We 'stand along the road' showing respect for fallen servicemen and women too. Army rangers who died in the Osama Bin Laden raid are treated differently than the Bank President who has a heat attack on the job.
Why?
We 'stand along the road side' because these people - police officers, firemen, and our military - have chosen professions where they risk their lives PROTECTING US. They ARE the sheepdogs.
The logger, the roofer, the bank president or truck driver can die on the job and the death is a sad event for the person's loved ones and family. And those in their circle of influence will be effected and suffer a loss. But it's not the same - and YOU free and freeaing - know that...you know the difference.
Of course I do, and that difference is exactly why statistics and math, to use your terminology, don't serve as the sole determinants of why people take the actions they do.
But I also know that there is an equally big difference between a person killed in an interaction with the police (or anybody for that matter) and somebody struck by lightning. And your argument that the risk of death by lightning strike and the risk of death during an interaction with the police are comparable is simply wrong. As was your statistical analysis, since you didn't compare against equivalent risk scenarios.
But none of that matters, since statistical analysis doesn't inform one as to the appropriate actions to take in individual situations. That's my point, and I suspect you know that too.
That's very commendable, but for the most part, cops do not protect you. If they did there would be no victims, crime etc.