Everyday risks: when statistics can't predict the future

We love data. For the past two years we have crunched numbers about dangers of every kind. And there are plenty of dangers about.

But – a big but – we're certainly not calculating machines. In fact, if there were such a thing as a risk-calculating machine that claimed to give you objective odds on danger, we'd be the first to warn of malfunctions. That's partly because although we think the numbers matter, they can never be the final word: the stories people tell are big influences on their sense of where danger lies – and why shouldn't they be? – since neither source of evidence, neither numbers nor stories is perfect. Each has strengths and weaknesses.

This is a perhaps surprising conclusion from writers at times almost geeky enough to have two hoods on our anoraks; that we think risk is seldom objective, nor solely a property of the world out there, but intimately bound up with our own perspectives, and so personal perspectives on danger are, usually, perfectly reasonable. More than that, we think they're essential. In fact, we think that one of the hazards with hazards is the way that some people use risk numbers almost as if they can foretell your fate. We prefer to think of risk as typically more like an uncertain bet on a horse using scraps of imperfect information mixed with your own judgment: the horse might come in. Or it might not…

So there are plenty of ways in which our sense of risk can be distorted, plenty of ways in which people can get the dangers wrong, and plenty more in which the numbers can be deceptive, too.

In the end, if we had to offer advice to the wary about risk, it would be to try to get to know the data that matter to you, get to know your own mind and the stories that influence you, and so learn how both stories and numbers can help… and deceive. Then do what you feel like.

Here are just five more of the hazards about hazards.

1 Don't let the news worry you

To put it crudely, we worry more that something might get us not because it's more likely to get us but because it would make better telly. Why does it make better telly and get on the news? Because it's vivid (and perhaps exciting), all of which makes it easier to call to mind. And if it's easier to call to mind, we think there's more about.

Researchers in the 1970s ran dozens of human experiments to discover what influenced people's estimation of risk. They noticed that after a natural disaster people took out more insurance, then with time took out less, because the risk is more salient immediately after a disaster, and people think about it. They called these habits of mind the availability heuristic.

It was found that tornadoes were seen as more frequent killers than asthma, although the latter caused 20 times more deaths. Thus vivid events are recalled not merely more vividly but in the belief there are more of them. In contrast, problems that are common are not surprising and are less likely to qualify as news. Another smoking death? And?

Although we'd be justified in describing this as a reporting bias, the media have no trouble justifying it on the grounds that people want to know about what's unusual and new. There is no way they could report risk proportionately and still be in business. It would mean thousands of times more articles on smoking than on death from measles. But it is a bias nevertheless. The unusual is, by the nature of news, disproportionately in your face, so you might think there's a lot of it about.

One effect is that it's easy to forget how radically reduced many fatal accidents are – the death of child pedestrians for example. In 2008 in England and Wales there were 1,471,100 girls aged between five and nine. The Office for National Statistics says 137 of them died from all causes. One was a pedestrian in a traffic accident. In 2010, there were no pedestrian deaths in this category.

2 Be wary of health screening

Reassurance – peace of mind – is often the health industry message. And screening sounds like a good way to get it. The impulse to "find out", to "check", imagines a day when doubt is put to rest. It's also easy nowadays to find clinics to examine and scan us for a worrying range of diseases that we might have without realising. There are effusive testimonials from people who have been "saved" by these tests. What could be the harm in having a check up? Possibly, quite a lot.

There are two main problems. First, there's an awful lot of ruin in a body that might, strangely, never do you much harm. "Finding out" worries us with all the things some of us never had to worry about. For example, one of the writers of this article has around a 50/50 chance of having prostate cancer at the moment and the other will have too, very shortly, since it is estimated from post-mortem data (from deaths in unrelated accidents) that about half of all men in their 50s have histological evidence of cancer in the prostate, which rises to 80% by age 80, according to Cancer Research UK.

CRUK then goes on to point out that "only one in 26 men (3.8%) will die from this disease". So, if 50% of men in their 50s discovered they had prostate cancer (13 out of the 26) but only one in 26 was to die from it, what do they all do, when no one knows if they are one of the 12 who will on average be OK or the one who won't? Finding out what you've got doesn't answer the doubt about whether there's anything to worry about, and so raises new doubts about what to do.

The second problem with finding out is that you might be told you've got something you haven't, and in some cases treated for it. False positives are common for the simple reason that if you test a million healthy people, even with a 99% accurate test, you will still have 10,000 wrong results.

