12 August 2018

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.

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