A crash course in probability

GULLIVER will soon fly from Heathrow to Milan on a British Airways Airbus A319. That flight has a one-in-4.8m chance of crashing. Shortly after he is jetting from Heathrow to JFK on a Virgin-operated A330. Chance of crashing? One in 5.4m. That means that he could apparently expect to fly on the route for 14,716 years before plummeting into the Atlantic.

These figures come courtesy of “Am I Going Down?”, a recently released iPhone app that claims to calculate the odds of a disaster on a particular flight. Users input three variables: the departure and arrival airports, the airline, and the type of plane used. The app's maker hasn't responded to requests to give a little more detail of its methodology, but one presumes that it is a simple weighting of the proportion of crashes associated with each of those variables in the past.

There are, of course, countless holes in such a simplistic approach. How does one decide the relative importance of the make of plane, airline or airport? Is past performance really an indicator of future performance? Does, for example, a Malaysia Airlines flight being shot out of the sky by Russian separatists make this event any more likely to happen again in the future? Is the calculation based on miles flown or the number of journeys? (As the take-off is the most dangerous phase of a flight, a 10,000 mile flight isn't twice as risky as a 5,000 mile one.) What about other important variables, such as the weather?

The 14,716 years figure caused us a bit of confusion. But reader guest-isjswsa jumped in on the comments thread to shed some light on it. It’s the average length of time people will fly before crashing, if lots and lots of them do it every day. An alternative way of expressing it would be to say that if you were to arrange to fly this route every day for the next 10,210 years, your chance of dying would be 50%. And if you wanted to book enough flights to be almost certain of crashing, you reach a 99% probability at 67,833 years of daily flights. (For those interested in the maths, there is more here.)

But perhaps this is a bit churlish. The idea behind the app is laudable, if not mathematically sound. Nic Johns, its creator, says he wants to reassure nervous flyers that they are all but guaranteed to reach their destination in one piece.

Of course, we all know this deep down. In real terms, it makes no difference if the chance of crashing is one in 1m or one in 9m; the likelihood is so small as to make the difference irrelevant. But there is a special place in our psyches for the fear of big, unlikely catastrophes. According to David Ropiek, author of "How Risky is it, Really?", the deadliest plane crash in history occurred in 1977 in Tenerife when 583 people were killed after two jumbos collided on the runway. Yet, that many people die from heart disease in America every eight hours. As Mr Ropiek explains, air crashes are considered catastrophes while heart attacks are not, because they fulfil three criteria:

A catastrophe has to be big, it has to happen all at once, and something about it has to be calamitous—disastrous—really bad.A plane crash certainly qualifies. It kills a lot of people all at once, in one place, and in a really horrific way. But heart disease [...] meets only one of those criteria. As awful as heart disease and stroke and diabetes are, they don't kill people in such vividly awful ways as plane crashes.
It bears repeating just how rare such deaths in the air are. Safety statistics collated by IATA, an airline association, show that in 2013 more than 3 billion people flew on commercial aircraft. During that time there were 81 accidents and 210 fatalities. What is more, this figure has been falling for years (although the two recent Malaysia Airlines disasters will mean a blip when the 2014 figures are released). By way of comparison, the World Health Organisation says there were over 1.2m road traffic deaths around the world in 2010. It is the leading cause of death among 15-29 year olds. The University of Oxford calculates that in 2006, Brits had odds of one in 36,512 of dying in a motor accident and one in 3.5m dying in a plane crash.

Of course, many more people drive than fly; hence it is not easy to compare the two types of travel in a meaningful way. It is not known how many car journeys people take around the world, but even if it was, one would have to decide whether to compare the number of discrete trips or the overall distance travelled (that is an important distinction because if you were travelling from London to Edinburgh, for example, you might reasonably choose between driving and flying). Suffice to say what we all know: the fear of flying is incommensurate with its risk. And, as this chart from an Economist piece last year highlights, that’s before we compare it to the really dangerous modes of transport, like using stairs.

Source: http://www.economist.com/blogs/gulliver/2015/01/air-safety