3 We're probably not experiencing a crime wave

Here's a radical insight about numbers: they go up and down. Oh yeah. From one week to the next, the number of murders, for example, varies. Everyone knows this. No one expects the same number of crashes on the road every day. No one thinks the short-term pattern of events will be perfectly smooth. So what happened when there were four independent murders in London on one day? What happened was a giant public scream – in the belief that it revealed a worsening pattern of violent behaviour far beyond the normal ups and downs of the short-term murder rate.

The question is: how do we know it's out of the ordinary? This is a case where stats can be powerful and helpful. Every murder is tragic, devastating families and friends. So it's important to know how many it takes on one day for us to tell if things are getting worse.

Imagine the calendar laid out on the floor, 365 blank spaces. Take last year's murder total, then count out an equivalent number of pieces of rice. Finally, throw the rice in the air over the calendar, aiming for a random distribution of rice grains/murders. One thing we can predict for sure is that the rice grains will not space themselves evenly. We can also be pretty sure that, in places, they will cluster, entirely by chance. So how likely is it that four grains will land on one square? Given London's total of murders, probability theory tells us that four grains in one space can be expected once in every three throws, ie four murders on one day can be expected to occur once every three years. And this is what happened. One of us, David Spiegelhalter, was able to predict almost precisely the number of days on which there would be one murder, two murders, three murders and four, and that over three years there would be 18 gaps of seven days between a murder (in the event, there were 19 such gaps). No new trend was necessary to produce these results.

4 Losing your job may be 16 times more likely than it looks

The rise in unemployment looks not too bad, given the size of the recession. At least, despite the misery of unemployment, plenty of economic commentators have been puzzled by why the numbers are lower than they expected. But is counting the unemployed the best measure of the risks of unemployment? Put aside suspicions of fiddled figures and this sounds like a stupid question. What else is there?

Well, there is the difference between stock and flow, and an argument to be had about which is most relevant to people's sense of the dangers of being jobless. Think of the job market like a great revolving door. On the inside are people in work; on the outside, the jobless. The stock of unemployed is the number of people outside the door at any one time. It is about a million higher than before the recession in 2008.

But the flow is the number of times someone goes through the door and stays on the wrong side long enough to be counted either as unemployed or inactive. This is dramatically bigger. Not 1 million, but more like 16 million jobs lost since late 2008 (though note that one person can lose more than one job in four years).

Once you're out, the flow back in is slower and more uncertain. By one measure, you're about twice as likely to get stuck outside for more than 12 months – and according to some research (much debated), you have an increased annual risk of death during your unemployment equal to smoking 12 cigarettes a day.

This flow turns out to be a torrent pretty much all the time, in boom and bust. The consequences, though, are not the same. In the decade before 2008, the rapidity of the flow back inside was usually at least equal to the flow out. The point is that the risk of being part of the flow now, a flow that is greater than we might judge from the unemployment numbers alone, takes on a more sinister aspect. And many more than 1 million have felt today's more uncertain chill of being on the outside.

5 If you must gamble, try roulette

Risk is the downside of chance. As a final example, here's one from the upside, gambling. Well, we say that, but of course the odds are that you will lose. Though if the UK lottery jackpot reaches more than £14m, it is possible to win for sure by buying tickets for all combinations of numbers, of which there are 14 million. Although tricky to organise, it would win all the subsidiary prizes as well, so you could make a tidy profit. Well, perhaps.

Because what if someone else wins too, and the jackpot is shared? You might be ruined. So even a sure thing can be risky.

So let's say you fancied a £100,000 Maserati, but sadly had only a pound. And let's assume you are a cool, rational customer who wants the best odds (admittedly this is an implausible combination of characteristics). If you buy a single lottery ticket, and if your choice of six numbers matches five winning balls plus the bonus number (a seventh ball drawn), then this generally wins about £100,000 and has a probability 1 in 2,330,636.

Or you could go for an accumulator on the horses: pick a meeting with six races, and in each race choose a horse at medium odds of around 6-1. An accumulator, in which the winnings of each race are passed to the next horse, will give you 7×7×7×7×7×7 = £117,000 if they all win. Given a bookmaker's margin of, say, 12% each bet, the true odds may be around 1 in 230,000 – 10 times as good as the lottery.

If you can find a casino that will let you bet just £1, place it on your lucky number between 1 and 36. When it wins, leave the £36 there or move it to another number. When that comes up, do the same again. Win and you will have £46,656. Move it to red, win and you will have £93,312, almost enough for your Maserati. The chances of this on a European roulette wheel with one zero are 1/37×1/37×1/37×18/37 = 1 in 104,120, twice as good as the horses.