I was thinking of archery, and was immediately reminded that Delta had done some good work on the subject some time ago: http://deltasdnd.blogspot.ca/2014/04/a-model-of-archery-for-d.html
There's some good stuff there, and I think the methodology is promising, but I think some upstream errors make it less useful/accurate than it could be. With that in mind, I set out to build on those ideas.
Delta used an article in an old Dragon magazine by Robert Barrow (Dragon #58, pp 47-49) as his starting point, which in turn cites Archery by Longman and Walrond, published New York, 1894. I was not able to find that edition online, but did find Archery by Longman and Walrond, London, 1894, which surely must be different edition (likely the original edition) of the same book. Unfortunately, the page numbering is different, and Barrow's citation of pp 240 leads us to a discussion of the history of the Royal Company of Archers in Scotland, which, while no doubt interesting in its own way, bears not at all on the matter to hand. There is a helpful chart on pp 264, which I would have surmised is the one used by Barrow, except that when I tabulated the data, it doesn't quite match the figures he quoted.
Barrow quotes 92%, 81%, 54% hits at 60, 80, and 100 yards, respectively. I calculated 96%, 86%, and 65%. Perhaps there was an error in his calculations; it was, after all, 1982, and he likely did not have a spreadsheet to do the calculations quickly and easily. Or perhaps he was simply using different data from a different part of the book and the editions are even more different than seems likely. In any case.
What I've done is write a little commandline tool that allows us to enter in a wide range of archery scores and get back out a hit rate for a given range and target size. The Archery data was useful, as it had a hit rate and a score, whereas most modern sources only list the score, and this was very useful to make sure I was getting sane results. I can set the output and input ranges and target sizes to be the same, and the compare the hit rate my model predicted based on the score with the actual hit rate in the data set. I found results were typically within 10% or so, which I'd say is more than good enough for our purposes.
One thing I can tell you - modern archers are much, much better than the archers in the Archery dataset.
So, with this tool in hand, I set out to find some data on how good archers are. I didn't just want a soup of scores, I wanted some guidance/interpretation of what those scores meant. Eventually, I found this site, which helpfully lists scores for 6 "classes" of archers, from 3rd class to Grandmaster. It didn't go all the way to Grandmaster for the 720 round scores I had calibrated my tool for, but this site helpfully allows you to convert a score from one type of round to another (using a similar approach to the CLI tool I made).
So, this got me scores with meanings attached, and my tool allows the conversion of these scores into hit rates for any target size and any range. Results of my investigations in a subsequent post.