*yawn*...

too many variables

After extensive test-shooting and analysis of shot-groups, I've realized that 5-shot groups and especially 3-shot groups do far more to bolster our egos than they do to help us evaluate the accuracy of our rifles and ammunition.  Below are some of the best 3-shot groups that I've fired from a semi-automatic AR-15 at 100 yards.  One of the groups has an extreme spread of 0.088"  So do I have a sub 1/10th MOA rifle?    Can I shoot groups like this consistently?  No way!  I had to cherry-pick  these groups.  




















5-shot groups don't help us that much more either.  The 5-shot groups pictured below were also fired from a semi-automatic AR-15 from 100 yards.  One of these groups has an extreme spread of exactly 1/4 MOA.  So do I have a 1/4 MOA AR-15?  Not!  I would have to discount a whole lot of other 5-shot groups that speak to the contrary to honestly make that claim.



















Now, take a look at this last set of pictures.  Every single group pictured below  is a 10-shot group fired from a semi-automatic AR-15 at 100 yards and every single one of those groups (and many, many more) have extreme spreads of less than one inch.  With all those groups repeatedly coming in under one inch, I am quite confident that the rifles and ammunition used are truly capable of sub-MOA accuracy.


















Remember Rick Jamison's quotes from the second post in this thread:

I definitely agree, but it was still nice living in ignorance for a few years.
That said, I do think the occasional flier is do to a lack of restraint on my part… I am still a little jumpy on the trigger, and I have squeezed it only to notice at that moment a slight shadow in the scope, a bad habit that I hope will be remedied through more range time.

Honestly,, What is the big discovery here. That after 3 shots Variability like  trigger press, sight alighnment, breath control. Wind, Temperature, etc will actually open up on a 10 shot group..........

3 shots gives you a more then adequate  sense ones  Ammo's accuracy before Human variability gets involved and messes it all up.  Shooting with a jig or a rest is nice and all, but has never been relevent to how I shoot.


I'll stick with my 3 shot groups for sighting in when  someone comes up with something better.... cause I ain't seeing it here....

Originally Posted By Harv24: Honestly,, What is the big discovery here. That after 3 shots Variability like  trigger press, sight alighnment, breath control. Wind, Temperature, etc will actually open up on a 10 shot group.......... 3 shots gives you a more then adequate  sense ones  Ammo's accuracy before Human variability gets involved and messes it all up.  Shooting with a jig or a rest is nice and all, but has never been relevent to how I shoot. I'll stick with my 3 shot groups for sighting in when  someone comes up with something better.... cause I ain't seeing it here....

Did you miss the part about 10-shot groups fired from a MACHINE REST?

Keep rolling your eyes, but there is very compelling information in this thread that undermines the logic of using 3-shot groups to determine the accuracy of a rifle and of ammo.  

Yes I did, and if I shot using a rest all the time, it would be great, but I am still not seeing anything earthshattering here to convinvce me to switch.

Round to Round dispersion and Bias are a fact of life with ammo, Shooting a 10  or 20  or 50 rd group is not going to change it, just  show it, along  with increased variability

All a 10 shot group is really good for is to show a shooters consistency and his ability to control the sight picture, and trigger manipulation while controling his breathing.

Ever see a shooter firing a 10 rd string of fire  shooting Highpower and pull all shots in the X ring??? vs one where some of the hits are in the 9 ring...

I guess I'm just an Internet commando so I'll go back to my 3 shot group

Three shot groups do not give a true picture of the radial dispersion of a rifle and ammunition combination.  That is the point to this thread and that is what the factual data in the first posts of this thread shows.  That is why the US Military requires 10-shot groups for the accuracy testing of the ammunition used by our Armed Forces.  That is why Rick Jamison uses 10-shot-groups when he is testing the accuracy of ammuntion using his machine rest.

.....

more data coming...

The ten 3-shot groups that were fired for the above post measured (from smallest to largest):

0.40"
0.57"
0.64"
0.74"
0.80"
0.85"
1.03"
1.13"
1.19"
1.54"

The variation between the smallest and largest group above is 74%!

Besides firing the above groups today, I also fired three 10-shot groups from 50 yards for another thirty rounds of XM193.

