Great marksmanship is defined by consistency or repeatability. That is, being able to repeat shots with the same weapons and under the same conditions consistently. Given all the physics involved (aka internal, external, and terminal ballistics), a shooter repeating a shot (i.e., placing two bullets on exactly the same spot) is basically a matter of luck. For short distances, we often can see great shooters placing many shots around the same spot but the impact area (or mark) is certainly bigger than a single bullet’s diameter. For long-range distances, placing shots on exactly the same impact area is a matter of even more luck. 

A way to approximate the consistency of a shooter is to shoot multiple times under the same conditions, with the same weapon and ammo followed by analysis of the groups the shots form. For example, it is a popular belief that good shooters can get groups that are less than an MOA (more on this later) at 100 yards. The shape and size of the group can help determine not only the level or consistency of a shooter but also the diagnosis of certain issues with the shooter, the weapon, or the ammo.  

For the rest of this post, we will focus on the size of a group and we will leave the interpretations of the shape for a future post. There are multiple factors that can affect the size and shape of a shot group. They include the shooter’s technique, the quality of the firearm, and the type of ammunition being used. By analyzing size and shape of shot groups, firearm instructors can identify patterns of error and the factors that may be contributing to those patterns, all in the name of helping shooters make the necessary adjustments to improve their consistency and accuracy.

Since a picture is worth a thousand words, take a look at the two shot groups shown in the above figure side by side. Which one do you think is better?

If you had to pause and think for a moment, you’d appreciate that precisely determining which shot group covers a smaller area is easier said than done with the naked eye. This is already the case without even getting into alternative group size calculation measures we will describe in the following sections. Since precision is core to the discipline of marksmanship let’s dig deeper into the basics of shot group analytics.

The Old Way

To measure the size of a group, at least three shots are needed. The number of shots that a group should have and the number of groups a shooter should repeat before proceeding with an evaluation are also a matter of regular discussion that we will revisit later. At AccuShoot, we like the 5×5 group drills shooting five rounds, five times with five different points of aim. 

Traditionally, the size of a group has been measured using a variety of tools, such as a string, a ruler, or calipers to estimate the distance among shots or to the point of aim (PoA). Depending on the number shots in the group you might require two by two comparisons to establish the two shots that are most separated.

You can use calipers or a ruler to measure the furthest distance between two shots and write it down on your target or in your notebook. But unless you later enter it into a spreadsheet, it gets quite cumbersome to make comparisons across groups on the same target, groups in multiple targets you shot the same day, or across different training sessions over the years.

AccuShoot, on the other hand, gives you a treasure trove of complementary metrics and presents them without any grunt work on your part. You only need to choose the metric that you prefer. Plus you get all that data digitized and stored forever so you can compare groups across weapons, ammo, shooters, etc. Those are great tricks that help track the evolution of a shooter’s performance over time. Digitization is a powerful enabler indeed as it allows us to offer innovative features such as normalization of your shots across multiple targets.

Think of the old methods as the typewriter and AccuShoot as a modern text editor. Using  an old typewriter, it is hard to count words, search words, compare paragraphs, use an auto-corrector, etc. Using a text editor, all of that becomes trivial and the number of additional things you can do with your data is almost infinite. For example, in AccuShoot, you can select or unselect shots to include them in your analysis and get immediately updated results. 

Without a doubt, the age-old methods are more time consuming and error prone compared to modern software driven solutions like AccuShoot, which can provide detailed feedback to the shooter both during and after the shooting session. By regularly analyzing shot groups, you can identify and address any issues that may be affecting your marksmanship and become a more proficient marksman over time.

Group Size Methods

Roughly speaking, there are three ways to measure the size of a shot group.  

• Distance-based Methods aka String Methods:  Where the distance between the Point of Aim (PoA) and the Point of Impact (PoI) of each shot is measured and then all the distances are added (or averaged). The smaller the distance (or the average), the better the group. This is one of the oldest methods and it is actually named string because a real string was used to measure the distance.

• Area-based Methods: These methods try to measure the area that the group covers. Specifically, the statistical center of the shots is computed and then a shape such as a rectangle or circle is chosen. There is a whole family of these methods depending on what shots are actually considered for the statistical center and the lengths of the rectangle’s sides or the radius of the circle. For example, using the average distance to the Point of Aim, the median or the maximum distance.

• Angular-based Methods: These methods consider the maximum length between two of the impacts and the distance at which the shots were performed to compute an angular measure. The two most popular are milliradians (MIL) and Minute of Angle (MOA). These angular measures are fundamental to long-range shooting and to adjust sights for both pistols and rifles and fully deserve their own blog post at a later date.

An important yet oft neglected factor that affects all the methods is the treatment of missed shots. You cannot simply ignore them during group size computation if you want to establish a rank of best groups since groups with misses can score better than groups with no misses.

Group Size Basics in AccuShoot

AccuShoot offers three types of drills: Rapid, Slow, and Group. Independent of the type of drill performed, AccuShoot provides the group analysis results. No matter if you shoot for speed, accuracy or the smallest group size, group analysis is always there for your reference, as long as there are at least three hits.

Let’s start with some basic definitions before we get into group size measures:

• Target is a 2-dimensional space. Each point in the target is defined by means of two coordinates. The coordinates are relative to the Point of Aim. 

