Judging risk

Study shows: risk doubled! Headlines like this are meant to scare you, and they often work. Yet the most important piece of information is almost always missing: doubled from what starting point? If you can read probabilities, you stay calm about such reports and recognise when real caution is warranted. You need this more often than you think: when you cycle without a helmet, at a vaccination appointment and with every warning that pops up online.

What a probability says

A probability describes how often something happens in the long run. If a bag holds 3 red and 7 blue marbles, the probability of red is $\frac{3}{10}$, so 30 percent. That does not mean 10 draws will contain exactly 3 reds. It means: draw very often and the share of reds approaches 30 percent. Probabilities are statements about many attempts, not promises about a single one. When two independent events both have to happen, you multiply their probabilities: draw twice and put the marble back in between, and the chance of red twice is 0.3 times 0.3, so 0.09 or 9 percent.

Absolute or relative, that is the question

Now back to the headline. Suppose a risk rises from 1 in 100000 to 2 in 100000. In relative terms it has doubled, plus 100 percent, which sounds enormous. In absolute terms it has gone up by a single person per 100000 and stays tiny. Both descriptions are mathematically correct, but they feel completely different. Trustworthy information always gives the absolute numbers: from how many to how many, out of which group.

Rare events and our gut feeling

Our gut is a poor risk calculator. Spectacular, rare events like plane crashes or shark attacks get huge attention and therefore feel more likely than they are. Everyday risks like driving or smoking seem harmless because they are familiar. Per kilometre travelled, the plane is one of the safest ways to get around, yet more people fear flying than the car ride to the airport. Remember: how often you hear about something says little about how often it happens.

Comparing risks fairly

The best everyday trick: translate risks into natural frequencies. Instead of 0.2 percent, say 2 in 1000 people. Instead of risk halved, ask: from how many per 1000 to how many per 1000? The same reference group makes risks comparable. If a medicine lowers a risk from 6 to 3 per 1000, it helps 3 in 1000 people. You can then weigh that against costs and side effects, without panic and without playing it down.