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The Trouble With 3-Shot Groups (Page 6 of 12)
Actually I'd like to propose a slightly practical definition of the desired result, which is that you have a target up, with a designated center point, and you would like to have the bullets hit as close as possible to that center point. We can define "as close as possible" in a manner that is both reasonably common-sensical, and also is easy to compute the math for. The statistics people like to define things like the standard deviation (that's the square root of the variance, right? Or is it the other way around ? :-) ) or something, not because it's inherently the "right" way to define the objective, but because it's so easy describe a curve that everyone is familiar with and can visualize, with just a couple of numbers (the mean and the variance) , and it is easy to compute it, and to compute what the probability is that you lie inside various parts of the curve. And these things were important especially in the old days before computers when you had to do everything by hand. So when I say 'common sense', I mean that the general goal of people is to hit a target, so you want to know how well your rifle will hit a target, especially given a finite number of shots. For that reason, you really do want to know a few things besides just an average distance from the target point, because that lets you know what kind of "fliers" and other exceptional behavior to expect in a small sample of shots. So computing the variance, for example, tells you the average deviation of a given shot from the other shots, not just from the center of the target itself... it helps you visualize the distribution bell curve using just one or two parameters. And as we know, everything is pretty much a bell curve in real life.... I don't know enough statistics to know what the best sample size is, but at least we can define what the objective is: "to hit the target!!", not just to have small groups. |
| I don't necessarily agree with the 10 shot group as a basis for any time of sighting in or regular shooting. But I will tell you this. If your spread is that big, I'd try different ammo. The inconsitanies of bulk manufactured loads in both headspace and powder is enough to make bullets wander all over the paper. If you shoot good ammo like hand loaded ammo, use good optics, there is no reason you shouldn't be able to put 3 rounds inside a quarter each and every time at 100yds unless your shooting technique is of. On my large 7mmSTW rifle, with 6.5-20x50mm Leupold scope, I had the same problem you mentioned in this thread. Shooting box ammo Winchester Ballistic Silvertips I had a problem getting tight shot groups. I also was running 9 different handloads with powder variences of 2grams apart. Shooting 5 shells of each load with FPS ranging 3400-3900 est. with the powder loads. All groups were much tighter than factory ammo but the slower loads proved to be the most consistant and accurate. The shot grouping was the difference of a group the size of a softball with factory ammo to a group of 5 that could fit inside a nickle. So yeah the 10 round test to me only shows how good a factory load is. I use 5 round groups to test my powder loads. Then sight in with 3rd groups. May not work for everyone but it works for me and it made a diffence to me of being an ok shot to making some shots I did not think I could hit. Like shooting a plastic orange pop bottle cap at 100yds several times in a row. |
| Interesting discussion. I see merit in many of the positions expressed. I prefer 3 shot groups--but like to compare the average of at least 3 -4 groups (for a total of 9-12 shots). For whatever reason, spread out this way my groups routinely hover around the 1" size. However, if I shoot a 10 shot group, they open up--I believe because I don't take the same time between shots which allows the barrel to heat up. The primary purpose of my guns is hunting/sporting. Unless things are crazy in a prairie dog town, I very rarely shoot quick enough to heat the barrel up. I think the 3 shot groups are more representative of accuracy for my style of hunting/shooting. Just my .02. |
There are two schools of thought on that. "There can be only one!" The Highlander construct.  "We are Texas Sharpshooter." The Borg Collective model. 
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This is a great thread, but I still having trouble understanding how there could be so much variation between a 3-round group and a 10-round group. Could it be trigger-control fatigue? I can shoot 20 round strings off the bench with very little variation. YMMV. |
LaRue Tactical Supporter, Former Air Assault Guy & SOPMOD Poster Child.
