Dave I suspect you are a lot smarter than I as I had a heck of a time following you down that trail, but I suspect we are discussing two different things and may not necessarily disagree in substance at least in the area at least in the area of statistics, emotions, reason and logic. It's really hard reconcile all those when trying to understand human behavior.
My point was only directed at the one aspect of relying on statistics all or in part to influence my behavior or that of others.
You are getting into emotions, causation of these emotions, interpretations of events and probabilities which guide populations or significant portions therein.
I began my formal study of human behavior in 1968 with courses in sociology, psychology, psychology, cultural anthropology, philosophy and followed that up with 30+ years of interviews, reading research administering various assessment instruments etc. and find myself scratching my head in confusion far more often than nodding my head in understanding.
If crimes appear to be more random and without reason, then the sense that they can be avoided through rational thought or action would be weakened.
You have touched on an excellent point with the exception, at least for me being seemingly minor, but vastly different, either way I believe it accounts for the dissonance between statically probability and peoples' reaction to it.
In my experience crime does not "appear" to be more random and without reason, it is. I discussed this with members of state and federal law enforcement and surprisingly some members of organized crime when it first began to, at least seem to us, to be really taking off. I'd bore you to death with an explanation/discussion.
As causation became so nebulous, how to react to, modify, understand it became all but impossible. Eyes all across TBN have glazed over if they've made it this far so I'll stop; way off topic, sorry.