Almost a moa 10 shot group, my current shooting goal, thanks to your inspiration! Since my ARmalite is sporting a WOA match barrel and I have plenty of accessories, it's been suggested that the shooter or manufactuer of the ammo might be holding back the rifle......

Ah.  Your file name of your pic suggests that group was fired with 80 grain Noslers.

One at a time....On to the Bergers! And Tac instead of Varget......must be the load, not the shooter.....

With My SIG 556 I was lucky to get 10" groups at 100 yards with Heavy match ammo. That was from a sand bag rest trying an aimpoint, ACOG and a 18X Leopold scope with LaRue mount. The guys on the SIG forum said I couldn't shoot and when I sent it back to SIG they replaced the barrel and then they banned me for showing a picture of the warranty work. SIG 556 owners love 3 shot groups as do AK 47 owners. I heard they might even switch to 2 shot groups to feel better about their shooting.

I dont know what Army you were in but when I was in the Army, mid 80's thru early 90's, we qualified on paper targets for accuracy from 25, 50, 75,and 100 meters and then went to pop-up targets afterwards out to 600 meters. Our qualification was the paper target accuracy part of the qualification. "The pop-up targets were just for training". And all with iron sights I might add!

All completely irrelevent to the subject matter of this thread.  "Qualifying" has nothing to do with statistically significant accuracy testing.

FYI, the U.S. mil-spec for accuracy acceptance testing of ammunition requires 10-shot groups.  Also, the mil-spec for accuracy acceptance testing of the M16 and M4 requires 10-shot groups.

The main purpose of shooting test groups, once the rifle is sighted in, is to test the accuracy potential of the firearm.  Consequently, you would want to remove as much of the human element as possible as well as other factors, like heat buildup, that could affect same.



So, the only reason a shot group in excess of 3 shots would make sense would be if the rifle was in a rigid mount and the group was very slowly fired with negligible environmental concerns.



For most of us though, our accuracy tests consist of shooting from a sandbag on a bench.  The more shots you fire, especially with heavy military triggers and negative environmental conditions (ie. wind gusts), the more you introduce human error and other variables that would create false negatives on your test groups.  



The OP makes a valid point about multiple 3 shot groups with multiple centers.  However, he also, by shooting lots of 3 shot groups, has introduced much more human error, barrel heat buildup, and environmental variables to the test.  So wheter you are shooting many 3 shot groups or one 10 shot group, you are creating false negatives unless variables are striclty controlled.



So for me, I'll stick with my 3 shot groups!

<Keep comments on topic please - Z>








I’ve posted reams of first hand data in this thread that prove that you are verbalizing from your anal orifice.  Instead of just running your mouth, why don’t you try posting some statistically significant first hand data that you think proves that 3-shot groups are superior to 10-shot groups as a "more reliable indicator when it comes to predicting what a load is likely to do in the future."  We’ll analyze your data and determine if it has any validity.  





Since I first started this thread almost four years ago, not one, NOT ONE single loudmouth detractor posting in this thread has been able to post one iota of first hand data that proves that 3-shot groups are superior to 10-shot groups as a statistically significant method of analyzing  the precision of a given barrel/ammunition combination.  Here’s your chance to be the very first.






 

<Keep
comments on topic please - Z>

Allan Jones wrote an excellent article relating to this subject, Statistics Is Not A Dirty Word. This seems an appropriate place for the link, as it should prove of interest to those participating in this thread.

An excerpt:

While I was on vacation one year, an outdoor writer called for me at Speer and ended up transferred to our quality department. His question was a great one: "What is the least number of shots fired in one group that gives me high confidence that the whole batch is accurate?"

A PhD statistician went to work, applying all the classic statistical methods to the questions. Even if I could, I won't attempt to document his work here, but the number he derived was seven. "Doc" was able to demonstrate a jump in statistical confidence level between a five- and a seven-shot group that was remarkable.

With 3 rounds you get a 76% assurance of validity, at 6 rounds you get a 90 percent assurance.

