Archery: Variable Range Increments

Following up from yesterday's post. A reminder on methodology.

I've taken men's longbow classifications from the Braintree Bowmen in the UK, ranging from 3rd class to Grandmaster Bowman; analyzed them with a tool I made to convert archery scores into to-hit rates on a d20; and applied those results to a variety of ranges for a 65cm target, which I reckon to be comparable to shooting at a human torso.

Each line on the chart represents a score in a "720 round" of archery, converted to be hit/miss against a 65cm target at the stated range.

Analyzing this chart, a thought occurred to me: instead of fixed range increments and a rising attack bonus, what if we had fixed attack bonuses/penalties and range increments that vary with level?

What we get is a system that seems (to me) much more verisimilitudinous. At short range, there's little to no difference in skill. At long range, shots that are essentially impossible for an unskilled bowmen will be easy for a skilled shooter.

What we give up is some granularity in progression, as we probably don't want the range increments to change in such small steps between levels that it makes no real difference.

65cm target	0	-5	-10	-15	-20
3rd Class	5m	10m	15m	20m	25m
2nd Class	10m	20m	30m	40m	50m
Bowman	15m	30m	45m	50m	65m
Master Bowman	20m	40m	60m	80m	100m
Grandmaster Bowman	25m	50m	75m	100m	125m
World-Class Bowman	30m	60m	90m	120m	150m

Now, how about changing target size? The following charts show the effects of changing the target size by doubles and halves.

 

What we can notice is that for each doubling of  target size, it's as if the lowest-skilled (31 score) bowman is shooting as if they were a middle-skill bowman (157 score). For the "Bowman", it's like shooting as a "Grandmaster Bowman", and so on.

So, changing target sizes can be fairly easily modeled by shifting the effective skill of the archer - double the target size, increase the effective skill two increments. So a "3rd-class" bowman shooting at a target 1.3m across would use the "Bowman" row on the chart.

This is for considered shots in good conditions. Later we will examine more adverse conditions.

Archery: Towards a Foundation

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.