A Different Angle on Accuracy and Precision

The other night, I had a dream that insisited that I should go back and re-read a webpage I had encountered about a week ago. This article was the key to a new way to look at accuracy, my dream told me. (Even my subconscious tries to sell me on clickbait, it seems!)

Firing from a squat position

I am not sure this article actually does that, but it makes for interesting reading, the little that I think I understand. Since I do not read Cyrillic and some of the translation choices are unusual, I am missing certain parts.
AKM Golden Ratio
One part that was very clear was:

…monograph of the Central Research Institute of Information “The effectiveness of automatic firing weapons”:“ 3.5. The degree of combining the midpoint of hits with the center of the target ..determines the accuracy of shooting”

This reminds me that the effective range of a weapon system is a product of target size and weapon system accuracy and precision.
Accuracy and Precision Explained

How Accurate Do You Need?

For an example, let us consider a system of a shooter, firearm and ammunition.
Firing semi-automatically, this system manages groups of about two and three-quarter minutes of angle/arc (MOA). This will not impress many of you, but we are considering this system shooting in combat conditions rather than on the target range.
2.75 MOA may be treated as three inches at 100 metres. (It is actually 2.858 inches at 100 yards/91 metres, but we will treat it as the former for purposes of illustration)
A human head is about six inches wide. Providing our shooter can aim and shoot competently, we can expect our shooter to make most head shots within 200 metres. Not too shabby!
Most decisive rifle combat takes place at under 200 metres. Most likely targets will not expose an area much larger than a head. Our three MOA shooter’s accuracy and precision is quite adequate.
As an aside, would it not be more realistic to make all combat targets head-sized? Since targets would only need to be A4-size, this would save paper and money!
The vital area of a deer is also around six inches or more. And most hunters try to take deer at well under 200 metres.
Make things even simpler for yourself by zeroing your rifle to 200 metres. 72% of rifle engagements occur at 200 metres or less.
Learn the correct holdover/aiming point for the rare times you will need a longer shot. There is unlikely to be time to fiddle with your sights and dial up the range.
What about torso shots? A human is about 18 inches across the shoulders, about three times the width of the head. Our shooter should be able to put bullets within a torso out to about 600 metres. 
It is worth remembering, however, that a bullet takes around a second to reach 600 metres. Even if you are a trained sniper, you will have to make a shot like this as a surprise attack.
If the enemy is aware of you and dodging, ducking and dashing, hits are going to be more a product of luck than skill. Might be better to save ammo until it may be used more effectively?
Shots against active, distant targets are best left to the machine guns, mortars and artillery. A machine gun that was firing at 2.75 MOA would probably be well regarded. At 600 metres it would put most of its burst into an area less than man-sized.
Full frontal torso shots may actually be rare under certain combat conditions. Many targets will be in cover and not exposing much more than their heads. What torso shots can be made, will be against targets crossing your line of sight or moving obliquely.
If we consider the apparent average torso width here as about twelve inches, we can expect our shooter to make hits out to 400 metres, should targets be actually visible at this distance. 97% of rifle engagements do not exceed 400 metres.
Our shooter should keep his rifle at a 200 metre zero and aim somewhere between armpit- and chin-height. This will produce a hit somewhere on the torso from 200 metres+. A higher aim point may be needed as range approaches 400 metres and beyond. The bullet will hit about 30 cm low of the aim point at 300 metres, three-quarters of a metre low at 400 metres.
Time of flight to 300 or 400 metres will be about a third of a second, so he should lead his target a little, but not too much.
So far we have only considered semi-automatic fire. If our shooter fires on fully automatic and measures the diameter of the group produced, effective range for automatic fire against head and torso targets may be calculated.


The Russian article makes the point that there is little point in adopting a more accurate/precise rifle if the sights are flawed.
The small group the AN-94’s hyperburst produces just makes it more probable for both rounds to miss the intended target if the aim point is wrong.
Generally, it is the shooter rather than the weapon or ammo that is the limiting factor.
Many of you reading this are capable of shooting a rifle better than 2.75 MOA.
If so, you are have adequate precision for realistic combat/defensive scenarios, which are most likely at less than 200 metres.
The ideal iron sight for combat would probably be an L-flip sight with a 5mm aperture zeroed to 200m and a 1.75mm aperture zeroed to 400m.
But, for such an application, does even higher precision actually contribute to a real increase in functionality?
As long as the group we shoot is smaller than the area of the likely target, at likely engagement ranges, is a smaller group actually a practical advantage?
Is it even possible that a tighter group may decrease our chances of hitting the intended target if our aim is slightly off?
Something to ponder before you hand over your hard-earned cash for the latest customization or accessory to give your defensive or deer rifle even greater sub-MOA performance?