<Keep
comments on topic please - Z>

And 10-shot groups capture the out-lyers that 7-shot groups often fail to.

The point that's often missed here is that once a rifle/ammo combination are shooting to a certain level of accuracy the addition of extra shots is not likely to expand the shot group by a large amount. If someone is shooting a 3moa 5 shot group, it's likely that an additional 5 shots will add another couple of moa to that group. If someone is shooting a .2moa 5 shot group, another 5 shots isn't likely to turn that into a massively larger group. Rather than bang the 10-shot drum in every case, it would be more productive to consider the groups being fired before demanding that additional shots be taken.

I have posted this info before, these are IBS aggregate records for both 5 and 10 shot groups.

Heavy Benchrest, 100 yards:
5 ten-shot group aggregate - .1898moa
5 five-shot group aggregate - .1386moa
Difference: .0512moa

Heavy Benchrest, 200 yards:
5 ten-shot group aggregate - .2234moa
5 five-shot group aggregate - .1616moa
Difference: .0618moa

Heavy Benchrest, 300 yards:
5 ten-shot group aggregate - .3495moa
5 five-shot group aggregate - .4095
Difference: -.06moa (The 10 shot group aggregate is actually smaller than the 5 shot group aggregate in this case)

Real world data here bears out that once a certain level of accuracy is achieved, the addition of more shots, while likely to open up the groups a small amount, isn't even guaranteed to make groups larger. In each of these cases the addition or subtraction of the extra shots doesn't even make a tenth of a moa difference. In this light, I once again suggest that rather than bang the 10-shot drum at every possible chance we recognize that 10 shots aren't always necessary to get a valid idea of the consistency capability of a rifle/ammo combination. Failing that, I can only assume that you've petitioned the IBS to scrap every 5 shot record they have, explaining to them that their records are statistically meaningless.

Science; you fail at it.  I suggest you go back and actually read the whole thread to discover the critical points that you've obviously missed.

No, it's quite clear what this thread is about. It's also clear that when someone says something you either can't rebut or don't want to address you simply insult them and then ignore everything they've said.

<Keep
comments on topic please - Z>

<Keep
comments on topic please - Z>

<Keep
comments on topic please - Z>

Naturally. I just thought it was interesting that a statistician had laid minimum shot count, at that one greater than the three or five shots so often advocated, lending credence to the 10 shot argument.

To that end, though, don't 20 shot groups catch more than 10 shot?

They absolutely do.  However, with an accurate barrel and ammunition, 20-shot groups tend to mask as much, or more information as they capture over 10-shot groups.  As the reams of first hand data posted in this thread demonstrate (and which have been corroborated by the findigs and practices of such individuals and organizations as: Rick Jamison, the United States Army Marksmanship Unit, The Federal Bureau of Investigation, Crane Naval Surface Warfare) multiple 10-shot groups maximize the usable information obtainable and give us a high degree of probablility of the expected accuracy level of a barrel/ammunition combination.  This is why the organizations mentioned above, as well as the US mil-spec for acceptance testing of both ammunition and firearms require multiple 10-shot groups.

<We're discussing rifle shooting, not howitzers. Please stay on topic. - Z>

.......

Zhukov, so you are saying ballistics for one is not similar or the same as another?  Really?

Some of you may need to get off the internet and see the effects in the real world, because the principals for one apply to the other.  And I have killed enough people to prove it.

I totally understand your point. I myself have doubts when I see someone talk about how they're shooting .5moa with M193 through their basic AR. My whole point here is that at some level it is valid to say that you can get a decent enough idea of the accuracy potential of the gun/ammo combination from 5 rounds. Now, more rounds is better, and I'm not going to dispute that. The point is that there is sometimes this knee-jerk reaction that "oh, only 5 rounds? that's totally meaningless data." That simply isn't the case. While those little benchrest groups may be 30% larger with the addition of extra shots in most cases, what that translates to in our shooting environment is a guy who consistently shoots say .75 moa 5 shot groups is likely going to be in the area of 1 moa for a 10 shot group. Based on the fact that we see that 5 shot groups are on average X percent smaller than 10 shot groups, we can make an educated guess as to where we'll be with more shots. Again, my issue isn't with telling people to shoot more shots for a group, my issue is with the notion that there is no level of consistency where 5 shot groups have any meaning.

