March 17, 2021 - 7:00am

The new integrated defence review has been released, and there’s a line in it which is interesting. It is “likely”, it says, that a terrorist group will launch a “successful CRBN [chemical, radiological, biological or nuclear] attack by 2030”.

That sounds bad. But … what does it mean?

I’m not sure. For one thing, it’s not clear whether it means a successful attack in the UK, or a successful attack anywhere. Obviously, an attack somewhere in the world is more likely than attack in a particular place in the world.

Also, it’s not clear what “likely” means. When I hear the word “likely” I tend to assume it means “more likely than not”, i.e. a greater than 50% chance; but people interpret these words differently. (“A real possibility” means a 20% chance to some people and an 80% chance to others, for instance.)

Third, “a successful CRBN attack” makes us think of nuclear bombs in the centre of London. It’s worth remembering, though, that the Tokyo subway sarin attack of 1995 would count as a “CRBN attack”. It was pretty nasty — 13 people died.

But the fact that they were CRBN doesn’t make them worse. You could very easily kill 13 people with an entirely conventional, old-fashioned bomb or gun, none of this fancy stuff at all, and in fact quite a few people have in the not-too-distant past. A 15-kiloton atomic bomb in Canary Wharf would be a CRBN attack, but so were the Salisbury novichok poisonings. It’s a category that contains a lot of very dissimilar things. I’d say it’s more than likely — it’s damn near certain, in fact — that something you could describe as a “chemical attack” will happen somewhere in the world by 2050, and that it’s more than 50% likely that we’ll see one in the UK.

So how likely would a real disaster be? A nuclear bomb in a city?

Interestingly, we can make a decent stab at this. Terrorist attacks, like earthquakes and meteorite strikes, follow a power-law distribution. Small ones are common, but larger ones get rapidly rarer, with (according to this 2006 paper, anyway) a scaling parameter of 2.5. That sounds complicated but it just means “a terrorist attack that’s twice as large is about 2 to the power 2.5 (about 5.5) times as unlikely”. This paper finds something similar.

If I’ve understood it correctly (quite a big if), it works out you can expect to see X terrorist attacks with Y deaths each year, where X is the total average number of attacks per year multiplied by Y^-2.5.

The 2006 paper said that between 1968 and 2005 there were about 10,000 terrorist events that killed or injured one or more victims, up to and including the 1998 Nairobi car bombs that injured at least 4,000 people. That’s about 270 a year.

Eyeballing their graph:

About one in every 30 of those attacks should kill 10 or more people, so about eight a year. About one in every 500 should kill 100 or more, so that’s about one every two years. About one in every 10,000 of those attacks should kill 1,000 or more. So that’s about one every 40 years.

How about extrapolating to really big attacks, city-killers, 10,000 or more? The sort that would take a nuclear bomb or something really catastrophic?

Well: it looks, if I really crudely draw the line down by holding a pencil against my computer screen, as though it’d be somewhere in the 10^-5 region: that is, about one in every 100,000 of these events will kill more than 10,000 people. Given 270 events a year, that’s about one every 370 years. So it could happen, but it’s not very likely in any given year.

A couple of caveats: first, power law distributions become increasingly useless for predictions at the higher ends of the distribution; and second, never trust a man who has tried to estimate a number by holding a pencil against his computer screen. But it’s probably within that order of magnitude.

Of course, there are other ways things can go terribly wrong without terrorists needing to get involved. A good old-fashioned world war would do it. The forecast aggregator Metaculus thinks there’s a 20% chance of two or more nuclear bombs being detonated in war by 2050 and a 17% chance of “World War Three” by the same time. Those sound like scary figures. But if we’re interested in “successful CRBN attacks”, that’s probably the sort of likelihood we’re talking about.

Update: This article originally stated that at least 4,000 people died in the 1998 Nairobi killings. That was incorrect, and has now been amended to say that at least 4,000 injuries occurred.

Tom Chivers is a science writer. His second book, How to Read Numbers, is out now.