Crash Course in Rifle

A friend of mine was reading about the training of conscripts in Taiwan. He referenced some of the articles I have written about making training more relevant. These include my blog on the “Murray System” and the book that derived from it, my book “Crash Combat”.
Crash Combat is about unarmed and non-firearm combat. For a more generic training program, where would I start?
Probably, near the start, would be an introduction to practical use of the rifle, taught in several phases:

Introduction Phase

• Basic safety and orientation.
• Perceive, Recognize, Engage.
• Load, unload and clearing.
• Anatomy for shooters: The Lethal T, the belt-buckle aim and the armpit line.
No one goes past the introduction phase until the instructor is convinced all students are competent and mature in their handling of firearms and their behaviour on the range.

Phase One

This phase teaches shooting from behind cover, from various positions. It ingrains the habit of always using available cover, while teaching shooting posture fundamentals.
Firing from a squat position
Start with prone position and move on to other positions such as kneeling, sitting and squatting.
Key points:
• Fire around rather than over cover when possible.
• Keep low. Never be reluctant to get close to the dirt.
• Always use cover when possible.
• Use cover when reloading and clearing stoppages.
• What parts of a gun not to rest in contact with hard cover when firing.
• Includes section on correct techniques to use when firing from windows.
Phase one is conducted with half-silhouette targets of various sizes, engaged at relatively short ranges, such as 20 to 50 metres. Sights zeroed to 200 metres are used for all shooting.
Emphasis in this phase is on building the student’s confidence in their shooting while teaching good shooting postures and tactical positions.
There are no scores, shots being judged as either hits or misses. Reactive targets that make a noise, fall or flash a light when hit will prove useful.

Phase Two

Phases two is dry firing. It is effectively kata for guns, or tai chi with triggers.
As recommended by Elliot, students practice mounting their rifle to bring it smoothly up to firing position. This is practised in the various postures learnt in phase one.
Mounting is combined with tracking, breathing and trigger exercises:
• Tracking involves keeping a mounted weapon moving to pursue, swing through and lead a moving target.
• Breathing involves synchronizing the respiratory cycle with the moment of firing to minimize unintended movement of the weapon.
• Trigger exercise is developing a trigger “press” that causes minimum displacement of the barrel.

Phase Three

Phase three is Quick Kill training.
Airguns/airsoft guns with the sights removed are used to engage small thrown targets. This builds on the instinctive pointing and tracking skills developed in phase two. Phase three teaches effective engagement skills for situations when there is insufficient time to align sights or when sights are not visible.

Phase Four

Introduction to room-clearing techniques. The likelihood of operations in urban terrain means a familiarity with room clearing must become a fundamental skill-set of any firearm user.
• Shooting on the move and while sidestepping.
For safety, phase four may be practised with airsoft weapons.

Phase Five

Phase five is a repeat of phase one, but the engagement range is increased up to 250m.
Students may be required to crawl to a firing position, or use other appropriate modes of tactical movement.
Target shooting, long-range shooting, volley fire and other fields can be taught later. Soldiers with an aptitude for these disciplines can be encouraged accordingly.
The five phases are designed to quickly produce riflemen that can respond quickly and accurately against threats that occur within likely engagement ranges and terrain.