Ballistics is ballistics .  The ballistics and the statistic behind them as produced by BRL don't take into account explosive effect.


You are totally incorrect when it comes to computation and gunnery, if you think that "area fire" play into the many of the chapters of the FM I am cite or the AM-2, AM-3 Tabular Firing Tables that the FMs are dirived from.  Data is computed to hit a point target, even if normally ballistics make that impossible.   On the gunnery side we don't get into the ECR, etc. That is more fire support and tactics.  A common thing heard in the gunner circle is chasing the mil, for accuracy.  

My feelings aren't hurt, but it seems it alright to say someone else is putting false info.  Even though that info is from the Army's Ballistics Research Labratory based on thousands of controlled firing.  But its not alright to contridict a back yard hobbiest who uses "many, most and multiple" as the assurance of validity numbers.

Ballistics are ballistics, whether they are cannon or small arms.  The ballistics and the statistic behind them as produced by BRL don't take into account explosive effect.  


On the gunnery side we don't get into the ECR, etc. That is more fire support and tactics.  A common thing heard in the gunner circle is chasing the mil, for accuracy.  You are totally incorrect when it comes to computation and gunnery, if you think that "area fire" plays into the many of the chapters of the FM I cite or the AM-2, AM-3 Tabular Firing Tables that the FMs are derived from.  TFTs contain data to hundredths and thousandths of mil for precision computation and depending on the misison that data is used.   Data is normally computed to hit a point target, the computer require a 10 digit (accurate to a meter) entry to compute data, even if normally ballistics make that impossible.  

My feelings aren't hurt, but it seems it alright to say someone else is putting false info.  Even though that info is from the Army's Ballistics Research Laboratory based on thousands of controlled firing.  But its not alright to contradict a back yard hobbyist who uses "many, most and multiple" as the assurance of validity numbers.

Makes sense to me.

So would it be safe to say that 7 shots would be a bare minimum and 10 shots are ideal?

Here's  a pic of another machine rest.  This time from the Crane Naval Surface Warfare Center.

To these untrained eyes, that looks a lot like part of a milling table with a very hefty barreled action bolted into it.  Which would make lots and lots of sense-precise control of the alignment of a very stout barreled action would eliminate or significantly control a whole lot of the potential human-induced errors involved in accuracy testing.

Here's another interesting pic.



Rifle magazine, 1986.

Do you realize that your skill level as a shooter or "human error" translates into ALL shot groups?  So basically what you are saying is that you can shoot all the 3 shot groups you want all day and your skill level or "human error" remains constant but when you shoot 5+ shot groups your skill level somehow decreases?  

We really need a very basic statistics course as a pre-requisite to posting on this forum..  This need doesn't just apply to posting about shot groups but also parts failures.

I agree completely that a basic understanding of statistics is essential to many of the issues discussed on these forums.  Unfortunately, the basic arithmetic needed for such understanding is "under emphasized" in today's culture.  I believe that anyone who can't do basic math (college algebra at the very least) is under-educated.  

But there's also the issue of what "science" is.  Most people think it's black magic done in laboratories, rather than a straightforward method of asking questions and determining appropriate conclusions.  Molon's scientific method in his accuracy testing is extremely good-he identifies sources of inaccuracy, reports them thoroughly, and controls them as much as possible.  This was the point of my discussion with him above about such things as machine rests; I don't think I'm the rifleman I would need to be to sufficiently control the human-rifle interface enough for testing from good rests the way Molon does to be effective for me.  In the case of ammunition accuracy testing, there are so many variables that it's important to both account for and have confidence in your control of as many variables as possible.  My loading techniques for developing loads for testing are extremely stringent, including re-zeroing my scale (I ONLY use balance scales for this!) for every round and using a very rigid routine for each step on the press.  All of that is within my control.  Which is the whole point.