There is a LOT of math involved in figuring out your population from which to draw a sample, and then how large a sample to draw. Statistics is like that-you infer qualities about the population (let's say a particular batch of your favorite load) from a randomly selected sample of that population. If you loaded 100 rounds of a known good load, you may not need more than 10 rounds to tell this batch is ok. If you loaded 1000, anywhere between 10 and 30 would probably be adequate. (I'm not referring to my stats text at the moment, so someone who has power effect numbers handy SHOULD correct me on this if needed.) |
"You cannot conquer a free man. The worst you can do is kill him." RAH
Borg Collective? I LOVE IT ! As in, "We are the borg - Your ass will be immolated" - or something like that..... height=8
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"You cannot conquer a free man. The worst you can do is kill him." RAH
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Originally Posted By mfingar:
This is a great thread, but I still having trouble understanding how there could be so much variation between a 3-round group and a 10-round group. Could it be trigger-control fatigue? I can shoot 20 round strings off the bench with very little variation. YMMV. As GHPorter mentioned above, 3-shot groups just don’t give you a complete picture of the accuracy of your rifle/ammunition combination. If the difference between 3-shot groups and 10-shot groups was merely the result of “variability like trigger press, sight alignment, breath control. . . wind, temperature” opening up a 10-shot group, you would find that the same sample number of rounds fired as 3-shot groups and over-layed on each other would have a much smaller mean radius than when that same sample number of rounds are fired as 10-shot groups and over-layed on each. However, this is absolutely not what occurs. Using say, 30 rounds as a sample number (statisticians consider 30 to be a large sample) and firing one set as three 10-shot groups and another set as ten 3-shot groups, we obtain nearly identical measurements for the mean radii of the composite groups. Here are a couple of examples that further illustrate and reinforce concepts previously presented in this thread. Recently, while testing another lot of IMI M193 using a free-floated 20” Colt HBAR, I fired three 10-shot groups from 100 yards and then over-layed those groups on each other using RSI Shooting Lab to form a 30-round composite group. The mean radius for that composite group was 0.94”. I then fired ten 3-shot groups using the same barrel and lot of ammunition and over-layed those groups on each other. The mean radius for this 30-round composite group was 0.99”. The difference between these two mean radii is statistically insignificant. 
Here is another example using an even larger sample number. Using the same free-floated Colt HBAR as above, I fired five 10-shot groups from 100 yards using a load topped with 55 grain FMJ bullets. The five 10-shot groups were over-layed on each other to produce a 50-round composite group with a mean radius of 0.70”. The average extreme spread for all five groups was 2.30”. 
I then proceeded to fire another 50 rounds of the same load in 3-shot groups for a total of sixteen 3-shot groups (with an extra 2-shot group at the end.) Several of the groups were sub-MOA. group #06: 0.66” group #12: 0.92” group #13: 0.59” group #15: 0.41” group #16: 0.63” However, several other groups had extreme spreads of well over 2”. group #02: 2.53” group #07: 2.89” group #08: 2.39” group #09: 2.86” group #11: 2.47” So which of the above sets of 3-shot groups best represents the accuracy of this load? Obviously, neither do. Also, the statistical center of many of the groups, (both large and small) was located at different locations on the target. Pictured below is the first 3-shot group of the Hornady 55 grain FMJ load and beneath that the first three, 3-shot groups over-layed on each other. 
As we continue to sequentially over-lay the 3-shot groups on each, the pieces of the puzzle begin to fill in the gaps giving us a more complete view of the entire picture. 
Finally, when all of the 50 rounds fired in 3-shot groups have been over-layed on each other, we have a composite group that looks remarkably similar to the 50 round composite group formed from the five 10-shot groups with a correspondingly similar mean radius. 
Here’s the target from this shooting session that the Internet Commando would have posted. 
