by Stubborn Mule on 24 December 2010 · 11 comments

Everyone knows hang-gliding is risky. How could throwing yourself off a mountain not be? But then again, driving across town is risky too. In both cases, the risks are in fact very low and assessing and comparing small risks is tricky.

Ronald A. Howard, the pioneer of the field of decision analysis (not the Happy Days star turned director) put it this way:

A problem we continually face in describing risks is how to discuss small probabilities. It appears that many people consider probabilities less than 1 in 100 to be “too small to worry about.” Yet many of life’s serious risks, and medical risks in particular, often fall into this range.

R. A. Howard (1989)

Howard’s solution was to come up with a better scale than percentages to measure small risks. Shopping for coffee you would not ask for 0.00025 tons  (unless you were naturally irritating), you would ask for 250 grams. In the same way, talking about a 1/125,000 or 0.000008 risk of death associated with a hang-gliding flight is rather awkward. With that in mind. Howard coined the term “microprobability” (μp) to refer to an event with a chance of 1 in 1 million and a 1 in 1 million chance of death he calls a “micromort” (μmt). We can now describe the risk of hang-gliding as 8 micromorts and you would have to drive around 3,000km in a car before accumulating a risk of 8μmt, which helps compare these two remote risks.

Before going too far with micromorts, it is worth getting a sense of just how small the probabilities involved really are. Howard observes that the chance of flipping a coin 20 times and getting 20 heads in a row is around 1μp and the chance of being dealt a royal flush in poker is about 1.5μp. In a post about visualising risk I wrote about “risk characterisation theatres” or, for more remote risks, a “risk characterisation stadium”. The lonely little spot in this stadium of 10,000 seats represents a risk of 100μp.

One enthusiastic user of the micromort for comparing remote risks is Professor David Spiegelhalter, a British statistician who holds the professorship of the “Public Understanding of Risk” at the University of Cambridge. He recently gave a public lecture on quantifying uncertainty at the London School of Economics*. The chart below provides a micromort comparison adapted from some of the mortality statistics appearing in Spiegelhalter’s lecture. They are UK figures and some would certainly vary from country to country.

Risk Ranking

Based on these figures, a car trip across town comes in at a mere 0.003μmt (or perhaps 3 “nanomorts”) and so is much less risk, if less fun, than a hang-gliding flight.

It is worth noting that assessing the risk of different modes of travel can be controversial. It is important to be very clear whether comparisons are being made based on risk per annum, risk per unit distance or risk per trip. These different approaches will result in very different figures. For example, for most people plane trips are relatively infrequent (which will make annual risks look better), but the distances travelled are much greater (so the per unit distance risk will look much better than the per trip risk).

Here are two final statistics to round out the context for the micromort unit of measurement: the average risk of premature death (i.e. dying of non-natural causes) in a single day for someone living in a developed nation is about 1μmt and the risk for a British soldier serving in Afghanistan for one day is about 33μmt.

*Thanks to Stephen from the SURF group for bringing this lecture to my attention.

Possibly Related Posts (automatically generated):

{ 8 comments… read them below or add one }

1 Mark L December 25, 2010 at 9:58 pm

Another fascinating piece from the Mule.

I think the following can’t be correct though:
> the average risk of premature death for someone living
> in a developed nation is about 1μmt

The homicide rate alone (surely a homicide must result in a premature death)
in developed countries is around 1.5 per 100,000 population annually
(except in the USA where it is over 3 times higher). See for example:
This gives an annual risk of 15μmt. Lifetime risk would have to be
at least an order of magnitude higher still. And of course there are many
other ways to die prematurely.

2 Stubborn Mule December 25, 2010 at 10:30 pm

Mark: I probably should have been a bit more explicit there: in order to make the comparison to Afghanistan, that 1μmt figure is the risk of premature death (i.e. non-natural causes) in a single day. Like the other figures here, the data is from the UK where there were approximately 18,000 deaths from “external causes or morbidity and mortality”. I’ve tweaked the wording in the post to make it clearer that I was referring to the risk in a single day.

3 Mark L December 25, 2010 at 10:44 pm

Much clearer, thanks!

4 Mitch November 9, 2012 at 4:59 am

Marl L: That number’s only ttrue if you include suicide as a form of homicide. Take that out, and the US isn’t even in the top 40.


5 Stubborn Mule November 11, 2012 at 9:59 pm

@Mitch: according the these FBI stats, the US murder rate was running at 48 per million population in 2010. That should put them at #6 in the list you posted. So, while they are not in the top 40 in that list, it looks as thought that is because they are just missing from the list, rather than because their murder rate is low!

6 Mark L November 11, 2012 at 10:06 pm

Mitch: The same website confirms the 15μmt for Australia and has the US at 59μmt — http://www.nationmaster.com/graph/cri_mur_per_100_peo-murders-per-100-000-people

7 Mitch November 12, 2012 at 1:20 am

Ah, thanks for the correction.

8 Ross Presser November 15, 2012 at 2:18 am

From the bottom of the graph on that Murders per capita site:

DEFINITION: Number of convictions for intentional homicides in the given year. Per capita figures expressed per 1 million population.

SOURCE: European Institute for Crime Prevention and Control International Statistics on Crime and Justice, 2011

Leave a Comment

{ 3 trackbacks }

Previous post:

Next post: