Mike McDaniel has a post at the American Thinker entitled Gun Fights: Is the "three threes" rule accurate? He looks at several studies dealing with the distances at which gun fights are initiated. Of course, the second "three" deals with the number of rounds shot, which does not factor into any of the charts.
A common teaching tool among professional is the “three threes:” gunfights take place within three yards, take three seconds and no more than three rounds are fired. As a means of focusing student’s minds on the realities that when things go bad, they go bad fast, and one must be prepared for that, it’s a useful idea, but does it represent the truth? That depends on to whose statistics one refers, also whether the “gunfights” involve citizens or on-duty policer officers. In 2021, Chris Baker at Lucky Gunner provided pertinent details.
Interestingly enough, most of our data for the "three threes" rule come from law enforcement sources. But as McDaniel points out, law enforcement shootings may not match civilian shooting data. After all, civilians don't usually go after dangerous criminals on purpose, and normally aren't the target of dangerous criminals either. The more useful numbers come from Tom Givens of Rangemaster Firearms Training. Please see the graph provided at the highlighted article, which indicate that 87% of the shootings studied occurred at between 3 and 5 yards.
What lessons can we learn from these admittedly limited statistics? We might revise the threes rule to “around three yards+.” We don’t know the duration of these incidents, the accuracy of the anecdotes, nor the numbers of rounds fired. Experience suggests three rounds is in the ballpark, but that applies to the innocent shooter. More may be fired by bad guys.
Statistics are useful for generally constraining your training to the most likely of scenarios. So, McDaniel's "around three yards+" seems like good advice. The truth is that whatever you are confronted with will be what you have to defend. For most of us, the time we have to train is quite limited, with work, family and other responsibilities taking up most of our time. Of course, we should all be prepared, but understand that it is the bad guy who will chose the time and place to attack.