## Shooting and MOA

May 2nd, 2011

In working up WarSpike I often find myself down a rabbit hole of tangents and weird thoughts. Chasing new information and concepts and seeing where it leads me. Invariably this destroys much of the work I have already down, torn to shreds by some new ‘obvious’ notion exposing the flaws in my thinking. This may all sound like an utter disaster from a designers point of view, but this is where the magic happens, and interesting concepts come up from the chaos. What follows is born out of my determination to squeeze MOA (Minutes of Angle) into the shooting rules of WarSpike – which is a ridiculous idea seeing as the intent of WarSpike is to make a *fast*, simple, and intuitive, percentile system. What is presented below is all my thinking and justifications. It may not make it into WarSpike ‘as is’ but it will inform my designs in the future.

### Shooting

In WarSpike, shooting is modelled on real world ballistics and weapon characteristics. It’s not an exact simulation, more a rough model of the core concepts and important facts. All these concepts are then condensed, streamlined, and used as a basis for the rules. This grounds the rules in reality, yet I hope the final rules will also be quick and easy to understand. Like the other rules relating to combat there is the auto-hit concept at its heart, and all of this article is basically working out the base auto-hit range, and extrapolating percentage chances from that.

### MOA

1 MOA is equal to one sixtieth (1/60) of one degree, and it subtends to about 1” at 100 yards. This is a liner effect and double the distance will result in twice the deviation. So at 200 yards it would be 2″, at 300 yards it would be 3”.

MOA is used as a measure of a firearms accuracy. Under ideal conditions a rifle with 1 MOA is capable of grouping shoots within 1” of the centre of the target at 100 yards.

- MOA:1 @ 100 yards will put bullets within 1” of centre.
- MOA:1 @ 200 yards will put bullets within 2” of centre.
- MOA:1 @ 400 yards will put bullets within 4” of centre.

We can draw a circle around the centre of the target that encompasses all the bullet holes (specifically the centre point of the hole) at a given range. This circle creates a disc with the following areas.

- A 1” diameter disc has an area of 3.14.
- A 2” diameter disc has and area of 12.56.
- A 4” diameter disc has and area of 50.24.

Looking at this data we see that there is another pattern;

- The 1” disc has a surface area exactly one quarter of the 2”disc.
- The 2” disk has a surface area exactly one quarter of the 4”disc.

This lead to an idea;

### Premise

If a marksman, armed with a 1 MOA rifle, can hit a 1” diameter disc target 100% of the time at 100 yards – and if the range is increased to greater than 100 yards then they are 99% or less accurate – so 100 yards is the maximum of their ‘100%’ shooting ability;

We know that 1 MOA grouping of shots at 200 yards is 2”. A 2” disc is four times the size of the 1” disc. If the shoots are randomly placed over the surface of the 2” disc, we can assume that some of the shots will fall closer to the centre: within a central 1” disc. As the 1” disc is one quarter the area of the 2” disk, we can say that one quarter of the shots will land within the 1” disc.

So at 200 yards this marksman will hit a 1” disk 25% of the time. We can then construct a table of ranges and chances to hit for a given his specific level of ability.

- MOA:1 @ 100 yards = 100%
- MOA:1 @ 200 yards = 25%
- MOA:1 @ 400 yards = 6.25%
- MOA:1 @ 800 yards = 1.5625%

In looking at this chart we notice that each doubling of range decreases that chance to hit to one quarter. We can fill in the steps in between to make a more complete table.

- MOA:1 @ 100 yards = 100%
- MOA:1 @ 150 yards = 50%
- MOA:1 @ 200 yards = 25%
- MOA:1 @ 300 yards = 12.5%
- MOA:1 @ 400 yards = 6.25%
- MOA:1 @ 600 yards = 3.125%
- MOA:1 @ 800 yards = 1.5625%

Roughly speaking each increase of range by half, in turn halves the chance to hit. It’s not perfect: as, for example, really adding half again to 150 yards would result in 225 yards. Not 200 yards. So this does not fit the pattern we observed earlier. So the real number would be a bit less than 150 yards – around 133 yards for the 50% chance, but 150 is nice and neat so we’ll leave it for now.

