which was taught to me by an engineer(!) and was used by him in the construction of some seriously well know buildings: PROBABILITY x THREAT = RISK Low probability of a small threat being realised, you are dealing with low risk situations. High probability of a small threat being realised, you are dealing with something you must take more seriously. For example, if assessment of a building plan concluded a real, but low, probability that the building will fall down with people in it, you would revisit the plans!  If there was a high probability that the building's cosmetic exterior would not maintain its shiny appeal because of weather damage, you may decide to just roll with it and build in a maintenance programme. The problem situation which bedevils decision-making around policing and mental health is: very low probability of a significant threat being realised .  For example, there are over a million arrests a year in the United Kingdom and in that context, deaths in custody or following police contact are statistically rare.  Having said that, there are some obvious warning signs and predictors and drugs and alcohol, resistance and mental ill-health are right up there with the best of them. The investigation and / or prosecution of offenders with mental health problems is as complex as it gets but it is often not time critical.  Police officers and CPS are weighing up, the strength of the evidence, the victim's wishes, the public interest in preventing any further offending