After another year of COVID-19, a sensible new year’s resolution is to accept that many people, however literate or well-informed about current affairs, are not good with numbers, especially large numbers. This manifests itself in two principal ways. People struggle to think in probabilistic terms and they find it hard to comprehend very large numbers.

Everyone knows that Leitrim is not going to win the hurling championship anytime soon and would be slow to back their chances even at generous odds, like 20 to one. But they understand that only an eejit will offer 20 to one against Limerick.

Betting odds are conceptually first cousins to probabilities, but public understanding rarely extends beyond betting on sports. Nobody seeks answers to questions like “what are the odds of catching COVID-19 if I spend three hours in a crowded pub?”

Managing a pandemic and advising the Government and the public about precautionary behaviour is an exercise in the explanation of risk

Pity the epidemiologists who have been struggling to explain risks about infection, without resorting to sporting analogies.

Managing a pandemic and advising the Government and the public about precautionary behaviour is an exercise in the explanation of risk.

Most people just do not think this way, not because they are dim or lazy but because they do not study probability and statistics at school.

Attempting to explain to a neighbour that the rate of infection among younger children had risen sharply since November, he responded: “I don’t believe it, my eight-year-old goes to the school down the road, and they have had no cases.”

I explain that there are 3,300 primary schools in Ireland and that lots of them have had plenty of cases. He does not buy it, not because he is being obtuse, but because he does not think to draw conclusions only from adequately large samples. Direct personal experience may be vivid, but it is not representative.

Why do the polling companies interview 1,000 people at minimum before they tell us that party political support has shifted? If 10 interviews would suffice, they could save lots of money and effort, but they know that the results would be unreliable. They would surely like to see data from a few hundred schools before saying anything about infection in the six to 12 age group.

Mathematical theorem

There is a mathematical theorem called the Law of Large Numbers, first understood four centuries ago, which says that the bigger the sample the more accurate the measurement.

How many people have you met who say: “Nobody I know has caught COVID-19?”, a popular refrain last year but sadly becoming less frequent? How many think that Ireland has been doing better than the UK in controlling the virus recently?

Per million population, the infection rate has at times been higher in the Republic, and the UK has not done very well in comparison to other western European countries.

But people do not easily think about rates of infection per million, and the news media tend to report raw numbers without context.

To say that 5,000 people were testing positive for COVID-19 a few weeks ago told very little about the risk of picking up the infection. To begin with, testing is not comprehensive and the true underlying figure might have been 10,000 or even more.

People can stay infective for about a fortnight, which is why virologists keep track of the 14-day cumulative figure.

If that was steady at 140,000, corresponding to a constant 10,000 new infections every day, this implies, in a population in the Republic of five million, that one person in every 36 was a carrier.

Every location, including bars, restaurants, or retail outlets with 100 people present, could have three or four infected people on the premises.

People self-isolate when they get the result of a positive test, the sample is not random and so the actual risk might be lower

People self-isolate when they get the result of a positive test, the sample is not random and so the actual risk might be lower. But rising daily case rates imply higher risk, other things equal and this would be better understood if the figures were communicated in terms of infection risk, rather than as raw numbers.

Until the financial crash in 2008, the word “billion” was not part of the popular vocabulary in Ireland. A million was a large number, adequate for all practical purposes.

TV presenters regularly failed to report that some bank had gone down for €10bn and instead reported the damage as €10m. They may as well have said “a bank went bust for lots of money”.

But very few react with sufficient horror when the latest capital cost over-run is revealed as €2bn versus €1bn.

Smaller absolute numbers, like the price of a car or a house, seem to be the limit of perception and the difference between very large numbers somehow fails to register.

People would certainly notice if the invoice for a new car was double what they had bargained for.

Have a prosperous and safe, 2022.