Actually, IIRC, the stats were from an IACP (International Association of Chiefs of Police) study, don't recall the date, but you can find it cited in Ayoob's "The Semi-Automatic Pistol in Police Service". I expect you can also get ahold of a copy of the original study if you try. I always did wonder how the reports could reconcile a 2.7 rounds per encounter stat with a published hit probability in the same report of 20%.

Now, those were averages. I recall a western highway patrol unit that was running mid 60% with round guns. NYPD has had some notable incidents where multiple officers emptied their Glocks with minimal results. Training is the more important issue, but the trigger of the average stock auto isn't as stiff as the average stock revolver, therefore easier to hit the target with. Our average qual scores went up when we made the transition back in the early 1990's. In fact, we went something like 8 years without anyone who required qualification enhancement (PC for remedial) training.

The number of shots/encounter I'm quoting are from the last publicly available NYPD Police Firearms Discharge Report that I studied. At 33K cops, they make up the bulk of the FBI stats anyway. NYPD incidentally, is meteculous in their stat keeping. The widely publicized old stats included AD/ND/UD incidents, suicides, putting down critters and other discharges that weren't 'gunfights'. The first time NYPD only counted actual BG/GG armed encounters the average number of shots jumped from 2.7 to 4.7. That was before they accounted for 'shootings' and 'gunfights' differently. And yes, the numbers do change somewhat from year to year.

Perhaps the most troubling part of the NYPD report was the section on unintentional discharges. 75% of them happened during what most of us would consider routine handling, including loading/unloading. The disturbing part of the report was that 50% of those UDs causing personal injury, generally of the person handling the weapon.