### Calibrate Auto-hit.

Armed with all this information we can now calibrate a person’s shooting ability based on the maximum range they can hit a 1” target 100% of the time. This range is called their ‘**base range**‘. We can use their base range, and the above rules, to calculate their chances to hit at greater ranges.

If a person is armed with a pistol, and has a base range of 10 (can hit a 1” target 100% of the time as *10 yards*, but at 11 or more yards they are 99% or less) then we can use this figure to calculate their chances of hitting at greater ranges. Increasing the range by half, to 15 yards, will decrease the chance to hit by half: 50%.

- 100% @ 10 yards
- 50% @ 15 yards
- 25% at 20 yards
- 12.5 % at 30 yards
- 6.25% at 40 yards
- 3.125% at 60 yards
- 1.5625 at 80 yards

This is a complete breakdown of their chances to hit at each range band. By knowing their base range is 10, we can work out all the other range baned and their percentage chances to hit at each range band.

This can be written as ‘Pistol: 100% @10 yards’ or this can be shortened by stripping out all the repeating and no variable data. We know it’s 100%, and it’s measured in yards, so there is no need to use them. ‘Pistol: 10’

### Weapons MOA

Weapons which are not 1 MOA will decrease the range a marksman will autohit (100%). Basically 2 MOA results in one quarter of the hits of MOA:1 on a 1” target at 100 yards. So we can say that is a person who autohits at 100 yards, but is using a weapon is 2 MOA, will have one quarter the hits they would will an 1 MOA weapon.

Looking at the earlier chart we see that *doubling* range results in a quarter of the chance to hit. So it stands to reason that *halving* the range will quadruple their chances. From this we can work out the new range of the auto-hit: as increasing 1 MOA to 2 MOA will quarter the chance to hit 1″ target at 100 yards, but halving the range will quadruple the chance. So 2 MOA will be 100% at half range: 50 yards.

Therefore a person with calibrated 100% autohit @ 100 yards will have the following percentage chances to hit when using weapons with the follow MOA;

- 1 MOA = 100% a 100 yards
- 2 MOA = 25% a 100 yards
- 3 MOA = 12.5% a 100 yards
- 4 MOA = 6.25% a 100 yards
- 5 MOA = 3.125% a 100 yards
- 6 MOA = 1.5625% a 100 yards

We can then use this as a basis to work out the new auto-hit range for a given MOA.

- 1 MOA = 100% at 100 yards
- 2 MOA = 100% at 50 yards
- 3 MOA = 100% at 37.5 yards
- 4 MOA = 100% at 25 yards
- 5 MOA = 100% at 18.75 yards
- 6 MOA = 100% at 12 yards

Using this data we can work out a rule for the effect of a weapon’s accuracy one the marksman’s auto-hit range.

- 1 MOA – no change.
- 2 MOA will result in half the base range.
- 3 MOA will result in (roughly) a third of the base range.
- 4 MOA will result in quarter of the base range.

### Notes

There is a lot more that has to be build on top of this concept. Snipers need additional skills. They need this shooting skill, but also a special (separate) skill to work out how to alter their sights to account for bullet drop and windage. Pistols and assault rifles generally have MOA far great than 1, 3-6 or more! This may sound bad, but in WarSpike the human target is not 1”, it’s a diameter equal to their Stature: a 6′ man would present a kill zone target area 6” across, which makes it much easier to hit with an assault rifle – assuming they are not moving!

Categories: Concepts, Rules, Thoughts |

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This is a fantastic system Philip. I like the breakdown and seems to me a good way to work this into a faster rule set would be to gauge the MOA toward a common base size, like 25mm disks. That would allow you to target most miniatures in certain percentages very easily. Larger bases would be larger critters and thus easier to hit.

That may be an idea for the Tactical Sphere, speed rules there, and base sizes are a good visual cue 😉 It should match my ‘real world’ thoughts that a 6′ man has a critical target area 6″ centered on the chest. It about the same as paper target markings. Most creatures using 25mm base area human sized and around 6′?