The groups measured (from smallest to largest):

1.24"
1.46"
1.97"

The variation between the smallest and largest of these three groups is only 37%.  Using the same total number of rounds in a set, but firing one set using ten 3-shot groups and the other using three 10-shot groups shows that the group to group variation of the 10-shot groups is far less than  that of the 3-shot groups, half as much in this case. This shows again that 10-shot groups are a more consistent indicator of rifle and ammunition accuracy or as Rick Jamison stated, "Ten shots are a more reliable indicator when it comes to predicting what a load is likely to do in the future."

MEAN RADIUS

Before I can continue with The Trouble With 3-Shot Groups, I need to define the concept of "mean radius" (also called average group radius.)  Mean radius is the method of measurement used by the US Military for accuracy testing of ammunition.  It provides a more useful analysis of the consistency of ammunition and rifle accuracy.

The typical method used to measure a group consists of measuring the distance between the centers of the two most outlying shots of a group.  This would be the "extreme spread" of the group.  We are essentially measuring the distance between the two worst shots of a group.  Take a look at the two targets below.  



Most people would intuitively conclude that the second target shown is the "better" group. Measuring the two groups using the "extreme spread" method, we find that both groups measure 2.1".  Once again with the typical method of measuring groups we are measuring the distance between the two worst shots of the group.  This method tells us nothing about the other eight shots in the group.  So how can we quantitatively show that the second group is better than the first?  (Yes,  we could score the groups using "X-ring" count, but this does not give us any differential information about all those shots in the X-ring.)  This is were the mean radius method comes in.  It will give us that extra information we need to better analyze our groups, rifles and ammuntion.  If I just reported the measurements of the two groups above using the extreme spread meathod, without a picture, you would assume that the two groups were very much the same.  Using the mean radius method shows that the second group is much more consistent.  It has a mean radius of 0.43" compared to 0.78" for the first group.

Below is a brief description of the mean radius using M193 and XM193 specifications for examples.  It is a repost from How Accurate is XM193?

U.S. military specifications for M193 (MIL-C-9963) call for an accuracy requirement of a two-inch mean radius at 200 yards (using 10-shot groups). Federal XM193 calls for a four-inch mean radius at 200 yards. Right from the start we can see that Federal XM193 is only required to group half as accurately as U.S. M193.

To understand the actual size of the groups we are talking about we need to understand the difference between group size as measured in extreme spread versus groups measured using the mean radius. Below is a picture of a 10-shot group of Federal XM193 fired at 100 yards. The group size or extreme spread measures 2.34" or 2.34 minutes of angle.* The mean radius of this same group is only 0.72".




Mean radius as defined in Hatcher's Notebook "is the average distance of all the shots from the center of the group. It is usually about one third the group diameter" (extreme spread).

"To obtain the mean radius of a shot group, measure the heights of all shots above an arbitrarily chosen horizontal line. Average these measurements. The result is the height of the center of the group above the chosen line. Then in the same way get the horizontal distance of the center from some vertical line, such as for instance, the left edge of the target. These two measurements will locate the group center.

"Now measure the distance of each shot from this center. The average of these measures is the mean radius."

Once you get the hang of measuring groups using the mean radius it becomes very simple to do. While being very simple to do, it is also very time consuming. Modern software programs such as RSI Shooting Lab make determining the mean radius a snap.

The picture below is a screen snapshot from RSI Shooting Lab using the group from the above target. The red cross is the center of the group (a little high and right of the aiming point). The long red line shows the two shots forming the extreme spread or group size. The yellow line from the red cross to one of the shots is a radius. Measure all the radii and take the average to obtain the mean radius.




Using Hatcher's one-third rule and applying it to my group above you can see that while not exact it is close enough for "government work."
2.34" (extreme spread) divided by 3 equals 0.78" (mean radius). Actual mean radius being 0.72".

Finally, applying Hatcher's one-third rule to Federal's requirement for XM193 of a 4" mean radius at 200 yards for three, 10-shot groups, we see that it only needs to group into a 12" average group for three 10-shot groups at 200 yards!

4" (mean radius ) times 3 equals 12" (extreme spread). 12" at 200 yards is 6 minutes of angle or 6" at 100 yards.


to be continued...

Excellent information.

I think it's about time we launched a "tack this thread" campaign, this is a clear and concise explanation of a very relevant issue to serious shooters.

