Skip to main content

The risk library  /  What a risk costs

Art. 03 · What a risk costs · 3 min read

Why the average is a fair basis for a decision

“It either happens or it doesn’t” is the commonest objection to risk maths. It is a fair objection, and it has a precise answer.

Flip a coin once. The average outcome, half a head, never happens. For a single flip, the average describes nothing you will actually experience, and anyone who tells you to plan around it is being silly.

Flip it five hundred times and something changes. The proportion of heads stops wandering and settles near half, and it does so reliably enough that you could take a bet on it. Nothing about any individual flip changed. What changed is how many of them there were.

100% 50% 0% PROPORTION OF HEADS SO FAR WILD 1 flip 10 50 500 flips NUMBER OF FLIPS SO FAR
Fig. 4 · The running proportion of heads. Early on the average is meaningless; by a few hundred flips it is trustworthy enough to plan around. The line never stops moving. It just stops moving much.

Your business is not one flip. It is a few dozen risks, running across every month, for as long as you trade. Multiply properties, vehicles, employees and years together and you are well into the part of the graph where the average is a sound basis for planning.

But the objection is right in one specific case, and it is the important one. When a single event can end the business, you do not get a long run. You get one flip that matters. There, the average is actively misleading: an event with a 1-in-500 chance of costing you everything has a modest risk cost and an unacceptable outcome.

That distinction does most of the work in this series. Many small, independent risks: the average is decision-grade, and you should probably carry them yourself. One rare, ruinous risk: the average tells you almost nothing, and that is exactly what insurance is for.

Use it

  • Sort your risks into two piles. "Annoying if it happens" and "over if it happens." They deserve completely different reasoning.
  • Use averages on the first pile. Frequent, survivable losses average out. That is where risk cost is a reliable guide.
  • Ignore averages on the second. For a business-ending risk the right question is not "what does it cost on average" but "could we survive it, and at what price can we hand it to someone else."

Want this run against your own numbers?

We put ranges, not single figures, against the risks your business actually carries.

Speak with an expert

Explanatory content only. This article describes how insurance and risk decisions work in general terms; it is not insurance, legal, actuarial, or investment advice, and it is not a recommendation to buy, keep or cancel any cover. Every figure and diagram is illustrative, chosen to make a mechanism visible, not to describe any particular business.