What is risk?

On the face of it, the word ‘risk’ has a very straightforward meaning. It basically means the chance of something happening. The word ‘chance’ tends to be used for pleasant outcomes whereas ‘risk’ is used when the outcome may be unpleasant. So we talk about the ‘chance’ of a pay-rise, but the ‘risk’ of losing your job.

The chance of a pregnant mother having a girl is about 50%. The chance of a horse with odds of 2 to 1 winning a race is actually 33% (for every 3 races (2+1) the horse is expected to win once). If the odds are 3 to 2, then in five races (3+2) the horse should win twice, ie. 40%.

This is all straightforward. However, whilst the word ‘chance’ is generally used in absolute statements and can stand alone, the word ‘risk’ often has ‘increased’ or ‘decreased’ beside it. This means that it is relative to the original risk, which unfortunately is often not stated. This can lead to uninformed emotional reactions, rather than accurate judgements of the true situation.

Fictitious example 1

Reported in The Daily Concept: Shock findings: cutting down vitamin C intake decreases risk of ‘lopsided-ear syndrome’ by 30%

A typical healthy pregnant mother is told by researchers that cutting down on vitamin C in the diet decreases the risk of the baby having one ear marginally smaller than the other by 30%. Surely all good mothers will now avoid fruit to ensure a perfect baby? After all 30% is a big number, doesn’t that mean 3 babies in 10? One of those three could be mine! Well, it’s just not true. You haven’t been told something crucial to judging the situation, namely: how likely the ‘lopsided-ear condition’ is to begin with. Without this, 30% means nothing at all in absolute terms. 30% of what?

In fact, ‘lopsided-ear syndrome’ affects 2 babies per thousand, so the risk will go down to 1.4 babies per thousand: from a very tiny 0.002% to an ever so slightly tinier 0.0014%. Suppose that, with her usual intake of vitamin C, this mother could go on having babies indefinitely: she could expect only one of her first 500 to have the syndrome. (Two in a thousand is one in five hundred.) Whereas, if she moderates her vitamin C intake she could give birth to 714 unaffected children and only one with this disability.

Fictitious example 2

Now another example with effectively the same values. You will probably feel differently about this even though the numbers are identical, because this time it is about chance, or good luck.

Imagine a raffle where 500 tickets are sold. You discover that there is an ancient chant that increases by 30% the chance of ticket 139 coming up. You perform the chant and then bet on 139 turning up. If you do this 100 times, how many times will you win?

Answer: without the chant, ticket 139 is only as likely as any of the others to be drawn, so that would be a 1 in 500 chance (ie., the same as the 2 in 1000 chance of the ‘lop-sided ear syndrome’ in the example above). With the chant, your chances are increased by 30% – a 1.33 in 500 chance. So you are still very unlikely to win at all in the 100 draws – in fact you would have to play 357 times to expect to win just once.

So when does 30% mean 30% of the time?

The human mind tends to believe that the 30% increase in risk/chance applies not to the original risk/chance but to the number of cases involved – even though when we examine it, the opposite is clearly true. A 30% increase in any risk seems very frightening and a 30% increase in any possibility of good luck very encouraging, as though it means that we will be the loser or the winner 30% of the time. Of course, there is a scenario where this is true, but only when the original risk/chance is 50%.

For instance, let’s say 50% of babies are male. Imagine that parents could change their diet to decrease the chance of a male birth by 30%. This would reduce the number of male births by 30% (of the 50% original chance), ie. 15 births per hundred. You would end up with 35 boys for every 65 girls – 30% fewer boys.

To go back to our raffle example: you have now found another ancient chant that increases by 30% the chance of an even number being chosen. If you perform this chant and then bet 100 times on the draw being an even number, how many times will you win? Without the chant, you would expect to win 50 times out of 100 draws. With the chant, you would expect to get an additional 30% (of 50, ie.15) even draws, which means 65 even, 35 odd.

We all seem to start out with a mindset which imagines the above scenario whenever we see a percentage increased or decreased risk. However, the difference between 65 wins per hundred (when the 30% increased chance relates to an original risk of 50%), and 1 win in 357 (when the original risk was 0.002%) shows how important it is to bear the original risk in mind when assessing something of this sort.

The things they don’t tell you

There is also something else not being mentioned. Consider our imaginary ‘lopsided-ear syndrome’ example again. You may feel that although the risk of this problem is slight, it might be as well to cut out vitamin C to be on the safe side and protect your baby. But you might think “I’m sure there are risks in not having vitamin C! Why wasn’t that in the article? I must be wrong about that.”. Well, just because it wasn’t mentioned doesn’t mean it’s not true. You are right – scurvy (vitamin C deficiency) is a very serious and ultimately fatal disease: and cutting out vitamin C altogether will certainly lead to scurvy.

You, the reader of The Daily Concept, might have assumed that you’d be told this in the story about ‘lopsided-ear syndrome’ and vitamin C: however, to be fair to the journalist and editor, if all the possible information about benefits and risks of vitamin C were included in the article – and all the equivalent information in all the other articles – the paper would be hundreds of pages long every day. On the other hand, printing the original risk of the syndrome affecting two babies per 1,000 should not be too much of a burden on the paper, and then we’d all be able to work it out.

It is also possible the journalists – who, in fairness, aren’t necessarily scientists – don’t themselves realise the importance of this fact.

If they did, wouldn’t they write a story headed Dangerous call for pregnant mothers to reduce vitamin C intake?

Judging between risks

To take a real example: there has been a lot of controversy about the MMR vaccine leading to autism. Without going into the science behind this, it is undoubtedly true that a lot of parents have felt that, because of the risk of autism, MMR was a bad thing – and as there was no easily available alternative many chose to take the risk of having no vaccination. It is doubtful that they were ever told in the press what the actual risk of autism was: much less that they were informed in a concrete way of the risks associated with a population where measles, mumps and rubella are widespread as a result of non-vaccination. Although we did hear a lot about a possible “increased risk of autism” (resulting from MMR) and on the other hand “the loss of herd immunity” (resulting from lack of vaccination), it is impossible to make a good informed judgement on the issue without knowing, for example, what the risk of autism developing is with and without the MMR vaccine. (If you took an interest in this story, ask yourself – did you ever read what the actual risk of autism was?) And then, what is the risk of death or disability resulting from measles, mumps and rubella? You need to know all these things to weigh up the situation properly and make the best and safest decision.

Another example relates to train crashes. You might have heard somewhere that privatisation of the railways has led to a 50% increase in train crashes. So, surely all sensible people will use their cars more. But this is to ignore the risk of car crashes. We do need to look at this too, because in fact even with this increase in risk trains are still safer than cars. How many people do you know or know of who have been in train crashes? How many have been in car accidents?

Points to remember

Never assume, when you are reading about an increased or decreased risk of something, that you are being given all the information needed to make an wise choice. This is unfortunately not usually the case.

With an increased or decreased risk, you need to know what the original risk was before you can tell how serious it is.

Before deciding on a course of action, you need to know the risks involved in any alternative approach. Always remember that choosing to do nothing could be more risky than choosing to do something!