

This only happens with infinite many tries, but let us consider the case where the probability of your survival based on the statistics is 1%, those are quite slim chances of survival.

So, you need to make 9.

6 million car trips in order for your survival chances to drop to 1%.

How does this calculation look like for airplanes?.Repeating the same procedure, you arrive at this conclusion:You need to make over 93 million trips by plane in order for your survival rate to drop to 1%.

In fact, the survival rate looks something like this as a function of N (based on the above statistics):It takes quite a few tries for the probability of survival to drop, in fact, for N=1000 000 the probability of survival is still over 95%!.This is kind of reassuring.

You know when are you going to make a million airplane trips?.Never.

If you take 1 flight a day, it would take you:So, if you live to be above 100, it would take you about 27 lifetimes for your probability of survival with a plane to be 95%.

This is quite reassuring, I feel better concerning my feelings about airplanes now…Just not to get too positive too early, I remind myself always of Murphy’s law:What ever can happen, will happenObviously, plane and car crashes happen sometimes, but we can be sure that they are highly improbable.

If you want to know more about the effects of highly improbable events, I would suggest that you read The Black Swan by Nassim Taleb, a very interesting read:The Black Swan: Second Edition: The Impact of the Highly Improbable: With a new section: "On…A black swan is an event, positive or negative, that is deemed improbable yet causes massive consequences.

In this…amzn.

toAll in all, based on these very stipulating statistics that I’ve written down in this article, you should feel safe in using a car or a plane for traveling.

But don’t forget, it is all randomness and luck.

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