When to carry? We must remember that statistical improbablity does not mean impossibility! There are some events where the consequences of an event are so severe that, even if the odds are remote, the consequences demand that action be taken to address that consequence. For example, the vast majority of Americans will never have their house burn down (a very low probabilty), but the financial consequences are so huge if it does happen that we carry fire insurance on our house.
The same can be said with regarding to carrying a firearm when legally allowed to do so. It is not the probability that matters, it is the possibility. There had never been a gunman hit the Aurora movie theater before, and the odds it would happen were statistically minute, but it did happen. Trolley Square in Utah had never had an active shooter before, the odds were minute, but it was possible and it did happen. I could continue to offer lists of active shooters, robberies, home invasions, etc. The consequence of being unprepared: Your life or the life of your loved ones, or serious bodily injury.
Statistical probabilty only works on a macro scale, not a micro scale. If 10,000 homicides occur in the US each year (a made-up number) out of 300,000,000 people an over-simplified analysis would state that you have a one in 30,000 chance of being a homicide victim (good odds); however, if you are one of the 10,000 your odds were 100%. In other words, the macro number means nothing when the event occurs in your life or to you.
Further, irrational behavior by definition cannot be rationally predicted on a micro level. So we can predict at a macro level that a psycho will go off somewhere this year (e.g. Sandy Hook), but we cannot predict when, where, and to whom it will occur. Thus relying on statistics to "feel safe" is irrelevant. One's feelings are just that - an emotion - and reality may or may not reflect that emotion. A 2 year old feels safe playing in the street, but reality says otherwise. If, like the movie "Minority Report," we could predict where, when, and how a crime would take place, we would be there with police to arrest them beforehand, or you and I would not go there, but that is never the case.
We can avoid stupid people who are doing stupid things at stupid times and at stupid places, but sometimes evil comes to us. If we are not prepared, we, or our loved ones, may pay the ultimate price.
When all is said and done, what we are really talking about is the "inconvenience" of constant carry.
Remember: Preparation is a minor inconvenience suffered if it is never proved necessary. Lack of preparation can have deadly consequences.