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The principles apply uniformly, but the impact diminishes when guns and ammunition get more accurate. Take a good benchrest gun that will shoot 10 shots into 0.25 moa and the 3-shot groups will not seem to be as variable as they do with XM193 in an AR. Exactly why shooting groups with ammo or guns that are not very accurate is often a chasing your tail exercise. Not scientific, but illuminating, I like to shoot dots. One shot per dot. With an accurate AR I like 1" dots at 100 yards, 3" at 200 (hard to see smaller ones for me). If I shoot a series of one shot groups at dots I tend to concentrate equally on each shot, set up each time the same way, etc. I can quickly see patterns, poor zero, etc. and make adjustments. I do something similar with reloads. If I have to validate a new lot of powder, for example, I drop back 10-15%, but precisely load a single round of each powder increment. I can shoot each one, from the lightest up, watching for pressure signs and for velocities to come into the range I am expecting, and compare with previous lot(s). Once I establish a coarse baseline for the lot and whether it is suitable to use, I can start working at finding the nodes where SD tightens and tune out my final loading recipe. This works well with new powders too, as long as you have some sort of generic baseline for the caliber/bullet/powder combination. If you like to "work without a net" so to speak, and build loads where nothing is published, best to learn how to use strain gauges and use them. |
Paul
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Excellent write-up. 10 shots, or more, per target is the way to go. The more rounds fired, the better the indication of accuracy. Most excellent machine rest. I wish I had the extra money for one. The best I can do, without driving to SC, is to use a long bench bag for the front and a bag for the rear...and hope that I don't pull one. Usually, I can call the ones that I didn't do well. |
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Excellent results can be obtained from accuracy/precision testing using simple and inexpensive front and rear "sand bags" such as those made by Caldwell.
I conducted a comparison between using the Caldwell bags versus using my Sinclair Bench-rest and Protektor rear bag. Using one of my Krieger barreled AR-15s and hand-loaded 52 grain Sierra MatchKings I was able to obtain a 10-shot group from 50 yards measuring 0.340" using the Caldwell bags. Using the same barrel and hand-loads with the Sinclair rest, I fired a 10-shot group from 50 yards that measured 0.316". This doesn't mean I'm going to give up my Sinclair rest, but it shows you're not altogether handicapped without one. 
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Molon, Thanks for taking the time and trouble to test and explain all this. I promise to stop shooting three-round groups. BTW, does Mean Radius = CEP (Circular Error Probable)? en.wikipedia.org/wiki/Circular_error_probable |
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Thanks for the thread as well Molon. When I first got into AR's, I wanted to see just how accurate I could personally get with an AR. I was also interested in Bench rest at the time, but they would not let me do it with an AR. I built the rifle and it virtually took a whole summer of testing and reloading to get to what I felt was my personal best. From that point it became a "six sigma" kinda thing (may not be the right term). Any increase in accuracy was taking more than I could do or find to do. The lessons I learned both in technique and equipment were worth the summer it took. Now that I have had a break, I would like to pick it up again and play with the chronograph some more. I settled on 10 shot groups as well. I have always thought it would be fun to have a "Put up or Shutup Shootout" sometime for AR's only. 10 shots, 100 yards, most accurate group wins the entry fees. I love the black rifle as much as I like accuracy but I will leave the commandoing to the glory hounds or the ones who get paid for it that actually count |
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Nice work, Molon. It's kind of a humbling experience when those tight 3-shot groups I've been so proud of apparently aren't so great after all.  After all of this data backing up the 10-shot group sampling method, I can picture a new line of targets that automatically burst into flames if only three rounds are fired! The "Internet Commando" target. ETA: What do you know, post # 223. Is that a sign  
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Worf: No! Men do not roar. Women roar. Then they hurl heavy objects. (dreamily) And claw at you.
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After reading this thread a bit ago...I only shoot ten round groups now. Denny SPR 18 1:7 barrel...LaRue Upper, Giessel Trigger, Leup Mk4 3.5x10 Staying in practice for the Tea Party.... I shot 10 times but can't figure out where the missing round is....its in there somewhere.. 
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Handloads mike |
"Taking fire, breaking right" The last thing my brother in law said before his helo got shot down in Iraq... <img src=/images/smilies/icon_smile_dissapprove.gif border=0 align=middle>
WOW, the spellcheck works!!! thx Goatboy!!
WOW, the spellcheck works!!! thx Goatboy!!