Leading Targets for Lead

If some field manuals are to be believed, determining the lead for a moving target involves:
• Correctly determining the range to the target.
• Remembering the time a bullet will take to reach that distance.
• Estimating the speed of movement of the target. For added complexity estimate this in miles per hour and convert.
• Calculate how far the target will move in the time the bullet gets to reach it, and aim that distance ahead.
• Don't forget to halve the value if the target is moving obliquely.
You will probably have under a second to do this as the target dashes between cover.
Andrew G. Elliot, “Shooting to Kill”:
“The impossibility of judging this consciously will be realized when it is explained that a target moving at this range and speed scarcely allows time to place the rifle to the shoulder without making complicated mathematical calculations.
“In war, as distinct from print, there is hardly time to aim at all, and that is why the whole technique must become so natural that it is carried out without thought.
“…The secret of hitting a moving target is simple. Follow the target with your aim for a few seconds to judge its speed, then just before firing, quite instinctively and without any conscious allowance, you will find that you swing a little in front of the enemy.
Always keep your eye on the target, and for a moving one, on the front of it, so that- if you are shooting a running Nazi, focus the front buttons of his tunic.
“…In shooting moving targets, one need not worry about the sights. The Nazis will rarely give you any time for that!
“To prove that instinctive allowance is easier than conscious effort, it has been found that many men can shoot better in the semi-darkness than in daylight. I myself have often shot running rabbits with a rifle when the light was such that I could only just see the animal’s outline.”
Elliot was a big advocate of soldiers spending time practising raising, swinging through and dry-firing their rifles. This was time much better spent than squarebashing.
Note that swinging through is not the same as the tracking of a target that some manuals describe. Swing through overtakes the target.
The swing-through method of leading a target cannot always be used. From certain postures or firing positions it is difficult to use. In such an instance one must use the ambush method. Aim at a point in space and fire when the moving target is the correct lead distance from your aim point.
For simplicity, the following will assume targets are dismounted personnel. Shooting at drones, aircraft and vehicles will not be covered today.
Note that if you need to quantify a target's velocity, it is more useful to judge it in metres per second than units such as miles per hour or km/h. This is something that you can observe and make use of in the field.

Depths of Lead

Possibly the easiest technique to learn is found in field manuals for the M14. The M14 was zeroed to 250 metres so the nearer aim point is also lower to allow for hold-under.
Depth of Lead for Moving Target
The method is based around a measure I call a “depth of lead”. This is approximately the depth of a human torso, from sternum to spine. It is also roughly a foot if you are viewing your target side on. If the target is moving at an angle to you, the depth will appear smaller and the amount of lead you apply will be automatically reduced.
Bear in mind that lead is often overestimated. At less than 50 metres most moving targets will not need leading. Those that will will only need aim shifted towards the leading edge.
For targets that are more distant, or moving fast:
• If the target is moving slowly (less than 2 metres per second), and within 200m, aim at the leading edge or the button-line/belt-buckle.
• If speed is slow but range greater than 200m, add one depth of lead.
• If moving fast, but within 200 m, add one depth of lead.
• If moving fast AND beyond 200 m, add two depths of lead.
The amount of lead this gives may differ somewhat from a calculated value. Given all the other factors in play during combat, it is generally “close enough for government work”.
Two complimentary systems will be mentioned:

USMC Points of Aim

This first is that given in USMC MCRP 3.01A Rifle Marksmanship.
This is an excellent work for fundamentals and how to utilize iron sights.
The “point of aim” system appears to resemble the “point of depth” method, but has differences.
Marine Point of Aim for Lead
“One point of Aim” in the marine manual is actually aiming directly at the target's leading edge. (The above illustration could be clearer on this.)
“Two points of Aim” is placing the top corner of the trailing edge of the front post on the target's leading edge. Two points of aim is used for a fast-walking (2 m/s) target at 300 metres or a running (3+ m/s) target at 200 m.
These leads are reduced for targets not moving perpendicularly.
The actual offset this will produce will depend on the apparent width of the front post.

US Army Single Lead Rule

Single Lead Rule
The technique given for leading a target in US Army FM 3-22.9 (August 2008) at first glance seems the same as MCRP 3.01A.
The army “Single Lead Rule” actually uses the trailing edge corner of the post to sight with.
Unlike the marine method, the corner of the post is targeted on the centre rather than the leading edge. This technique automatically increases the amount of lead as distance increases. Lead is approximately 5 MOA. If you miss, increase lead.
7 mph is about 3 m/sec.
The manual notes: “At 100 meters, the rule begins to break down for targets moving at slight and large angles.”
Despite this, it seems a useful technique to get in the ballpark.
AT4 Slow TargetAT4 Fast Target
This aiming technique is very similar to that used for the AT4/M136 anti-tank weapon.
For a slow target the post is placed on the leading edge of the vehicle.
For faster targets one of the “horns” is placed on the centre of the target.
Aiming at faster targets such as jeeps and technicals does not yet seem to have made it into the copies of the manuals I have. Placing the horn on the leading edge seems like a logical place to start.
Amusingly, the copy of FM3-22.9 I have insists that iron sights on the M16/M4 are now only for backup. The entire section on leading a target only refers to the use of iron sights!
Below is an example of using the ACOG sight with a depth of lead-type method. Using frontal silhouettes is misleading.
Depth of lead with ACOG reticle

Aim Low! Avoid Disappointment!

