A log succumbing to gravity and crushing me is not going to refrain from action because it fears for its own self-preservation. It has no such motivation; it simply obeys the laws of physics. As such, there is less that can be done to reduce the peril; a threatening reputation will not stop the log from breaking its binds and maiming.
A living organism, conversely, must consider risk and reward in each of its pursuits. Any living being capable of motion and thought (an intelligent entity) seeks self-preservation and in turn develops fears to threats against that preservation. If I can evoke fear in an organism that would otherwise be dangerous to me, I can mitigate the peril imposed quite effectively as the self-preserving entity will avoid me for its own safety.
There is an idea in ecology of which I recently became aware called a trophic cascade. Consider A, B, and C as species in the food chain with A preying on B and B preying on C. If the threat posed against B by A is increased (say by an enlarged population or a more rigorous hunting technique), the population of B is decreased and members of species B adopt new behaviors as a means of avoiding species A. Additionally, species C experiences a glut of population growth as it is no longer being culled by species B.
Applying this concept to society it is possible to interpret the reduction in crime statistics to a trophic cascade. Criminals (species B) adopt newer, lower risk behaviors to avoid confrontations with Law Enforcement (species A), because they are aware that such confrontations are fatal. These new behaviors take the form of non-violent crime, such as identity theft and cyber-scamming, as such crimes (while still at risk of encountering courts) will not lead to direct interaction with the police. In this model, law-abiding citizenry (species C) experiences a greatly reduced amount of violent crime at the hands of the unruly (species B).
This poses an interesting complication. Does extinction of species B result in extinction of species A, or does species A begin to prey on species C for sustenance? Nature has shown us both cases, and for my model there will be no way to know until it happens. The latter is clearly fascism, but the former has yet to occur in society.
Species A needs to remain a dangerous enough force to be able to prey on species B (rather than the other way around), so that species C might benefit from the results of the trophic cascade. That is, species A must present a threat to self-preservation so intense that it invokes avoidance by fear. As long as species A can pose that threat, species B will be less inclined to take actions that involve species A, including launching attacks. Hence species A experiences a lowered peril ratio.
When considering law enforcement as apex predators rather than as a subset of the citizenry, it becomes clear the best course of action is avoidance and, in the event of interaction, taking the necessary precautions to avoid invoking the lethality of the predator. For entities within species C, this means avoiding sudden movements, staying still (allowing the officer to approach instead of approaching), and obeying the commands of the officer. For optimum safety in these situations, waiting to contest a wrongful arrest until the danger has passed (that is, in a legal venue) is the best practice.
[Labels A, B, and C used to indicate an order of predation; I am not trying to imply that any one population is greater or of more value than another.]
I am aware this is against one of the core beliefs in my flavor of Libertarianism (laws imposed to control behavior "for one's own protection"), but so long as the police continue to prey only on the criminal population (those that break other laws), it is from my perspective an acceptable compromise.