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"You cannot conquer a free man. The worst you can do is kill him." RAH
FOR 5.56 I would say MK262 
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| I guess I should clarify: a load for a given bullet weight and design that prints as I stated earlier is one I'd consider "match grade." Basically, you could theoretically develop a match grade load for any bullet. |
"You cannot conquer a free man. The worst you can do is kill him." RAH
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There's nothing wrong with using three shot groups. The only problem with the cited example is the step where "Our Hero" cherry picks one particularly good group as being representative and/or eliminates data points (fliers) he doesn't like from any group. The problem with shooting one ten shot group is that as it is one group, it represents ONE sample size, and therefore also cannot be viewed as representative. My method is to shoot three three shot groups and then average ALL three groups; eliminating "undesireable" data points (fliers) is not allowed in this method. This method gives me an average result over three separate set ups (each separate target must be set up for individually). It also helps to average out operator error or unusual operator performance on the + side (those unrepresentative "one hole" groups). Ultimately, there are any number of ways one can test ammuntion accuracy. The most important thing to remember is that ammo accuracy testing is largely relative, meaning, one is invariably comparing one load to another. Consistancy of method is the most important thing here. As long as one has confidence that the load one is shooting is the best load available for a particular rifle, how much better can one do? If, on the other hand, ammuntion testing and load development is all about bragging on the internet, well then, that's a different matter. |
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Originally posted by Coolio:
There's nothing wrong with using three shot groups. For the evaluation of the accuracy of a rifle/ammunition combination, yes, there is something wrong with using 3-shot groups and I’ve proven it over and over again in this thread through scientific testing and statistical analysis of the data. Originally posted by Coolio: The problem with shooting one ten shot group is that as it is one group, it represents ONE sample size, and therefore also cannot be viewed as representative. Nowhere in this thread have I advocated shooting just one 10-shot group to evaluate the accuracy of a rifle/ammunition combination. I follow the practice of the United States Army Marksmanship Unit and use at least three 10-shot groups (often more) to evaluate the accuracy of a given rifle/ammunition combination. The data and analysis of the use of three 10-shot groups that I've posted in this thread is legion. Also, because I use the mean radius to analyze a shot group, even a single 10-shot group gives me TEN data points for analysis. Originally posted by Coolio:
My method is to shoot three three shot groups and then average ALL three groups; Averaging the extreme spread of three 3-shot groups does very little to give you a valuable representation of the radial deviation of the rifle/ammunition combination. In this thread, I’ve presented the data from numerous tests that prove as much; scientific data and statistical analysis, not opinion. Originally posted by Coolio:
As long as one has confidence that the load one is shooting is the best load available for a particular rifle, how much better can one do? Averaging the extreme spread of three 3-shot groups does little more than give you a false sense of confidence about the accuracy of your rifle and ammunition. I deal in facts and science, not false beliefs with no scientific data to support them. |
Actually, it's not. Averaging the extreme spread of three 3-shot groups will not give you the same radial deviation as a single 9-shot group. This is due to the fact that the 3-shot groups can end up being centered on slightly different locations of the target and this is not accounted for by merely averaging their extreme spreads. |
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"You cannot conquer a free man. The worst you can do is kill him." RAH
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Is there a way to make reading this post manditiory before replying to any topic? I hear "why are your Krieger barreled uppers so expensive, you only promise sub moa and I can do that with surplus ammo and my model 1"  |
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No, he's referring to looking at the ammo's accuracy using 3 shot groups. Measuring using the aiming point as a reference would be no different than overlaying the three 3 shot goups...which is little different than shooting one 10 shot group. |
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| I shoot 3 shot groups so I can rest and my rifle can cool off. What I tend to notice is that my 1st group of the day will be quite small, 2nd and 3rd will open up, and 4th will approach the 1st group diameter again. It all seems like human error to me, which is why I try to relax between shots/groups. Its not practical for me to shoot 10 shot groups with a .300 win mag but this article definitely illustrates the benefits of having more sample to judge your accuracy/precision with and the false impressions a 3-shot group can leave us with.. |
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I wonder what the bench rest guys would think of this? They dedicate thousands and thousands of dollars to printing the tiniest groups possible.... And what do they shoot? 5 shot groups, almost exclusively 5 shot groups.... If that's a good enough testament of both rifle and shooter, its good enough for me. |
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Originally Posted By Wheres-Waldo:
I wonder what the bench rest guys would think of this? What exactly is it that you think they should think of this? I’ve learned a lot of things from the benchrest crowd, but the scientific application of the statistical analysis of shot-groups was not one of them. The great thing about science is that it is unbiased. It applies equally in all situations. Facts are facts, whether you apply them to a semi-automatic AR-15 or a finely tuned bolt-action benchrest rifle. A 5-shot group fired from a bench-rest rifle will not show a true picture of the radial deviation of that rifle/ammunition combination any more than a 5-shot group fired from a semi-automatic AR-15 will. The groups from the benchrest rifle will most definitely be much smaller, but the laws of science are not magically changed because those groups were fired from a benchrest rifle. Ammunition acceptance testing done at Lake City is performed using a barrel and bolt-action clamped in a machine rest to eliminate the human variable. The testing done at Lake City decades ago has proven that 5-shot groups do not give a true picture of the radial deviation of a barrel/ammunition combination. That’s why it is the policy of the U.S. Military that ammunition acceptance testing must be done using 10-shot groups. 
