Originally Posted by Cows
it is about rate of deaths or, to be more precise, the risk of occurrences which may lead to deaths
You're still confusing risk, likelihood and consequence.
The number of deaths in an event is the consequence (or cost or impact). If preventing deaths associated is your aim, "the risk of occurrences which may lead to deaths" is meaningless. You would use the likelihood of occurrences which lead to deaths.
Your question about how many air shows: straight forward risk won't tell you that because of random distribution and probability. If you're using positional risk, then you might be tempted to argue that doubling the number of air shows doubles the likelihood of a crash, but that is not the case, because frequency also affects other factors that affect likelihood.
Of course, the level of risk that is acceptable is an entirely different matter and has to decided separately from a dispassionate assessment of risk. Again, level of risk and acceptability are being confused here. As far as I can see, the only means of achieving zero risk of death caused (directly or indirectly) by air displays is to have zero air diaplays. If the argument is about what level of risk is acceptable, then everyone here is fully entitled to their opinion of that, but those opinions do not alter the actual level of risk. Likewise, the effectiveness of any risk assessment conducted for a particular event does not change the level of risk, simply the accuracy of the understanding of that risk and the value of any decisions based on the risk.
Originally Posted by Cows
That takes us on to consequences and under any definition multiple deaths would fall into a 'catastrophic' category. Rattling all that down, a basic RA matrix would result in an unacceptable (red) outcom
No, it doesn't. The risk doesn't become "unacceptable" just because of the severity of the outcome as you said yourself. If the probability of the event happening is small enough, a catastrophic outcome can still produce either a medium or even low risk. If you simply use the outcome as your measure of acceptability, we would have no airliners, high speed trains or nuclear power stations.
You, and others here, will only make proper sense of this when you stop confusing the terms risk, probability and consequence. Once you apply those terms correctly and consistently, you can assess the level of risk appropriately and tackle BOTH the factors in risk reduction. Reduce likely hood: training, assessment, currency, engineering standards, frequency, etc. Reduce impact: Separation from people and property, crash response, energy at impact, fire suppression, etc.