How To: Improve Shooting Accuracy And Hit What You're Aiming For
An Easy Way To Correctly Measure Accuracy and Precision
Whether you are target shooting or hunting, accuracy and precision are the most important skills you need to develop. Ok sure, safety is the most important skill to develop, but presumably if you only hit what you’re aiming for, you’re also safer. There are many classes and videos on how to improve your technique and shoot better (I would recommend an Appleseed), but not as many teaching how to measure your progress.
Before you go hunting, to a competition, or just out to the range, it would be good to measure your baseline. Can you expect to make that 100 yard shot? How likely are you to hit the target, whether that’s an ethical shot on an animal or hitting the bullseye every time?
In this article, I’ll provide you the language and tools to measure your capabilities. That will help you grow as a shooter, but most importantly, this will establish who among your buddies deserve the most bragging rights.
Accuracy vs Precision
(Target aggregations using ShotHero)
The target on the left demonstrates accurate shot placement. The target on the right demonstrates precise shot placement. Accuracy tells us how close we are to what we were aiming for, the bull’s eye in this case. Precision tells us how close the shots are to each other.
The black ring in the circle is approximately one inch in diameter. If our goal was to hit that one inch target, the precise shooter above would have missed every time while the accurate shooter would have hit 50% or more of the time even though they’re spread out. The accurate shooter would have won this competition.
Given the opportunity for a second round, however, the precise shooter could adjust their sights to hit the target every time. And if penalty points are deducted for missing the target, the accurate shooter above would end up behind.
If the target size on an animal is the size of the inner circle, neither of these shooters would consistently make a clean shot.
The goal of a shooter is simple… learn to shoot more precisely and also learn to adjust their rifle to be accurate at whatever range they are shooting at.
How do we measure: Apples to Apples
The first thing to do is standardize our measurement units. Units … those things we learned in physics that always have to be part of the answer. We’re all used to measurements like inches or centimeters. Those are basic units of length and great for measuring things. But if we only used distance measurements, we’d be missing some important information. Someone who kept their shots within a one inch circle at 25 yards is not shooting as well as someone who kept their shots within a one inch circle at 100 yards.
We need to include the shooting distance in our measurement to compare these two targets. And to do that, we could take the simple idea of dividing by the distance. One inch divided by 300 inches (25 yards) vs one inch divided by 1200 yards. That’s 0.0033 vs 0.000833. In this case, smaller is better. We can say with some confidence that the 100 yard shooter is shooting 4 times better than the 25 yard shooter (0.0033/0.000833 with repeating decimals is 4)!
What we’re measuring here is the spread over the distance.
Sadly for us, the shooting world doesn’t use this particular unitless measurement. We need to add another layer of math.
Think back to Geometry or Trigonometry. Any time we measured rise over run, we’re talking about the angle between two perpendicular lines. Here’s that rise over run re-envisioned:
That angle, ⍺, is a unitless metric that tells us how long (inches or centimeters) a measurement will be at any distance (25 yards or 100 yards). We’re not going to get into the math to calculate that because we have tools to do that for us, but it’s good to understand that the measurements we’re about to talk about are basically ⍺ times 2.
The two major metrics people use to describe this measurement are MOA or MIL.
MOA - Minutes of Angle
Originally (in math), this meant “Minutes of Arc”, but people started saying “Minutes of Angle”, and that’s the term we use now. What’s a minute of arc? Well, there are 360 degrees in a circle. Sixty being a popular measure in the English world, there are sixty “minutes” in every degree. So one MOA is one-sixtieth of a degree.
It’s not super important to remember all the details about it, but one MOA is approximately one inch (1.047) at 100 yards. Shooting less than one MOA is the first goal of most precision shooters.
MIL - “Thousandths”
Again, shooting differs from Math. In math, “MIL” would usually stand for milli-radians. Thousandths of a radian (a circle has 2π radians). If you’re unfamiliar with radians, just think of them as the metric version of degrees. That means, there would be approximately 6283.185 milliradians in a circle (where there would be 21,600 minutes of angle in a circle). That’s not a fun number to work with in the field, so various militaries rounded it to 6400. A little like rounding Pi to exactly equal 3, but that’s the military for you.
So we instead use the term “MIL” to mean one 6400th of a circle. Where one milli-radian would be exactly 10 centimeters at 100 meters, one MIL is only approximately 10 centimeters at 100 meters. People will sometimes say “mils” and sometimes say “milli-radians”, but technically in shooting, the measurements are in NATO-mils (in most countries).
But which one!?!
People who use metric measurements and much of the military tend to use MIL, while much of the US and shooting competitions tend to use MOA.
At the end of the day, it doesn’t matter. They’re both measurements of an angle. That’s the thing to keep in mind. It’s a way to measure the rise over the run so we can compare targets at any distance.
