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Posted: 4/24/2006 11:06:41 PM EDT
[Last Edit: 2/25/2017 5:09:36 PM EDT by Molon]
The Trouble With 3-Shot Groups

(The Distant Prequel to The Trouble With Tribbles)


As our story begins, we find our Hero sitting down at the shooting bench on the 100 yard line at his local range. Our Hero is a real Internet Commando. He has watched the movie Heat 87 times, is registered on all of the important Internet firearms forums, knows the difference between a "clip” and a "magazine” and attends every local gun show without fail.

His latest acquisition from the local gun show is a 16” barreled Frankengun that originally belonged to a Delta Force operator who was at the Battle of Mogadishu. (He could tell you the name of the operator, but then he’d have to k……well, you know.) The seller at the gun show let our Hero in on another secret too. Eugene Stoner himself helped the Delta operator assemble this particular AR-15.

Our hero settles into position on the bench and fires his first 3-shot group. (He only fires 3-shot groups because everyone from the Internet knows that you only have to fire 3-shot groups to test the accuracy of your rifle and ammunition.)

His first group forms a nice little triangle at the bottom of the 10-ring. Our Hero just knew this was going to be a good day. After all, he was using that XM193 ammunition. A former SEAL who was selling beef jerky at the gun show had told our Hero that the SEALs used ammo just like XM193 in Viet Nam and that a single shot in the buttocks from this ammo would "blow your head clean off!”

At the cease fire our Hero checks his first target. (Our Hero’s targets are NRA High Power type targets reduced for 100 yards. The X-ring measures 1.5” and the 10-ring measures 3.5”). Much to his satisfaction, his first group measures 1.16”, almost minute of angle! Now most Internet Commando wannabees would have stopped right there and gone home and spent the next 3 hours posting threads on the internet about their great accomplishment, but not our Hero. He makes the decision….to fire a second group!

group one





Our Hero has read reports of other Internet Commandos who have been able to achieve sub-minute of angle groups using XM193. After all, this ammo uses "Full Metal Jacket” bullets and is made to "Mil-spec.”

Our Hero carefully watches the bench-rest shooter three lanes down (who monitors the wind conditions on the range using a Wind Probe) and only fires immediately after the bench-rester does. He does this for three shots and then checks his target at the next cease fire.

Our Hero measures this target three times just to be sure. The group measures 0.93”! Hooah, a sub-minute of angle group! Our Hero is now one of the few, the proud, the real Internet Commandos who can claim to shoot sub-minute of angle groups using XM193!

group two





There’s just one little problem with that second group our Hero fired. It is centered in a different location on the target than the first one. The second group is centered 0.12” above the center of the target and the first group is centered 1.44” below the center of the target. Hmmm…

Well our Hero is a real Internet Commando so he can’t let details bother him. After all, sub-minute of angle is sub-minute of angle!

As our Hero starts to pack up his targets, something in the back of his mind starts to nag at him. He recalls the reports of the other Internet Commandos. They didn’t just shoot sub-minute of angle groups with XM193; they did it "all day long.”

Well, not wishing to be looked down upon by the other Internet Commandos our Hero decides to shoot one more 3-shoot group. After all, if his carbine and ammo could shoot two, sub-minute of angle groups, they could surely do it "all day long.”

So, our Hero settles back into position and again taking his cue from the bench-rester fires a third 3-shot group. Upon retrieving his third target and measuring the group our Hero can not believe his eyes. The group measures 2.5”! How can this be possible? He was using XM193 and not just any XM193. It was the fabled LOT #3, the most accurate and hard to come by of all the lots, yet this third group was larger than the first two groups combined! Hmmm… Our Hero wonders how he can ever show his avatar on an Internet forum again after firing such a group with XM193.

group three





Then, slowly our Hero starts to recall a word he has heard mentioned many times before on his favorite Internet forum. It starts with the letter F. Hmm . . .F . . .Fl . . . Flyer! That’s it, flyer! That low shot down at seven o’clock on the target is a flyer! It’s not the fault of the gun or the ammo, it’s a flyer. It's caused by user error, the loose nut behind the stock, the wind, the sun or any other excuse that can be dreamt of in your philosophy, but not the rifle or ammo.

The flyer is something to be discounted as if it never happened. (Why be concerned with reality when you are an Internet Commando?) Since that shot is discounted, why not discount that whole group as if it never happened? (After all, isn’t that what an Internet Commando does?) Our Hero decides to discount the entire group and throws the target in the trash. He makes a solemn vow to never mention this group to anyone. After all, he is a real Internet Commando.

Upon returning home our Hero makes all the usual posts on the Internet about his sub-minute of angle groups using XM193. True to his solemn vow, he makes no mention of his 2.5” group. At no time does he mention that these groups were 3-shot groups. Nor does he make any mention of the fact that the groups were centered in different locations on the target.

Our Hero ends his day wondering if his grandson, or great-grandson or even great great-grandson will remember the accomplishments of the real Internet Commandos or if their contributions to the shooting world will eventually be lost in time? He even wonders what his progeny might someday be named, James or possibly Tiberius? Hmmm…


Dedicated to DK-Prof for his shining example of "truth in accuracy reporting" in these two threads:

How Accurate is XM193?

Apparently, I suck at shooting.



....


