There’s a lot of confusion around the definitions of ‘risk’ vs that of ‘uncertainty.’
From the book Personal MBA,
“Risk are known unknowns. If you’re planning to pick up a friend from the airport, the probability that their flight will arrive several hours late is a Risk — you know in advance that the arrival time can change, so you plan accordingly. Uncertainty are unknown unknowns. You may be late picking up your friend from the airport because a meteorite demolishes your car an hour before you planned to leave for the airport. Who could predict that? You can’t reliably predict the future based on the past events in the face of Uncertainty.”
It’s also a very broad definition of risk; it applies to both good outcomes, not just bad ones. If you would have a ⅕ chance of being saved from an illness, with no downside, this could be considered ‘risky.’
Disagreeing with these definitions are common dictionaries and large parts of science and mathematics. In the Merriam-Webster dictionary, every definition of ‘risk’ is explicitly about possible negative events, not about general things with probability distributions. (https://www.merriam-webster.com/dictionary/risk)
There is even a science explicitly called “uncertainty quantification”, but none explicitly called “risk quantification”.
This is obviously something of a mess. Some business people get confused with mathematical quantifications of uncertainty, but other people would be confused by quantifications of socially positive “risks”.
The one area where these clashing definitions don’t really matter is for quantifiable negative risks. That is where most of the current discussion on the matter takes place, and I believe that it is this convenience which allows for the topic to otherwise remain in such a poor state.
To help clarify this, I turned to How to Measure Anything by Douglas Hubbard. Sure enough there is a reasonable interlude (called “A Purely Philosophical Interlude #2) on this exact topic. I suggest reading the section in it’s entirety, but here’s one part.
“The meaning of “uncertainty” and ”risk” and the distinction between them seems ambiguous even for some experts in the field and there are multiple definitions of each in use… Indeed, the decision sciences routinely write about “decisions under uncertainty” where uncertainty is defined with quantified probabilities. Physicists routinely talk about measuring uncertainty — again with probabilities.”
The lack of certainty. A state of having limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome.
Measurement of uncertainty
A set of possible states or outcomes where probabilities are assigned to each possible state or outcome — this also includes the application of a probability density function to continuous variables.
A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
Measurement of risk
A set of measured uncertainties where some possible outcomes are losses, and the magnitudes of those losses — this also includes loss functions over continuous variables.
So according to these definitions, risk is essentially a strict subset of uncertainty. Here, ‘risk management’ is basically ‘uncertainty management’ limited to unfortunate examples. I imagine that any mathematics that apply to risk would also apply to uncertainty, unless there is some relevant formulas only applicable for negative values. That said, this is the most sensible definition on the table. It’s what I’ll recommend.