Six years ago the Government’s chief drugs adviser, David Nutt, alerted us to a frightening addiction called “equasy”.

Equasy, as Nutt described it, was a pursuit that released adrenaline and pleasurable endorphins into the brain. It was also extremely dangerous, often fatal. Nutt reckoned that around one in every 350 usages of equasy resulted in acute physical harm. Worse still, this was an addiction that had in its grip tens of thousands of people across Britain, including small children.

Equasy was horse-riding. Nutt’s point was that, objectively speaking, riding a horse is a far more dangerous hobby than taking little MDMA pills, or ecstasy, in nightclubs. While he calculated that 1 in 350 horse-riding episodes resulted in harm, that was only the case with 1 in 10,000 episodes of ecstasy use. And yet ecstasy was a Class A banned drug and the object of great waves of concern from the media and politicians, while horse-riding was not.

Nutt’s reward for this provocative comparison was to be sacked as chief adviser by the then Home Secretary, Alan Johnson. Nutt had misunderstood his brief. His job as drugs adviser was to tell ministers how dangerous ecstasy and other banned drugs were, not how comparatively safe they were.

Yet even more depressing than Johnson’s intolerant response was the fact that it probably reflected majority public opinion. Many of us have an objection to thinking about risk and harm in a scientifically neutral way. We find it inappropriate, even offensive, to compare two activities such as popping Es and riding ponies, where one is widely seen as inherently sinful while the other is regarded as wholesome. These subjective moral spectacles are one of the reasons people tend to be rather bad at evaluating risk.

Smoking today fits well with this moral view of risky behaviour. Smoking is widely seen as a filthy habit. We don’t have a problem when doctors warn of the grave health risks from cigarettes. But eating a bacon sandwich? Not so much. That was why, when the World Health Organisation released a report last month suggesting that consuming processed meats increases the risk of developing colorectal cancer by 18 per cent, many raised an eyebrow. Some even inquired what the absolute risk was.

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A person’s risk of contracting this form of cancer over a lifetime, whether they eat processed meats or not, is around 6 in 100. This is known as the base rate. A person who regularly consumes processed meats has a 7 in 100 risk. Not such a dramatic jump as that 18 per cent headline figure suggested. That’s really how we should evaluate all health risks, by asking to be told the risk base rates.

But we seldom do. Moral spectacles are a major reason why we don’t. But they’re not the only psychological explanation. The US economist Steven Levitt, author of Freakonomics, has pointed out that an American child is around 100 times more likely to drown in a swimming pool than be accidentally shot by a parent’s gun. Americans are generally extremely careful about locking up their firearms to keep them out of the hands of children, but they’re much more cavalier about ensuring that the door to their backyard swimming pool is shut at all times.

So what’s going on here? The answer is fear of regret. When we evaluate risks we’re often not thinking of the objective likelihood of a bad thing happening, but how terrible we will feel if it does happen and we did not take steps to prevent it. An unsecured gun is a more frightening mental image than an unsecured back door – and people react accordingly.

The media plays a role in exacerbating these psychological biases. Plane crashes get blanket coverage; car crashes do not. Cyclist deaths in London get considerable media attention. The base rates for these transport fatalities are seldom reported. When people die of alcohol poisoning, it doesn’t make the evening news. But every single death from ecstasy makes headlines, generating plentiful debate. Sometimes this kind of coverage creates a self-reinforcing “availability cascade”, massively distorting public impressions of the relative riskiness of activities.

There seems to be a human urge to want to believe that things happen for a reason. Experiments by the psychologist Icek Ajzen suggest that if base rates are subtly presented to people as somehow “causal” they are much more likely to be taken on board by those people when they estimate probabilities. The mind can deal with plausible stories much more easily than arbitrary statistical facts.

This isn’t all a negative story. In some instances it’s rather civilised that we neglect base rates. Think of when it is suggested that the authorities resort to racial profiling to detect criminals. Many of us baulk at denying each person’s individuality, at stereotyping whole classes of people, even if it might make our police and intelligence services marginally more efficient.

What does any of this have to do with economics? Well, the neglect of statistical base rates explains why many people buy insurance policies that are priced well in excess of their statistical “expected values”, thus creating an enduring source of profits for insurance companies.

It also has implications for the magic dust that is responsibility for our prosperity: entrepreneurship. It’s difficult to estimate the base rates of success for people who start their own business ventures. The data is lacking. But there are good reasons for thinking they are low. Failure is overwhelmingly more likely than success. Yet we don’t particularly want entrepreneurs to ponder the odds of success. If they focused on the high risk of failure they might not take the risk and stick with something safer. If the great entrepreneurs of history – from Guglielmo Marconi to Bill Gates – had made these calculations, we might all be the worse off for it. We want entrepreneurs to have a head full of self-belief, not base rates.