I've heard the generalized "gunfight statistics" mentioned now and again. I've even heard the FBI mentioned in relation to them, and I've also heard of other major LE agencies having been involved in gathering info on shooting incidents over the years, as well. Some agencies have gathered such statistics and numbers since at least the 60's, and earlier. From how I've heard it mentioned by other LE instructors, this "FBI statistic" goes back to their days of carrying service revolvers.
I remember when I was a younger instructor, with a little more than 10 years serving as an instructor, the head instructor used to mention in classes a generalized categorization of deadly force incidents. He summed it up by mentioning that according to some LE statistics, most shootings occurred in diminished light, within 6 feet, and were over within 2-3 seconds. I've also heard it said that it might involve up to 4 rounds being fired.
Some instructors like to discuss different versions of the NYPD SOP 9 statistics, and there are certainly other LE-sourced training materials that go into detail about other agency reviews of OIS incidents.
I attended one of the traveling field classes of the FBI's LEOKA program about 10 years ago, and FWIW, the instructor didn't mention a neat one-size-fits-all "statistical ratio" of distance/time/shots-fired, although he did go into details about many other aspects of LE shootings and the criminals involved in them.
Ditto in a class I attended taught by former Chief, now Dr Steven A. Rhoads (40 year police veteran with experience in Virginia, Colorado and Illinois), called Detecting Danger. It's a class taught to LE, involving detection of the verbal and nonverbal clues transmitted by offenders who are anticipating the use of violence. While it naturally involves close contact situations, and discusses examples of OIS incidents, there wasn't any neatly wrapped up distance/time/number-of-shots-fired statistics offered to students.
I've attended 2 or 3 of the 1-day I've Been Shot classes taught by Lawrence Blum Ph.D., a clinical psychologist who "has treated hundreds of peace officers in the aftermath of lethal force encounters, traumatic crisis incidents, and the day-to-day challenges of police work". A good friend of mine was interviewed by him (so he could return to work) when he was involved in a couple of OIS incidents when he worked for LAPD. Lots of info in his 1-day seminars about incidents in which cops have been seriously injured, but nothing so neatly wrapped up in a statistical ratio package.