Hi Mike
Welcome to the Forums.
Personally I think that for most organisations using numeric risk matrices is an unnecessary distraction, with many problems that tend to come up time after time:
First there is the problem that they give the perception of a scientific approach but are far from being a Quantified Risk Assessment for the simple reason that it is very rare that there is sufficient data to come up with anything like accurate assesments of the probability of something going wrong with the result of severity X happening.
As example, it used to be the case that about 10 people a year fell to their deaths whilst doing roofwork. But to work out what is reasonably practicable STATISTICALLY you need to be able to work out what the Individual Risk (IR) of death is per annum - See HSE "R2P" for explanation of the concept of IR within a discussion of the tolerability of risk.
But we don't know how many people do "roofwork". Might have a reasonably accurate idea of the number of people whose job title is "roofer" (or slater or something similar) BUT it's not just roofers who do roofwork.
I have investigated 10 fatal accidents during roofwork. Only about half of the victims would be described as "roofers".
So, you don't know the population at risk, you don't know how many hours on average per year that population work on roofs and hence you cannot work out the IR with any level of certainty.
Hence, it is more effective to look at the task (with any mitigations) and assess the level of risk than to try and play a numbers game which is pseudoscience.
Next the assessors almost routinely apply a worst case scenario to accident severity whilst not doing the same for occupational health risks.
So, back to those roofers, statistically they are much more likely to do die prematurely from occupational ill health (e.g. due to exposure to asbestos) than from dying from a fall. Just takes longer.
.....and the assessors determine severity according to the hazard rather than risk.
So, as example if using a scale of say 1-5, where 5 is one or more fatalities, then a 5 for a driver on a high speed road but a lower number if the speed limit is 20 or 30 mph. This is statistically nonsensical as per passenger kilometre it is MUCH more likely that A death will happen on a low speed than on a high speed road - even if that death is more likely to be to another road user (pedestrian, cyclist etc) than the driver or the passenger in their vehicle.
Then, amongst all the other issues, there is the question of volume of risk.
Back to the roofer, does the matrix recognise that only ONE person is only on the roof for two hours and reduce the risk compared to a scenario where there are 10 people working on the roof for a week?
Similarly if you have a construction site with a crane you can work out a number for the risk. What do you do if there are five cranes. Do you write out a separate line for each as the risk MUST be about five times higher. If you only have one line it follows that your calculation will underestimate the total risk.
So, you go for five lines in your matrix to solve that problem!!
If you have 100 people hitting nails with hammers will you write out 100 lines on your matrix to adequately assess the total risk faced by those hitting nails with hammers or will you take a sensible approach and dump the numbers game?
As has been said, HSE does NOT endorse these matrices and I don;t think it ever has.
What happens far too often is that people fiddle the numbers to make them work and cheats shouldn't prosper.