• Rounds is the number of shots configured in the drill. We expect an impact per round but often some shots miss the target or a shooter can mistakenly shoot more rounds than expected.  

• Hits are shots that impact the target.
• Misses are shots that miss the target. Duh!

• PoA or Point of Aim is the exact point of the target which the shooter desires to hit. This point is independent of all sighting adjustments the shooter needs to perform to compensate for elevation or windage (adjusting a scope, holding over, etc.)  It is the point where the shooter expects to see a bullet hole (or impact if using metal targets). The PoA determines the center of the coordinate system on the target. In AccuShoot, the PoA is configurable for each target.

• Point of Impact is the point where one of the shots impacted. For each impact, AccuShoot provides the order, the score (given by its placement on a certain area of the target), the coordinates, the distance to the PoA, and a vector that indicates the angle at which the PoI is regarding the PoA. For example, in the screenshot above, you can see that the shot #4 got a score of 7 and is placed on the coordinate -0.44, -3.92 and its distance to the PoA is 3.94 inches. On the Time and Shots panel you can see the exact time at which the shot was detected, the split time with respect to the previous shot, and the score.

• Average Point of Impact or Statistical Center: Given a group of n impacts, the Average Point of Impact represents the statistical center of the impact and is computed as follows: (∑xi/ n,  ∑yi/ n)

• Extreme Spread is the distance between the centers of the two most distant impacts in the group of shots on the target.

Whether you use the AccuShoot mobile app or upload a picture of your target to the desktop app, the system crunches the numbers instantaneously and presents you with a detailed analysis of your group drill performance through an amazing array of metrics. The artifacts and measures described above are all included in your D.O.P.E. (Data On Previous Engagements). Next up, we provide a quick overview of the different ways AccuShoot can measure the size of your groups.

Group Size Methods in AccuShoot

Below, we will use the same group of shots from the same session but with different size calculation methods for consistency sake.

Unlike the other group size methods, String Measurement is a distance-based method that measures the distances from the Point of Aim to each shot. The total distance along with average, median, minimum, and maximum are presented next to the graphical depiction of the strings.

In contrast to the distance-based one above, below are all the area-based groups size methods available in AccuShoot.

Oriented Spread is the default method AccuShoot uses for your shot groups. It marks the smallest possible rectangle containing all your shots and can be oriented at any angle as the name suggests. AccuShoot provides not only the total group size but also the width and height, the exact statistical center and the offset (distance to the PoA) as well as the offset deviation for windage and elevation. 

Maximum Spread draws the smallest possible rectangle that contains all the shots. A single bad shot can obviously impact your results dramatically even if the remaining ones are grouped close together. As such, this is more of a perfectionist’s measure.

Average Spread takes into account the average horizontal and vertical distances from the Point of Aim (PoA) for all your shots to calculate the average point of impact (PoI). AccuShoot then uses the average horizontal and vertical distances to draw a smaller vertical rectangle which by definition will leave some of your shots outside.

Median Spread follows a similar logic to that of Average Spread and draws a vertical rectangle by using the median distances instead of average ones. This rectangle may be larger or smaller than the average spread one depending on how your shots are placed. The more spread out they are, the smaller the median one.

The Max Group Radius method draws a circle with a radius corresponding to the longest distance from the Point of Aim (PoA). The coordinate of the circle’s center point, the offset length as well as its vertical (elevation) and horizontal (windage) siblings are displayed in the accompanying table, which also contains radius and diameter length.

The Average Group Radius method draws a circle with a radius corresponding to the average distance from the Point of Aim (PoA). Once again, the coordinate of the circle’s center point, the offset length as well as its vertical (elevation) and horizontal (windage) siblings are in the accompanying table, which also contains radius and diameter length.

Median Group Radius follows the same logic as Average Group Radius, except it uses median distances vs. averages. Similar to that of spread-based methods the more spread out your shots, the smaller the Median Group Radius compared with the Average Group Radius.

In addition to the graphical shot group analytics and their corresponding metrics, for each group drill session, AccuShoot displays the distances used to calculate the aforementioned metrics at the bottom of the page.

Additional Metrics

In your D.O.P.E., when you go to the session detail view, you will notice that AccuShoot displays lots of metadata about the session (e.g., distance, weapon) that are configured by you, the user. Below those, the following computed metrics are available for your information. For completeness sake, let’s quickly go over the ones we haven’t covered before.

• Roundness  the convex hull of the impacts that define the perimeter of the group is computed and then compared.

• Consistency has five levels starting from beginner and ending with the highest level, expert.

• Score is the oriented spread area in square inches. The lower the number, the better for group drills.

• Penalties account for the subtractions from your score for things like misses and extras.

• Hits are shots within the target area.

• Extras are shots that exceed the allowed amount per the current drill settings.

• Misses are shots outside the target area.

Remember the question we posed at the beginning of this post? Given all that we shared so far, have you got any idea which shot group is the better one? This is already a long blog post. We will zero in on that answer in our next post so please stay tuned.

One last thing, if you made it this far, it’s about time you join the AccuShoot nation and start improving your marksmanship skills in a fun, engaging and data-driven way. As usual, let us know of any questions along the way as we value any feedback helping us digitize marksmanship for the masses.