Originally Posted By PanzerMK7: I think it's about time we launched a "tack this thread" campaign, this is a clear and concise explanation of a very relevant issue to serious shooters.

+1


Excellent stuff - thanks Molon!!

tag

That is one of the great thing about the AR in 223.  Due to the cheap ammo and low recoil, you can really test the accuracy of your weapon.

I'm afraid my 375 H&H is not going to get the same kind of workout.  The bubbas only shoot a dozen or so rounds a year for a reason.

I suggested on a hunting board one time that three shot groups do not really tell you that much, and was nearly lynched.

Tag.......

to watch the shattering of egos.


For the record.  I too had the issue of wandering zero using 3 shot groups.  I'd have it all centered up and then suddenly they'd all be on one side or the other.  I stopped moving my sights and fired 10 rounds.  I found my center quickly and was able to adjust.  Now, sometimes they stack to one edge or the other even in 10s but when I plotted them all on graph paper (50) they were nicely centered on the bull and 97% fell into a 2" square area.  Maybe a bit smaller circle but it was easy to measure the square.

My gun shoots about 2 MoA.  A little less with match bullets but 2 MoA is what I get if I do it ALL right.

I do tend to shoot 7 shot groups more though.  I do flinch on occasion and I can tell when I do it and I do it more the more I fire.  When I want to test the gun and ammo more I do 7 shot groups.  When I want to know what I can do consistantly I do 10 or sometimes 15.  

Uglygun said

You might fire several 3 shot groups, but if the rifle is actually a 2.5 MOA rifle it's possible that 3 shot groups may cluster in ways that suggest it's capable of potentially better accuracy if the shooter interprets the data wrong they may be lead to the conclusion that the rifle has a wandering zero. However, if the shooter shot a larger sample size they may very well see everything that needs to be shown in 1 group, the rifle's accuracy is subpar and explains beyond a doubt that the zero is not wandering.

Now that is about as well put as it can be. Since I often would only be using my weapon for several shots and then the barrel cools some I will continue to shoot 5 shot groups for my purposes as I need to know what to expect from the gun under those conditions.
JRandyH

i always sight in with 3 shot groups kneeling or prone...
once i am happy with the 3 shot group, fire a group of 10 shots...
final zero based on the center of circle around those shots...
fire another 10... and make sure my group is holding tight to center...

stand up and fire 10 shots...
rapid fire 10 shots...

i always thought 3MOA at 100yds was a good group with an AR (factory barrel/M193 ball ammo)... doesn't that translate to about a 15" group at 500yds (about the size of an adult torso)? anything outside of that is 7.62x51 territory...

Even 5-shot groups can be very misleading - if trying to evaluate ammo or rifle.

The impetus for my thread about XM193 accuracy that Molon referenced in his first post was two 5-shot groups that I shot with Federal XM193.

These were the two groups that I originally shot:



Each by itself might appear to indicate that XM193 is practically 1 MOA ammo (which we know is clearly not correct), but taken together they illustrate exactly the point that Molon was making with his initial post, since the two groups were shot one after the other, with the same point of aim.

Here's my weak photoshop attempt to show what the "correct" 10-shot group might have looked like


... which I guess still isn't BAD for XM193, and probably still a "lucky" 10-shot group, given the known limiations of the ammo.


So I agree wholeheartedly with Molon (and have learned a lot from him).  The point is not jsut that 3 shot groups are unreliable as indicators of accuracy, but that it is risky to use anything less than 10-shot groups.

Excellent analysis, Molon! You've convinced me to test accuracy only using 10-shot groups. It just makes sense.

I was going to say that a three-shot group might make sense for simply zeroing in, as opposed to accuracy testing, but now it appears that even zeroing benefits greatly from a larger sampling of shots.

All of this, of course, is common sense: The larger your sample, the more statistically valid your results.

John

As explained in my previous post, the "mean radius" method of measuring groups gives us information about each shot in the group, not just the two worst shots of the group as is the case when measuring the extreme spread.  The following comparisons will be made using the mean radius of the different groups, so you may want to review the previous explanation of the mean radius.

Besides doing a composite target of the ten 3-shot groups fired with XM193, I also did a composite target of the three 10-shot groups.  Here they are, side by side for comparison.  Remember, each composite target has a total of thirty shots in it (for what the statisticians call a "large sample.")