How do we measure: Terms and Metrics
There are a lot of statistics people have used to describe accuracy and precision. In the shooting world, different people prefer different descriptions, so it’s good to understand what they mean. For each measurement, it’s worth noting that we measure from the center of the hole in the paper, not from the outer edges. To make a measurement, it’s easier to measure from the outer edges, of course, but then subtract the diameter of one bullet (half a bullet from each circle) to get the center-to-center distance.
Point of Aim (POA) - The location you were aiming at. Usually the bullseye.
Point of Impact (POI) - The location you hit. Usually, this is measured as the average location of all the shots. This is often split into a horizontal and vertical component (there’s that trigonometry again) because aim adjustments are made separately for horizontal and vertical aim. It is a measurement of how accurate you are.
Group Size or Extreme Spread - The longest distance between any two points. This might be the most common way to describe the overall size of a group of shots because it’s so easy to measure. It’s similar to the diameter of a circle that would cover all the shots and some people use the terms interchangeably. When someone says they shot “sub MOA”, they are usually saying their Group Size was less than 1 MOA. That’s pretty good!
Smallest Covering Circle - This is very similar to the Group Size. It is the diameter of a circle that would cover the center of every shot. It will always be equal to or slightly larger than the Group Size because … math. It’s pretty hard to calculate, so most people just use Group Size. Others prefer this statistic because it may slightly better represent the full spread of all possible shots.
Mean Radius - The average radius of the group of shots from the Point of Impact. This is a very useful metric that can help us measure the bulk of the data and lessen the impact of one or two outliers. Shooters always complain about “fliers”, the one shot that ruined their Group Size. Mean Radius is a way to describe your most likely shot placement, not just your worst case capability.
Radial Standard Deviation - Math would disagree with us again, but in shooting measurements, this usually means the standard deviation of shots with respect to a circle centered at the Point of Impact. It is a radius and much like the Mean Radius, gives us an idea of how many shots we’d expect to see inside a given circle. A circle at one Standard Deviation’s radius should contain about 68% of all shots taken. At two Standard Deviations, it should contain about 95% of shots taken. At three Standard Deviations, it would contain about 99.7% of all shots taken. So you can lay odds on whether or not you’d hit a target based on one, two, or three standard deviations.
(CEP) Circular Error Probably 50 / 90 - Here’s another one that’s hard to calculate, but gives good statistical information. The CEP 50 is the smallest circle radius that would cover 50% of the shots and CEP 90 is the smallest radius that would cover 90% of the shots. This is different from the Mean Radius precisely because this is a median measure instead of a mean. It throws out the outliers rather than including them in the weighting. It’s far harder to calculate, but with a program doing the heavy lifting, could be the most useful measurement you have.
Extents and Diagonal - This is not as common, but the extents are the measurements of the full width or full height of the spread. The diagonal is the length of the diagonal line across a rectangle described by the extents (it’s the square root of the width squared plus the height squared). It’s fairly easy to measure and used to be popular for that reason, but not in use as much these days.
Measurement Tool: ShotHero
There are many tools out there, and I’m a big fan of ones that you can use in the field right from your phone: SubMOA (iPhone) and RangeBuddy (Android). I used this frequently when I got started, but later I wanted more features. I wanted:
- More precision than my fingertips offered to select shots on targets
- Something free to use that didn’t store my data
- A way to aggregate multiple groups into a single group
- A service that allowed export to CSV
- To be able to select the specific metrics I’m interested in tracking
- To do all this from any computer
So I created ShotHero. (Dark and Light modes available)
I’m not going to go into great detail on how it works. The help page does that well, I hope. You can add any target and, with a few mouse clicks, get a wealth of statistical information:
The most powerful feature of ShotHero is its ability to aggregate multiple targets into a single image:
There is a lot of talk about how many shots it takes to make a “group” that is representative of your shooting skill. Three is certainly too small. Five is borderline. Ten is pretty good. Twenty or more is great.
The problem is that if you have that many shots at one target, you might not be able to see individual holes anymore. It’s better to take multiple targets so you can see the individual bullet holes, but then group them together in one aggregated target to calculate and visualize your MOA or MIL.
That’s what ShotHero does.
You can, of course, still use it on smaller groups to brag to your friends about your perfect three or five shot group!
But to measure your own shooting, try using multiple targets and aggregate them together. Above, I have a target with 5 shots taken at every bullseye at 100 yards. That’s 25 shots and is a great sample size. The second image aggregates all those targets into one.
With the data from this set of targets, in particular the CEP and the POI, I can know what my capabilities are, make adjustments to my shooting, and just as importantly … track my improvement over time.
ShotHero will give you all the measurements you need in MIL, MOA, inches, and millimeters and let you export that data to CSV. And it doesn’t gather any of your data while doing so.
I’ve learned a lot while tracking my shooting progress, and I hope this article and ShotHero can help others as well!
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