I think this is a question of methodology. If you have an aggressor at 50', but don't take any action and he closes to 10' before you shot him did you have a successful 10' gunfight or a screwed up 50' gunfight?
I end to go with successful 10' ...
When does the fight start? When you think their might be a fight or at the first trigger press?
Here I think it's when you identify the threat, 'reasonable man' standard. A guy with a knife at 50' isn't much of a threat - he can become one quickly, but somebody on the other side of the street from me, waving a knife and screaming in my direction, cannot be shot without more obvious danger (IMHO). A guy with a rifle, taking aim, is different.
I don't know that there is any way to get really useful metrics about encounter distances.
Well, not much more is worth the effort for
me to do; sounds like a nice Master's thesis for a Criminology student. The easy data sources just don't have a lot of data verification and vocabulary standardization.
But part of that thesis ought to be why the distance makes a difference.
As I have thought about it, I think I sorted my results into three categories because it seems to me to break down by how much time one has to aim (and, on seeing the incident reports, I couldn't justify any more precision). I'd call them "no time to aim", "time for a sight picture" and "do I really want to take this shot?" distances. Using myself as my standard, I don't think there would be much difference in how I approached the actual task of shooting when the target is at 18 feet or 27 feet or 36 feet.
Time to aim is going to have differences based on a number of factors besides distance, e.g. weapon, movement, light/dark, other people, home/out, etc.
Other people, of course, may have different training and experience that would make those variations in distance more significant. Just being younger than I am, or having better vision, may extend your shooting abilities beyond mine (which, honestly, wouldn't be much of a stretch
)