Because it is what was taught in basic, many shooters assume that “center of mass” is the optimum approach to bullet placement. It isn't.
Firstly, “center of mass” is something of a misnomer. What we are actually attempting is placing the bullet in the centre of visible shape. While the term “center of mass” is freely used, it is seldom defined. I think of it as the centre of an X drawn from shoulders to hips, but I suspect others may use different visualizations.
If you have learnt a little anatomy, such as reading “Attack, Avoid, Survive”, you will understand that putting a bullet into the centre of shape will often avoid hitting the central nervous system unless the enemy is running straight at you.
Often you will not have a shot at the torso. When a head appears around cover, firing at its centre will often result in a miss. A better point of aim is about an inch below the visible area.
Center of mass does have its uses. It is taught since it is felt to be easy to learn, and it is because it is what we have always done. Against a vehicular target, center of mass (or leading edge) is a good aimpoint. If you are springing an ambush, chaos and disruption are primary objectives. Multiple wounding shots or near misses may be more effective in that context than a lesser number of clean kills.
In “Attack, Avoid, Survive” and “Survival Weapons”. I explained shot placement in the context of anatomy. If you have a relatively good view of your target, or sufficient time, this is your best approach.
The following two illustrations are of interest:
Shot Placement for Snipers
The first is taken from a WW2 manual for American snipers (FM21-75 Feb, 1944 p.172). The rifle was zeroed to 400 yards and the shooter encouraged to use offset aiming rather than adjusting their sights. Note that at 400 yards the intended target appears to be the armpit-level line, as advocated in my own books. At less than 400 yards, the sniper is recommended to aim twelve inches below the intended point of impact.
M14 Aim Points
The second illustration is from a manual for the M14, which was zeroed to 250 metres. At ranges of less than 200 metres the round would hit high so soldiers were taught to aim at the bottom edge of the “center mass”.
Most military rifles are zeroed to 300 yards or metres. Some older models have battle sights set for 400 yards. Yet most combat shots are made at less than 200 metres, where the bullet is expected to hit several inches above the point of aim! Any wonder that shooting directly at a face will so often miss?
In combat, it is common for troops to shoot high anyway. This is partially stress, but also poor visibility makes targets appear more distant. Fog, smoke or darkness, or a low shooting posture, will cause a shooter to tend to fire high, Differences in elevation will also have an effect.
Firing through a sloped windscreen will tend to deflect a bullet upwards. This occurs if outside firing in or inside firing out. The solution is to aim low.
Often a target will be at a higher or lower elevation. You may be firing down from a hill, or being fired upon from an upper window or roof.
The actual range to the target is not a straight line between the shooter and target. Imagine a right-angled triangle, with the shooter at one corner and the target at the other. It doesn't matter which is higher, since the effect is exactly the same both “uphill” and “downhill”. The direct distance between shooter and target would be the hypotenuse of the triangle. As far as the bullet and gravity are concerned, the relevant distance is horizontal, the length of the triangle base. The true or horizontal range will always be shorter than the slant range.
Using a 5:4:3 triangle for illustration, the horizontal distance will be 20-40% less than the direct line between target and shooter. Shots up or from elevations tend to hit high.
There are two solutions to these effects. If you have any choice in the matter, zero your combat rifle to 200 metres so that it tends to hit what you point at. This gives a mid-range trajectory of only two or three inches.
For longer ranged shots, learn the correct holdover and offset aim-point. Tactically, you are often better off waiting for an enemy to get close or pass by.
Long-range engagements are better left to machine-gunners, mortars, snipers and riflemen with aptitude.
The second solution is to make the belt-buckle your default point of aim. I believe there is an episode of the Simpsons where Homer claims the family moto is “Aim Low! Avoid Disappointment!”.
• If you are at a higher or lower elevation, aim at the target's belt-buckle.
• If you are uncertain of the range, aim at the belt-buckle. A short shot may still glance off the ground and hit the target.
• If the target is moving, visualize the belt-buckle and aim for it. This method automatically tends to adjust for relative angle of motion. If the target is moving obliquely aiming for the buckle will put less lead on the shot.
• If a target is moving towards you, aim for the belt buckle or lower. The use of shots at the pelvis against charging enemies is explained in Attack, Avoid, Survive.
• Unless range is very short, snap shots should be aimed at the belt-buckle.
• A target may be prone, or looking around cover. Aim your shot about an inch below the visible target area. A low shot may still endanger the target.