That’s a frequently used formula for security, and it’s dumb there too, manipulated to explain away problems or get money.
Impact is more like “perceived impact to me” and risk is over a timeline that matters to the assessor of risk.
War hawks see nuclear war as medium probability, low impact. Most people see climate change as something impactful in a timeframe they don’t give a shit about, and terrorism is medium or high impact with medium or high probability in a timeframe that matters to them.
Sorry you feel that it’s dumb, because it’s not so much a formula as the basic concept (in words) of a expected value, which is perhaps the most fundamental concept in statistics, ML, decision theory, game theory, economics, medical decision and more. As I mentioned, the application of this concept gets much spicier (and more useful) once you start accounting for random variables, priors, model assumptions, etc. There are centuries of academic and practical thought devoted to these topics.
The “definition” of risk that I gave is a useful heuristic, even for my cat. He seems to calculate the probability of being caught on the kitchen counters, conditional on the number of people home and the time of day. He knows that he may get spritzed for violations and can balance this against the reward (simply chillin’ = stern warning; eviscerating a briefly undefended loaf of fresh challah = direct barrage from the water bottle). Clearly, this shrewd exploitation of Lady Luck is a learned behavior. (Whether is consciously strategic behavior or just serendipitously adaptive cat programming is actually immaterial in the game theoretic sense—mixed strategy Nash equilibria that result from evolutionary dynamics are equivalent to those that arise from strategic deduction).
Impact is more like “perceived impact to me” and risk is over a timeline that matters to the assessor of risk.
War hawks see nuclear war as medium probability, low impact. Most people see climate change as something impactful in a timeframe they don’t give a shit about, and terrorism is medium or high impact with medium or high probability in a timeframe that matters to them.