Friday, 31 July 2015

On Archery

When I presented missile range penalties for Explore, I gave a to-hit penalty of -1 per range increment over 20’ (where ranges go up as 20’, 30’, 40’, 60’ etc., doubling every other category). This fits the main overriding requirement - "simple" – but was unsatisfactory for a number of reasons which have niggled:

1)      Does this increase in difficulty reflect the real world?
2)      What about large or small targets?
3)      What about shooting long range against mass targets?
4)      Should there be a damage penalty for long range?

I left this for a while to ponder over, until I realised that I could resolve the first three together, the fourth I'll talk about another day.

The revised rules are:

For missile attacks there is a to-hit penalty of -3 per range increment over 30'.
Large or small creatures get a penalty versus missile attacks equal to their size.
Missile attacks versus mass targets get -6 at any range.
If you care which of the mass targets is hit, roll to choose a target, then roll to hit it.

The details of how I derived these rules follows, but the derivation itself is of less importance than the fact that they are derived from observations, not purely arbitrary, which is a core design philosophy for Explore. When you design this way you find that the rules work together, whereas with independent rulings they often don't mesh well.

To-Hit Penalties For Range
Following Delta's post on archery accuracy, I agree that it is best to model increasing the range to a target by instead reducing the size of the target. That is, if you double the range of a target then that's the same as making the target one half the diameter. Also I agree you can model the distribution of shots as a bivariate normal distribution (i.e. both the x and y positions of the shot are normally distributed). Adjusting the figures to match the data he cites for "Britain's finest archers" I get the same answers as his calculations. For the range categories in Explore you get:

Target #







I have extended the list past normal ranges as those values will apply at shorter range for lesser archers, added the "simplified" range category, and the equivalent target numbers and chances with 2d10 (open).
Each increased range category equates to halving the area of the target,  and as such you would expect the ratio of successive chances to tend towards 2. You can see this at the bottom end of the results (10%, 4.9%, 2.5% etc). This matches exactly adding three onto the target number in Explore.
On the right half we give the new rule for Explore (each increase in range gives -3). We can get an exact match for the start of the results, or the end of the results, but not both together. I have opted for the low range results to be accurate, with the long range ones being half the predicted, with the hand-waving explanation that long range presents extra difficulties in judging distance.

Point Blank Range
In Explore "finest archer" would be +13 (+3 from stat, +10 rank bonus). The lowest parry you can get is 4 (10 -3 for stat -3 for surprise), so that's the parry for a stationary target. So the standard target # they need would be -9, hence they're getting 11 penalty for range, so roughly four range categories. So this would make point blank to be 30'. This is a slight increase from the previous 20', but as range penalties are now quite severe that seems fair.

Large and Small Targets
For large targets, +5 in size makes you double the height and six times the weight, so 2 x 1.73 x 1.73 times bigger so 3.46 times the cross-section. Hence for every +3 in size you’re roughly double the cross section, so present the same size target as being one range step nearer, so should get -3 versus missiles. Thus you should get a penalty versus missiles equal to your size (which is a +3 bonus versus missiles for halflings).

Shots versus Mass Targets
Consider shooting at a mass of targets compared to a target placed 30' away. A single person 40' away would fill half that target. Four people 80' away would also fill half that target, and even 512 people at 960' away. Hence each group of people is the same difficulty to hit - it's the density of the troops that matters. Since troops are unlikely to completely fill the target, I'm going with -6 versus massed troops (instead of -3).

In summary, following Delta's observations about real world archery gives us a single principle that gives us rules for three different situations.


  1. Finally I have a chance to post my thoughts on this here. I concur with Delta's analysis about treating range as reducing target size, but I think this falls apart somewhat when firing at long-range dispersed targets. I think of the dispersed target as a big area that the archer is just trying to drop an arrow into somewhere. The target is quite large, so it's not hard to hit the area. But what's important here is, how much of the target area actually has a target in it? And also, what's the effect of angle of incidence -- what you really want is the projection of the actual target area into a plane orthogonal to the arrow's direction of flight (also allowing for potential overlap/shadowing of individual targets). If (to choose a simple example) the target area is 50% real target and 50% empty space, then it's simple in your system: just apply an additional -3. So I think you're baking in some assumptions about density of the massed troops. Personally I think 50% density is a bit high, but that's probably because we have different mental images of the targets.

    I guess one question is, where do you transition from shooting at an individual target, vs. at an area that is n% full of targets?

    Another thought that occurs -- you could have archers shoot at one individual target in a mass, and if they miss by, um, not very much (depending on the density and other modifiers) you could rule that they hit SOMEBODY, just not the guy they were aiming for.

  2. Thanks Leland. I've answered these questions in a new post -