The 3-shot composite target has a mean radius of 0.45" (indicated by the inner blue circle.)

The 10-shot composite target has a mean radius of 0.42" (also indicated by the inner blue circle.)

Finally, I did a composite target of all the groups together for a total of sixty shots in the group.



The mean radius of the sixty-shot composite group is 0.44".  This sixty-shot composite gives us a pretty good idea of what we can expect from the ammunition and rifle in question when fired from 50 yards.  Just as importantly, the thirty-shot composite groups come quite close to the same results differing by only a couple one hundredths of an inch from the sixty-shot group.

What does all this have to do with the trouble with 3-shot groups?  I'll explain further in my next post.

Since the mean radius method of measuring groups gives us a better picture of what is occuring with all the shots in the group, we can use the mean radius measurements to get  more accurate comparisons between groups.  The mean radii of the ten 3-shot groups from the above post are as follows (from smallest to largest):

0.17"
0.23"
0.25"
0.30"
0.32"
0.32"
0.46"
0.50"
0.50"
0.69"

The 3-shot groups have a variation of 75% from smallest to largest!

The mean radii of the three ten-shot groups from the above post measure:

0.34"
0.39"
0.50"

The 10-shot groups only have a group to group variation of 32%, less than half that of the 3-shot groups.  Once again this shows the vastly improved consistency of 10-shot groups compared to 3-shot groups.

If you recall from the above post, the sixty-shot composite group had a mean radius of .44".  Look at how much closer  the mean radii of the individual 10-shot groups come to the mean radius of the sixty-shot composite group than the mean radii of the 3-shot groups do and of course the mean radii of the three 10-shot groups overlayed on each other is even closer.  Consistency and a high degree of predictablility are what make the use of 10-shot groups far superior to 3-shot groups in evaluating the accuracy of our rifles and ammunition!

Stay tuned for the final chapter...

Originally Posted By Molon: Since the mean radius method of measuring groups gives us a better picture of what is occuring with all the shots in the group we can use the mean radius measurements to get  more accurate comparisons between groups.

...and more shots give more data points with which to calculate the mean radius.  Ten is a good arbitrary number; it's easy to manipulate mathematically, it lends itself to rounding for estimates, and so on.  And it allows more potential variation within each group, which is what we're interested in, right?

Originally Posted By GHPorter: Originally Posted By Molon: Since the mean radius method of measuring groups gives us a better picture of what is occuring with all the shots in the group we can use the mean radius measurements to get  more accurate comparisons between groups. ...and more shots give more data points with which to calculate the mean radius.  Ten is a good arbitrary number; it's easy to manipulate mathematically, it lends itself to rounding for estimates, and so on.  And it allows more potential variation within each group, which is what we're interested in, right?

I'd bet you guys just love that "NUMB3RS" show on tv, don't you?

I'd bet you guys just love that "NUMB3RS" show on tv, don't you?

"We all use math every day. To predict weather, to tell time, to handle money -- math is more than formulas and equations; it's logic, it's rationality. It's using your mind to solve the greatest mysteries we know."

 Charlie Eppes

...and it helps us improve our riflecraft.

I'd bet you guys just love that "NUMB3RS" show on tv, don't you?

Nope.  I'm a scientist.  If it can't be described accurately in numbers, it's just opinion.  More data means (exactly) more information.  Numbers from this data describe the variance in the load (and the rifle).

The problem with Scientists is they never have to test fly the planes they build or fight with the weapons they make....

Guys like Warner VonBraun build Rockets... but guys Like Chuck Yeager Fly them..... Big difference.....

Just something to think about..................................

Originally Posted By Harv24: Guys like Warner VonBraun build Rockets... but guys Like Chuck Yeager Fly them. . . .

. . . And both need the other. Can't we all just get along?

Originally Posted By Harv24: The problem with Scientists is they never have to test fly the planes they build or fight with the weapons they make.... Guys like Warner VonBraun build Rockets... but guys Like Chuck Yeager Fly them..... Big difference..... Just something to think about..................................

THIS scientist tests his own work.  That's why I bought a chronograph and I'm looking at a digital scale-once I can find one that's both accurate and consistent that I can afford.  Don't hold your breath...