from an American Rifleman article on the Lake City Ammunition Plant Originally Posted By Wheres-Waldo:
They dedicate thousands and thousands of dollars to printing the tiniest groups possible.... And what do they shoot? 5 shot groups, almost exclusively 5 shot groups.... Hmmm, because it just might be easier to get a smaller group when only using 5 shots in a group instead of 10 shots in a group. What exactly did you think that statement of yours proved? Even a semi-automatic AR-15 can produce “tiny” groups when only shooting 5-shot groups (though certainly never as small as a bench rest rifle). I seldom shoot 5-shot groups myself, but here’s one from my last shooting session with my Krieger barreled AR-15. It’s a 5-shot group fired from 100 yards going into less than a quarter of an inch. Too bad it's not a valid indicator of the accuracy level of this rifle. (Oh, by the way, there are entire divisions of benchrest competitions that compete using 10-shot groups. What could that possibly mean?) 
Originally Posted By Wheres-Waldo:
If that's a good enough testament of both rifle and shooter, its good enough for me. Denial can be the most pretentious of defense mechanisms. It requires no logical thought, no proof nor facts. All that is necessary is a disbelief of the reality of a situation. |
All hail Jeanne Assam!
| you know guys 10 round groups at 100 yrds can be informative. the only problem i see to the madness that ya'll are discussing is the exclusion of the man factor. i have rifles that shoot allot better than i am capable of most of the time. the key to the issue is most of the time. when i test a load for accuracy i generally use 5 shot groups. the only difference is that i shoot a 300 yrds exclusively. if the load i'm shooting doesn't group 0.75"'s at 300 yrds its not acceptable. i have several rifle that will consistently shoot 0.5 at 300 yrds. 0.5 is the magic number i'm looking for at 300 yrds. if the rifle groups 0.75 then the load is worth tweaking till it gets to the 0.5" mark. groups at 100 yrds are interesting but are to easy to repeat with regularity. a 50 yrd group is useless as repeatability is a certainty. the one thing i have noticed that is missing from this discussion is the reason most of these groups are as large as they are is sighting error. this alone will cause groups to open up markedly. when shooting a rifle with military sights, be them the national match variety or standard sights the reason for the large groups can be attributed to sighting error alone. having nothing to do with the load or weapons ability to group. as for the groups shot by the men and or women using scopes there are a multitude of reasons that the groups open up, again having nothing to do with the rifle or the load being shot at the time. this thread has been interesting, thus it has a great amount of academic value when you watch the sway of opinions alone. as for its value to the art of shooting groups it is, just what it is academic and of no intrinsic value. mean group size when shooting groups with basic iron sights is what it is, inconsistent at best. this thread is a good read though and that has merit in itself. on a lighter note for me when shooting groups for fun i like to shoot at 300 yrds to 600 yrds it has put the fun back into shooting for me. i have just recently acquired an ar platform gun and i intend to see what it is capable of in my hands at 300yrds and 600 yrds. happy shooting guys have fun. |
Whoooosh! That's the sound of the reams of scientific data that Molon has posted in this thread sailing over your head. |
ok, its a good read, but has no basis in fact. to many variables are left unaccounted for, to base the assumptions on fact and or reality. or as Mr Rodgers would put it --can we say facts. using small words now --better. now back to the fun. |
The Trouble With 3-Shot Groups (Page 6 of 12)
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