I have been thinking for awhile of developing a computer "Shooting Gallery" simulation, and I did it last night, on Microsoft Excel. This is a statistical simulation that will allow the user to "fire" thousands, or even millions, of rounds to find out about grouping characteristics. I won't get into specifics, but it is a fairly mathematically rigorous model, as I have some background in statistical analysis. What this simulation does is to allow the user to "fire" as many two-shot, three-shot, four-shot, and five-shot groups as wanted, and it develops group size data for further analysis. There were some interesting outcomes I found, one of which is how to evaluate fairly precisely the intrinsic accuracy capability of your rifle and ammunition. I won't go beyond this at present, as most people don't know much about statistical analysis.
A definition: Group size: The center-to-center distance between the two most widely-spaced bullet holes of the group (of any given number of shots) on the target.
What I found from the model is that under identical conditions the average group size relationships are generally as follows:
-An average of group sizes of a large number of two-shot groups is approximately 61% of the average group size of a large number of five-shot groups.
-An average of group sizes of a large number of three-shot groups is approximately 81% of the average group size of a large number of five-shot groups.
-An average of group sizes of a large number of four-shot groups is approximately 93% of the average group size of a large number of five-shot groups.
-The average group size of a large number of two-shot groups is about half the extreme spread to be expected of your rifle at any distance. Example: If you fire 50 two-shot groups, and get an average group size of 2" (range distance is unimportant), your rifle is capable of placing ALL of its shots in a 4"x4" square target at the same distance (i.e., 4" x 1/2 = 2").
-The average group size of a large number of three-shot groups is about 3/4 the extreme spread to be expected of your rifle. Example: If you fire 20 three-shot groups, and get an average group size of 3" (range distance is unimportant), your rifle is capable of placing ALL of its shots in a 4"x4" square target at the same distance (i.e., 4" x 3/4 = 3")
-The average group size of a large number of 5-shot groups is about 91% the extreme spread to be expected of your rifle. Example: If you fire five 5-shot groups, and get an average group size of 3.64" (range distance is unimportant), your rifle is capable of placing ALL of its shots in a 4"x4" square target at the same distance (i.e., 4" x 0.91 = 3.64"). Conversely, if your average 5-shot group size is 2", your rifle will put ALL its shots into a 2.20" square (2"/0.91) target.
For this information to be true, you do indeed need to fire a large number of groups - two or three groups just won't work. I'd suggest firing at least 20 groups, and even more is better. So if you really want to know exactly how accurate your rifle and ammunition combination is, then this is the way to find out.
I have always favored five-shot groups, as they are much more information-rich than lesser group numbers. If you think about it, there are actually ten 2-shot groups, nine 3-shot groups, and five 4-shot groups contained within a single 5-shot group. Therefore fewer 5-shot groups tells you far more about accuracy and grouping than the same number of two-shot and three-shot groups.
Just How Accurate Is Your Rifle?
Just How Accurate Is Your Rifle?
Last edited by DWalt on Sat Oct 22, 2011 5:24 pm, edited 4 times in total.
Re: Just How Accurate Is Your Rifle?
Very interesting and informative Dwalt. I totally understand the statistical analysis of what you are saying, as I studied and loved the subject in college. Your development of the program to do this, however is way out of my league.
This is really a neat study.
Clint
This is really a neat study.
Clint
[b][color=#0040FF]Time is the Essence of Life, Wine, and Great Guns[/color][/b]
Re: Just How Accurate Is Your Rifle?
The neat thing is that Excel generates all the random numbers and calculates everything for you. It only took about two hours to put together. It's important to recognize this method applies only to large numbers of data points (which Excel generates), and doesn't work too well on only a few, and there will be other variations. For example, the 91% factor used for 5-shot groups is an average, and can vary by several percentage points either way. However, even that variation can be statistically compensated for if needed (which I did not do in this case; after all, it's not a moon shot). But it's close enough for most anyone.
What I put together is what statisticians term a "Monte Carlo" simulation, and has a lot of business and forecasting applications.
What I put together is what statisticians term a "Monte Carlo" simulation, and has a lot of business and forecasting applications.
Re: Just How Accurate Is Your Rifle?
You two are sick puppies! On the other hand, it might 'xplain why NRA does 5 consecutive 5 shot groups and I do 1 shot groups (I pay for the ammo!!).
Though defensive violence will always be “a sad necessity” in the eyes of men of principle, it would be still more unfortunate if wrongdoers should dominate just men. - St. Augustine
Re: Just How Accurate Is Your Rifle?
Actually, five 5-shot groups are not that bad - essentially like 50 2-shot groups or 45 3-shot groups. For most serious lot acceptance evaluations of ammunition (such as by the military), the protocol used is to fire 10 5-shot groups, or maybe 5 or even 10 10-shot groups. More groups is always better, as it smooths out flyers and other systemic errors. However, more groups also mean more time in measuring and more analysis.
For my own work, I normally fire three 5-shot groups for preliminary evaluation,and five groups for more exhaustive analysis. One group may be misleading, yet that's what a lot of shooters do.
Once you get above about ten 5-shot groups, the averages tend to level out and there is not much reason to use more groups.
I once did some extensive analysis of patterns produced by 00 Buck in 12 gauge that involved measuring coordinates of all holes in over 200 targets, 9 holes per target. That took quite awhile, and I had to write another computer program to do the analysis afterwards. In fact it was probably the most comprehensive analysis of shotgun buckshot patterning that had ever been done by anyone. So many patterns were involved as there were several different shell types, several different shotguns, and several different distances involved.
For my own work, I normally fire three 5-shot groups for preliminary evaluation,and five groups for more exhaustive analysis. One group may be misleading, yet that's what a lot of shooters do.
Once you get above about ten 5-shot groups, the averages tend to level out and there is not much reason to use more groups.
I once did some extensive analysis of patterns produced by 00 Buck in 12 gauge that involved measuring coordinates of all holes in over 200 targets, 9 holes per target. That took quite awhile, and I had to write another computer program to do the analysis afterwards. In fact it was probably the most comprehensive analysis of shotgun buckshot patterning that had ever been done by anyone. So many patterns were involved as there were several different shell types, several different shotguns, and several different distances involved.
Re: Just How Accurate Is Your Rifle?
To put a finish to this discussion, I just ran a simulation of firing several hundred 10-shot groups. What I found is that averaging the group size of as few as three 10-shot groups will give you an excellent estimate of your rifle and ammunition's extreme dispersion. That is, if you fire an average 4" C-to-C group (average of three 10-shot groups) at whatever distance, your rifle will always put all of its shots into a 4" square at the same distance with the same ammunition. Of course, if you do this, make sure you fire from a sturdy bench over sandbags or whatever else you have to get a steady rest.