Werner never had a thing to do with anything Chuck flew; that was the other guys, the "Right Stuff" ones like Alan Sheppard and John Glenn who flew what Werner supervised the design of.  And they DID have a lot of input into the final products; they pretty much refused to "ride" in the Mercury capsule and demanded some sort of control, and that's a good thing for John Glenn too, since his had a problem.

I do not wear a lab coat, but I do think "deep thoughts" about my subject.

Lastly, I would like to demonstrate just how useful the techniques explained in this thread are for comparing the accuracy of different rifles and ammunition.  When evaulating the accuracy of a rifle/ammunition combination I like to use three 10-shot groups fired from 100 yards.  Those three groups by themselves give me plenty of information for evaluation, but I like to take the extra step and overlay those groups using RSI Shooting Lab to create a 30-round composite group.

For this demonstration I used a 30-round composite target of our beloved XM193 fired from a Colt 16" barrel from 100 yards and compared that to a 30-round composite target of match grade handloads fired from a Krieger barrel at 100 yards.  They say a  picture is worth a thousand words so here are the two composite targets side by side for comparison.






Even without examining the NUMB3RS, the visual presentation makes the results quite clear.  The mean radius of the match grade handload composite group is 0.25".  The mean radius of the XM193 composite group is 0.88"; that is 380% larger than the mean radius of the match grade composite group!

Originally Posted By GHPorter: I want to know more about that machine rest.  How about more pictures, a web site, anything!

I still haven't found a better picture of Rick Jamison's machine rest, but while looking through back issues of Shooting Times I came across a blurb by Layne Simpson talking about his own machine rest.

Originally Posted By Molon: Originally Posted By GHPorter: I want to know more about that machine rest.  How about more pictures, a web site, anything! I still haven't found a better picture of Rick Jamison's machine rest, but while looking through back issues of Shooting Times I came across a blurb by Layne Simpson talking about his own machine rest. home.comcast.net/~gocartmozart/machine_rest_layne_simpson.jpg

Cool!  Thanks a lot.

http://www.imagestation.com/picture/sraid205/p29d115831311a29fa258be6d310a8f1d/ef1d181f.jpg

This lone target shot yesterday, 80 or so rounds at 100 meters with peep sights off a rest, makes it hard to determine sub-moa. But it does show what 80 or so rounds shot in a half hour (due to cease fire) can do.

Thanks

Originally Posted By dropd57: www.imagestation.com/picture/sraid205/p29d115831311a29fa258be6d310a8f1d/ef1d181f.jpg This lone target shot yesterday, 80 or so rounds at 100 meters with peep sights off a rest, makes it hard to determine sub-moa. But it does show what 80 or so rounds shot in a half hour (due to cease fire) can do. Thanks

Nice shooting.  I was only able to capture about three-fourths of your shots since many of the rounds  probably went through the same hole, but your group meaures 3.3".  The mean radius of the group measures 0.91" (and may have been a little smaller if I had been able to capture all the rounds.)

Your zero is dead-on for elevation and only off by one click left for windage.  Here is a screen snap-shot of your group from RSI Shooting Lab.  The thin red cross shows the center of your group.



With your group centered on a High Power type target, all of your shots are in the 10-ring.  What ammunition did you use?

tag for grouping info

Good thread.

Speer manual, IIRC, recommended 7 shot groups for many of these reasons.  Wish I had it in front of me but I believe that they maintained from a statistical point that you could derive valid statistical data from a 7-shot sample size.

So what does this five and ten shot group tell you, distance was 105 yards.

Give me three 10-shot groups and I'll see what I can come up with.

Molon,

Thank you for the illustration! Please explain "Mean Raduis". I was shooting XM193,lot #099.  I just got 500 rounds,lot #117 and I hope it shoots as well.

I must admit however, the rifle has a Rock  River Nat'l Match lower and a White Oak Precision free floated service upper. The barrel is a Pacnor 1:12 twist.

I'd like to retire the Pacnor and have a Broughton 1:13 twist, canted land barrel put on by WOP but the Pacnor with over 5000 round on it apparently still shoots.

Thanks

Originally Posted By dropd57: Molon, Thank you for the illustration! Please explain "Mean Raduis". I was shooting XM193,lot #099.  I just got 500 rounds,lot #117 and I hope it shoots as well. I must admit however, the rifle has a Rock  River Nat'l Match lower and a White Oak Precision free floated service upper. The barrel is a Pacnor 1:12 twist. I'd like to retire the Pacnor and have a Broughton 1:13 twist, canted land barrel put on by WOP but the Pacnor with over 5000 round on it apparently still shoots. Thanks

dropd57,

On page three of this thread, about half way down the page, I have posted an explanation of "mean radius."  

