MEASURING ACCURACY

     There are many methods for measuring accuracy. If a gun is for self defense and the bullet path is in the same direction the gun is pointed it passes the accuracy test. Some shooters place a can on a fence post and 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 considered close enough for the kill it's considered plenty accurate. Most shooters use the concept of group or extreme spread as the basis for accuracy. To those new to shooting 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 measures the extreme spread of each group and averaging 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. Their reasoning is 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. This 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 shotguns fired at close range.

     Fig (A) is a drawing of an actual test target of one hundred shots. A circle is drawn around these shots The 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 the circle. Ninety nine is used since it represents almost all the shots fired while still allowing for the probability that a shot can end up on Mars.

Fig (A)

     As an example of shot dispersion the diameter of Fig (A) is three inches. This diameter represents the accuracy of a gun based on the use of specific ammunition shot from sand bags on a specific day with specific wind and temperature. It is important to understand that the diameter of the accuracy circle is controlled completely 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 are all within the discretion of the shooter and therefore can be controlled.

     What cannot be controlled by the shooter are 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 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, 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. In this example it is three inches although there is a remote probability that it may be larger. This is why benchrest shooters get tiny groups. The accuracy circle is tiny but not as tiny as the group. For those who shoot competitively the implication is that winners must be good and also lucky. Sometimes just lucky.

Fig (B)	Fig (C)	Fig (D)

     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"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 a 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. Locating each shot is required.

     Traditional groups can be used for rough estimates since there is a mathematical relationship between diameter and traditional groups but keep in mind the above requisites. 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. Problems arise when making relatively minor improvements after all the major changes have been made in an attempt 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 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 an easy to follow step by step method that will put you light years ahead of the other guys. .

     Statistics of Handgun Accuracy can be purchased directly from the publisher, from online bookstores, or ordered through your local bookstores and Amazon.

Home Measuring Accuracy Bullseye Shooting Reloading for Accuracy Statistical Process Control