Issues Magazine

Understand the Numbers

By Peter Bowditch

Understand the numbers? Don’t count on it.

Philosopher Douglas Hofstader is credited with inventing the word “innumeracy”, the numerical equivalent of illiteracy. That is, the inability to understand numbers. Three stories that are perennial media favourites got me thinking about how the public can be confused by numbers, and sometimes even deliberately misled.

First up is lottery winnings. The biggest lottery prize in Australia’s history was the $90 million NSW OzLotto draw in 2009. During the week leading up to the draw almost every commercial news broadcast I saw on television had some man-in-the-street interviews with people asking them how they would spend the money, following that with the bad news that the probability of winning was very low (about one in 45 million). It was never mentioned that the odds of winning are the same every week and have nothing to do with the size of the prize.

The problem is that many more people buy tickets when a big prize is on offer, so the probability of any individual number combination winning stays the same but the likelihood of having to share the prize increases, as does the likelihood that someone will win. (Millions more tickets are bought, so a larger subset of possible winning combinations is available.)

When Lotto had one of its first multi-million dollar prizes people ran syndicates to buy large numbers of tickets. If I remember correctly the prize was $13 million but was shared by over 30 winners. Imagine going into the boss’ office on Tuesday morning and telling him what you really thought of him and then getting the phone call to tell you that you had won not quite enough to buy a small home in Sydney’s western suburbs.

By the way, the $90 million prize was shared two ways. You can see I was not a winner, otherwise I would not be sitting here typing but would be driving my Aston Martin to the airport to catch a plane to my private island in the Whitsundays. Sad, isn’t it?

I am not a gambler, although I admit to buying Lotto tickets despite calculations showing no statistical significance between the chances of winning and zero. In laymen’s terms, that means that you don’t increase your chances of winning by buying a ticket so you might as well save your money. Isn’t maths fun?

Of course, warnings about gambling statistics mean nothing to true believers. I remember standing in the Rio casino in Las Vegas looking at a 2-metre-high sign saying that the Rio was the best casino in town because it returned a massive 97% to players. As far as I could see in all directions people were throwing money at slot machines and roulette tables (both of which return less than 97%, as it happens).

Do you remember the swine flu scare of a year or two back? I have seen much ridiculing of warnings made at the time about this new form of the virus, with much of the ridicule focused on the small number of deaths. One reason for the small number of deaths was the preparation undertaken following the previous avian flu scare. Also, the World Health Organisation didn’t declare swine flu as a pandemic because it was killing a lot of people. It was because of the rate of spread across the world. Again it was a statistical argument – that any new disease appearing in five or ten new countries each week, and for which no immediate cure is available, is cause for concern. A statistic that I only saw once but which put a whole new perspective on things was that the death rate among infected people exceeded that of the 1918 flu, which killed a significant proportion of the world’s population. We were lucky this time.

Now that we have looked at how people don’t understand very small numbers like the chance of winning Lotto and small numbers like the probability of dying of influenza, let’s look at a blatant case of abuse of a large number.

An anti-vaccination organisation cited the US Food and Drug Administration as saying that human papillomavirus vaccine caused a 73.3% increase in unrelated illnesses. This was obviously intended to scare potential users of the vaccine. But looking at the facts, the report actually said that 73.3% of subjects in clinical trials experienced an unrelated medical condition (which could have been toothache or pregnancy) during the entire course of the trial.

I remember having influenza and a sprained ankle, both of which occurred within 12 months of moving house. Relating these conditions to the move makes as much sense as the scare campaign against the vaccine does.

The news release forgot to mention that 76.8% of the placebo group suffered an unrelated condition during the trials, so perhaps doing nothing is worse than the vaccine.

Have a nice day. You have a 0.003% chance of having an extremely bad day at least once in your life but a whopping 14% chance of it happening on a Wednesday.

This article was first published in Australasian Science.