There are many different methods used when it comes to measuring accuracy. If a gun is being used for self defense and the bullet travels in the same direction the gun is pointed it passes the accuracy test. Some shooters place a can on a fence post. If they can knock the can off the post they judge the gun accurate. Hunters place a target at the estimated range they expect to find game and fire three shots. If the three shots make a small group deemed close enough for the kill this will do. Most shooters use the concept of group or extreme spread as the basis for accuracy. For you newbies the size of a group is determined by measuring the greatest distance between any two shots that make up the group.

The recommend standard in measuring groups is shooting five groups of five shots each and then measure the extreme spread of each group and average the results. This is based on the statistical premise that thirty samples are required to obtain significant results. For whatever reason gun magazines have decided that twenty five shots are sufficient. Many shooters ignore this scientific approach and shoot a number of three shot groups which can range from one to hundred groups and use whatever group is the smallest as reflecting the accuracy of the gun. They believe that this is the potential accuracy of the gun if everything happens to be right. Shooting groups in one form or other to determine accuracy has been used for years since it is based on the extreme spread of shots which has a basis in fact and also appeals to common sense.

What remains a mystery to many shooters is the natural dispersion of shots on the target around the point of aim. In fact the shot pattern of rifle and pistol shots appearing on the target resemble shotgun patterns of pellets if the shotgun is fired at close range. Fig (A) is a drawing of a actual test target of one hundred shots. A circle is drawn around these shots

Fig (A)

This circle represents the proper definition of accuracy. Accuracy being defined as the diameter of a circle that contains ninety nine percent of the total number of shots aimed at the center of this circle. This percentage is used since it is good to know the maximum spread of almost all the shots fired but also allowing for the probability that one shot can end up on Mars.

As an example the diameter of Fig(A)is three inches. This diameter is the accuracy of this gun based on this particular ammunition held in a ransom rest on a particular day with particular wind speeds and temperature. It is important to understand that the diameter of the accuracy circle is controlled entirely by the shooter. The gun , cartridge, components , powder, primer, case and manner of loading and the testing conditions determines the diameter of this circle. These can all be altered and therefore controlled by the shooter.

What can not be controlled by the shooter is the groups that form within this circle. Once a circle has been established the location of any shot inside the circle is due to pure chance. The first three shots may be a one holer and the next three measure as a three inch group or any thing in between. Groups form at random and there is no rhyme or reason or scientific explanation as to what size group will appear next.

Fig (B)

Fig (C)

Fig (D)

Fig(B,C,D) show three possible groups that can form within this three inch circle due to pure chance. It should be obvious that judging accuracy by shooting a few groups is not all that helpful. No group size can be larger than the diameter of the circle which in this example is three inches although there is the remote probability that it can happen. This is why benchrest shooters get teeny groups. The accuracy circle is teeny. But not as teeny as the groups. For those who shoot competitively this implies that winners must be good and also lucky. Some times just lucky.

Although groups form by chance there is a mathematical relationship between the size of the circle and the average size of the groups inside the circle. As the circle becomes smaller ( better accuracy) the average group size will also become smaller. If the diameter of the circle is known the average group size can be calculated. Using the 3 inch diameter circle for an example the average three shot group for this circle is 1-3/8 inches the average five shot group is 1-3/4 inches and for ten shot group it is 2-1/8 inches. On the other hand only knowing the average group size does not help to establish the diameter size. The reasons for this is the center of the diameter is not the same as the center of any group as can readily be seen in the figures above and cannot be located using group size. To locate the center the location of each shot is required.

Since there is a mathematical relationship between diameter and groups they can be used for rough estimates keeping in mind the above information. The use of five groups of five shots has its place and is useful in many instances. Filing flats on handgun bullets , badly cast bullets versus perfect casts and the effective range of guns used for defense come to mind.

The problem arises when making relatively small improvements after all the major changes have been made and attempting to wring out a little more accuracy.. This may be the gun, ammunition, reloading components or minor method changes. To detect small differences by shooting a few groups is akin to chasing rainbows. Twenty five to thirty groups of five would be minimum. A test this large would create its own variations which defeats the purpose of the test. Most of the data is buried in these groups and there is no way to select out shooter controlled errors such as flinches gusts of winds or a defective cartridges. To detect small differences such as primer differences , seating depth, powders etc. each shot has to be assigned a value and evaluated. This is a little more difficult and time consuming but well worth the effort.

Statistics of Handgun accuracy provides a easy to follow step by step method that will put you light years ahead of the other guys.

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Bullseye Shooting
Reloading for Accuracy
Measuring Handgun and Rifle Accuracy
Statistical Methods