The reason for shooting multiple shots is to obtain an estimate of the mean(accuracy) for the flight paths and an estimate of the variance (precision) of the flight paths.  The distribution that's used for the estimation of the mean and represents the data is the student's t distribution.  It's a liitle less peaked around the mean than the normal distribution and it's more probable to obtain results in the tail areas.   As the number of shots goes up from 3, the t distribution approaches the normal distribution by becomiing more peaked and narrower.  The probability of obtaining results in the tails of the curve is less.

The mean needs to be obtained to adjust the sights to effect accuracy.  The number of shots doesn't effect the value estimated for the mean very much in the range 5 to 10.  The difference is that an ~8% better estimate of the mean can be had with 10 shots over 5, but an estimate with 3 shots can be 17% worse than an estimate obtained with 5 shots.  That doesn't mean that it will be 17% worse, just that it can't be known any better than that.  Here "better" refers to the size of the interval that contains the estimated mean.  A 3 shot group has an interval of uncertainty that is 17% larger than a 3 shot group and one that is 26.4% lager than a 10 shot group.  So a 3 shot group may look small, but it is equivalent to a group that is indistinguishable from any group in a 26% larger range, than can be had with a 10 shot group.  More results means a narrower interval of values that are indistinguiahable with regard to being the true value of the estimated mean.

The real focus that's effected by shot number is precision, which is estimated by the standard deviation squared.  Precision is what folks want to know.  Whether it's the firearm, the ammo, the shooter, or as is normally the case a combination of factors, the focus is on precision, which is represented by variance.  The real precision of the system has an inherent variance which is being estimated.  The precision is not measured by spread, because spread simply represents some particular results obtained that are simply possibilities given some underlying and unknown variance.  That estimate of the variance represets the possible spread that can be obtained and that number is what one wants to know.   68% of the values will be within +/-  one std. deviation of the mean.  95% of the shots will be within +/- 2 std deviations of the mean.  The improvement in the estimate of the variance with 10 shots over 7 is a 3X narrower range for a 95% confidence in the estimate.

Note that in this thread, an average shot radius was used to estimate precision.  I believe Horcher's "divide by 3" formula was actulally a standard deviation calculation for a 10 shot group.  3 is the square root of 9, which is the "number of degrees of freedom" for a 10 shot group.  The "degrees of freedom" for this calculation is the number of shots minus 1.

Thank you, spunkets, for putting into eloquent words the rather tedious details of wading through practical statistics.  I actually like doing stats and I couldn't have teased all of that out.  'Course my Engineering Stats class was in something like 1994, but that's beside the point.  Thanks again!

You're welcome.  

I personally do not shoot less than 10 rounds per group.  It is a larger data sample.  Also, when you shoot for groups, you need to back up the performance of each shot with the speed of each round.  Ideally, you would want a chronograph at the muzzle and just in front of the target, to record both speeds giving you true BC of each round.  Some flyers can be shown with a greater deviation from the overall average.

50-shot groups, done methodically with set times between breaking it shot can give you the best repeatability, like so:

You can explain this to people and show them this thread but they will still never get it. I have determined that 6 out of 10 shooters are idiots.

And there is tons of scientific evidence (on these boards!) to back that up!

I finally got around to writing this up.


Unlike caliber .30 and caliber 7.62mm ammunition, there has never been a National Match standard for caliber 5.56mm/.223 Remington ammunition.  

In 1965, the caliber 7.62mm Match ammunition was standardized as M118 .  The 1965 lot of 7.62mm M118 National Match ammunition had an acceptance testing mean radius of 1.9” for 10-shot groups fired at 600 yards.  At that time, this was the smallest acceptance mean radius ever achieved for National Match ammunition since records were kept, starting in the year 1919.  Naturally, the ammunition was tested from machine-rested, bolt-actioned test barrels.  The composite target pictured below shows the twenty-seven, 10-shot acceptance groups (that’s 270 rounds!) of the 1965, M118 National Match ammunition fired from the test barrels at 600 yards.  The small circle has a diameter of 6” and the large circle has a diameter of 12”.