I was curious to hear if you were using XM193.  The mean radius of your group at 100 meters is 0.91" and adjusted for 100 yards it comes out to 0.83".  In a previous post on this page I showed a 30-round composite target I obtained using XM193 fired from 100 yards.  The mean radius of that composite group was 0.88".  It's kind of scary how we both ended up with basically the same results for XM193 when measured using the mean radius.

Originally Posted By GHPorter: I want to know more about that machine rest.  How about more pictures, a web site, anything!

This is the only other picture of Rick Jamison's machine rest setup that I've been able to find so far.

Molon,

5/10th of a mean radius spread between us! Is that correct? If so, that would suggest that lot to lot, xm193 is pretty consistant.

What rifle and barrel twist are you using? Hopefully, I didn't miss that being mentioned in the thread like I did "mean radius" and the prior spelling of it.

I feel that these slower twist barrels are great for reduced service matches and really gives those 1:6.5,7 and 8's a run for their money on the line.

The question is, have we really tapped out this round? Is there no more accuracy to gotten out of the xm193?

Also, would your replace this barrel and go for a 1:13 canted twist or would you just get another upper and leave this puppy alone?

Thanks

Originally Posted By dropd57: Molon, 5/10th of a mean radius spread between us! Is that correct? If so, that would suggest that lot to lot, xm193 is pretty consistant. What rifle and barrel twist are you using? Hopefully, I didn't miss that being mentioned in the thread like I did "mean radius" and the prior spelling of it. I feel that these slower twist barrels are great for reduced service matches and really gives those 1:6.5,7 and 8's a run for their money on the line. The question is, have we really tapped out this round? Is there no more accuracy to gotten out of the xm193? Also, would your replace this barrel and go for a 1:13 canted twist or would you just get another upper and leave this puppy alone? Thanks

dropd57,

Actually, the difference between our two composite groups of XM193 is 5/100ths of an inch for the mean radius measurement.  I suspect there is a large dose of coincidence involved here, but it's still kind of scary.  My groups of XM193 were fired from a Colt 16" HBAR  with a 1:9" twist.

As for the accuracy of XM193, you might be interested in reading DK-Prof's thread on that subject:  How Accurate is XM193?

Before you replace your barrel, you might want to try using some match grade ammuntion.  Here is a pic from a previous post showing a comparison of a 30-shot composite target of XM193 fired from 100 yards versus a 30-shot composite target fired using match grade ammuntion from the same distance.  Can you guess which amunition I prefer to use for any important shooting?

Here are the same two composite targets from the above post overlayed on High Power type targets to give you another perspective.

match grade



XM193

Here is another quote about 3-shot groups from another Precision Reloading article by Rick Jamison.


"Some shooters may have two or three three-shot groups to prove the load is really accurate. It really takes more shooting than that to make a judgment on a load’s accuracy potential. Three shots forming a tight cluster is nice to look at, but it is little more than an accident. Shooting three-shot groups to see how everything is working is essentially a waste of time and components."

I just came across this quote from an article in an old American Rifleman magazine.

"Mean radius is the mean distance of bullet impacts from center of the test group.  It is used in government ammunition acceptance because it takes account of every shot and comes close to maximizing the test information.  While there is no exact relationship between this measure and the simpler and more convenient group diameter, the 10-shot group diameter averages slightly over 3 times the mean radius."

These old back issues of American Rifleman (1950s, 1960s) make for some engaging reading.  Here is a pic from a July 1958 article pointing out why even 5-shot groups are misleading for evaluating the accuracy of ammunition.



Here is an interesting quote from the same article:

"To establish facts, repetitious tests must be performed to ascertain that the results can be obtained at will.  If 3 separate 10-shot targets  are first fired to establish a value, and then another 30-shot test fired using the changed powder, etc., and an improvement noted, then it can be said with some assurance that an improvement has been made."

This is one of the best threads i've ever read here, great job. Pay no attention to the people who can't grasp the concept, darwin will take care of them.

I'm glad you found the information useful.