Mapping stuff according to a binary scale, 1-2-4-8, is an exercise in utility. Just remember the basic idea: utility is about perceived value. What's valuable to one is not to another. So it goes with H, M, L: what's H to one project may be trivial to another.
When mapping value from qualitative to quantitative, the relative differences in the numbers have to be meaningful. That is, if H = 8, and M = 4, then the medium risks really need to be half the impact of the H's.
We see this in this sort of mapping:
- All the risks with impacts of $100K to $200K are mapped as 4 (M);
- Anything over $200K is 8 (H).
- Anything from $50K to $100K is 2 (L), and
- below $50K is 1 (VL).
These values could be scaled to any project size (K's could be M's in a defense project, or K's could be C's in a small IT project)
The important idea, if you are going to do arithmetic on the scaled values, is that between H and M and L and VL the quantitative values are meaningful. That is, an impact of $150K maps to 4; so also $175K. Both figures are on a meaningful scale from 4 to 8 (M to H).
So, now you can multiply '4' * 1 chance in 2 meaningfully. What you are doing is multiplying all the values on the scale between $100K and $200K by 0.5.
It's easier to communicate about 4 * 1 chance in 2 than to talk about all the values on the scale from $100K to $200K.
Application: Risk registers, of course!