From American Rifleman, September 1965





From American Rifleman, August 1962.



Everything else being equal, (which of course, it seldom is) a mean radius of 1.9” at 600 yards would have a mathematical equivalent of 0.32” at 100 yards.  Now, 100 yards is not 600 yards, but then, a semi-automatic AR-15 is not a machine-rested, bolt-actioned test barrel either.  For this reason, I like to use the mean radius of 0.32” for 10-shot groups fired at 100 yards as the benchmark for match-grade ammunition, when fired from a semi-automatic AR-15.  I personally prefer that my match-grade hand-loads have a mean radius “in the twos,” i.e. a mean radius of 0.2x”.  My best hand-loads fired from a semi-automatic AR-15 at 100 yards have had mean radii “in the ones,” i.e. a mean radius 0.1x”.  The 10-shot group pictured below has a mean radius of  0.13”.

....

It all depends on center of target.One shot groups( minus the group part) and if you hit the target. If the part of the target you hit is the center of the target. I could be on to something.I know I am a noob but only a single minded noob.With one shot left I would be my only claim to fame. I could make this claim. You have really hurt the feeling of a lot of wantabe Shooters.No Pain No Gain.LOL

Thanks for the great article. Next time I break out thr Seekins, I will try a 10 shot group and post back the results.

Shoot straight...

Jerry

Nice!

BigDozer66

RE: Trouble with 3-shot groups...

I think I posted on this thread that we have used 3-shot groups for ages and never missed a deer or elk because of it, or maybe I didn't, but I am not reading back 20 pages to find out!  

Seriously, the 10-shot group guys are of course right, more or less, "less" when you get a gun and shooter who all of a sudden put it all together with three, "more" from a statistical perspective, tho then you have to add shooting fatigue and some math thing involving the propensity to make mistakes to the mix..

Anyway, local range groupie Mr. Al Cada and I were at my range today monkeying around with some guns.  Near the end of the hot day we got the idea of throwing up some ten-shot groups.  Darn if one of them didn't turn out to be a 9-shot group becuz I only had 9 rounds left of that load to shoot it, but otherwise it was cool, except when it was hot. And it was HOT. I blew 5 straight primers in my carbine before a cup jammed the action and caused me to take notice as a result of leaving the gun and ammo in view of the sun.  It was 140 degrees F on the gun left to rot in the sun...NOT an ambient 140 thank goodness!!  At least it wasn't under the "tent".

Oh, I didn't post those groups.

Anyway, I have no pride, so here they are.  Funny thing is the loud-noisers, at least on the AK side, never post their groups.  I've always wondered why?  {no I haven't...}

So...

Here are a few.  Al agreed to stay put downrange and get a good closeup view of the proceedings.

I agreed to do some flop-down, impromptu shooting at 200 yards.

It was.........bright and ....hot.

The shooting "tent";



Here's a group shot with my hunting load,  presented by Mr Al Cada;.  I'll shoot the Norwegian hunting test with this load later this summer.  I killed a nice big buck with this load in my Ruger Ultralight last year and a mess of varmints with the AR10 since then.



A ten-shot group from the M15,



Now these bullets simply do not shoot as well from the AR10 as the Speers.  They do a little better from my Ruger Ultralight.  But watch;  Here is a 10-shot Rucksack Group;



Now here is the same bullet, shot from sitting, elbows rested on knees.  I held the crosshairs just below Al's chin;



Here are the guns.  I've posted groups from the carbine before.  Yup, the issues I mentioned before were with FC brass....not to be UN-expected.  I think FC uses the same primer hole spec fo both small and large rifle....

{Joke;  Ha Ha.}

Cheers.

Oh, the guns.....



I hope somebody can calculate my mean radius, cuz I cannot.

Here's the range.  Me coming back from checking targets.  

Oh, I forgot to take a pick of the range today, so this is one I took a while back;



I still think a month's worth of "One Shot Groups" would be best.

Mmmm.......