While the fable above is obviously fiction, the examples of targets shown are based on a real target of a 10-shot group fired from 100 yards using XM193. When all of the 3-shot groups from above are overlayed on a single target you see a much truer example of the limitations of the rifle and ammo. The gap made by the so-called “flyer” is filled in by the other seven shots of the whole group. You can see that when the first 3-shot group (which is centered 1.5” below the second 3-shot group) is displayed with the second 3-shot group you are actually seeing a much better indication of the total dispersion of the rifle and ammo combination. Most people fail to mention that their 3-shot groups are impacting at different locations on the target. This is why 10-shot groups are a much better indicator of a the radial dispersion of a rifle/ammunition combination.






the real target





Rick Jamison, the author of the Precision Reloading column in Shooting Times magazine approaches accuracy testing in a scientific manner. He uses a machine rest for testing and fires 10-shot groups. Here are his own words on the subject from one of his articles:

"There are stories of a single bullet that for no explained reason flies out of what might have been a tight cluster. This often occurs with a three-shot string and many times with a five-shot string. If you're lucky enough to fire a group without a flier, you can end up with a very tight group. However, usually what happens if another five or seven shots are fired to complete a 10-shot string, other bullets fill in the space between the main group and the flier to make a reasonably rounded group. Ten shots are a more reliable indicator when it comes to predicting what a load is likely to do in the future.

The problem with 10-shot groups is that when you report them, everyone thinks you aren't shooting very well or that the ammunition is not good because the group sizes are so much larger than three- or five-shot groups. Also, when we're firing three- or five-shot groups with a flier, it is only natural to assume that it was caused by a flinch or “pulling” the shot. Therefore, since the flier was our own fault, the tendency is to eliminate it from any reporting of group size."

machine rest





....


Here’s another example demonstrating that 3-shot groups do not provide a valid indicator of the radial dispersion of a rifle/ammunition combination. The test vehicle for this demonstration was a one of my AR-15s that has a free-floated Colt HBAR and is wearing a Leupold 3.5-10X40 LR/T.







Prior to beginning this demonstration, I fired a 10-shot control group at a distance of 50 yards using a hand-load topped with the Sierra 77 grain MatchKing. The target used is an NRA High Power type target reduced for 50 yards. The X-ring measures 0.75" and the 10-ring measures 1.75". The 10-shot control group had an extreme spread of 0.493”.




Next, I fired a couple of 3-shot groups from 50 yards using Federal XM193 ammunition. (Shooting was conducted at an indoor range, so wind was not a variable in this case.) The two targets are pictured below.



The center of the first 3-shot group was located approximately ¼ MOA high and ½ MOA to the right of the center of the target, which was the point-of-aim. However, the center of the second 3-shot group was located approximately 1.5 MOA low and ½ MOA to the left of the center of the target. The centers of just these two, 3-shot groups are almost 2 MOA apart in elevation.



The centers of the individual 3-shot groups are indicated below by the blue crosses.



I actually fired a total of ten, 3-shot groups in a row with the XM193 ammunition for a total of thirty shots. Thirty occurrences of something that is being studied is what the statistics types like to refer to as a "large sample." Using the RSI Shooting Lab software program I was able to overlay all ten of the 3-shot groups on each other for a 30-shot composite group.







This 30-shot composite group gives us a much better picture of the radial dispersion of the rifle/ammunition combination (and in this case particularly the ammunition) than 3-shot groups by themselves do. These 30 shots also give us give us a much better indication of where the center of the points-of-impact are.



....

The ten, 3-shot groups that were fired in a row for the above demonstration 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%!

In addition to firing the ten, 3-shot groups listed above, I also fired three, 10-shot groups in a row 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 the radial dispersion of a rifle/ammunition combination 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.”



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.”



....



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.)

A PRIMER ON THE MEAN RADIUS

The mean radius is a method of measurement of the dispersion of shot-groups that takes into account every shot in the group. It provides a more useful analysis of the consistency of ammunition and firearms (accuracy/precision) than the commonly used method of extreme spread.

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.

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)” for 10-shot groups.

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. 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.



Mean Radius Demonstration

Let’s say you fired a 5-shot group from 100 yards and the resulting target looks like this. (The X-ring measures 1.5” and the 10-ring measures 3.5”.)



The extreme spread of the group measures 2.83”, but we want to find the mean radius (or average group radius.) In order to find the mean radius we must first find the center of the group. By “eye-balling” the target most people would see that the group is centered to the left of the “X-ring” and probably a little high, but we need to find the exact location of the center of the group.

Locating the Center of the Group

The first step in finding the center of the group is to find the lowest shot of the group and draw a horizontal line through the center of that shot.



Next, find the left-most shot of the group and draw a vertical line through the center of that shot.



Now measure the distance from the horizontal line to the other four shots of the group that are above that line. Add those numbers together and divide by the total number of shots in the group (5).



2.50” + 1.03” + 2.01” + 1.30” = 6.84”

Divide by 5 to get 1.37”. This number is the elevation component of the center of the group.

Next we need to find the windage component of the center of the group. From the vertical line, measure the distance to the other four shots of the group that are to the right of the line. Add those numbers together and again divide by the total number of shots in the group (5).



1.76” + 2.54” + 0.45” + 1.19” = 5.94”

Divide by 5 to get 1.19” This is the windage component of the center of the group.

Finding the windage and elevation components of the center of the group is the most difficult part of this process. Once that is done the rest of the process is a piece of cake.

Using the windage and elevation components, locate the position on the target that is 1.37” (elevation component) above the horizontal line and 1.19” (windage component) to the right of the vertical line. This location is the center of the group!



Determining the Mean Radius

Now that we have located the position of the center of the group, the first step in determining the mean radius is to measure the distance from the center of the group to the center of one of the shots. This line is a single “radius”.



Now measure the distance from the center of the group to the center of each of the rest of the shots in the group. Add the measurements of all the radii together and then divide by the total number of shots in the group (5).



0.85” + 1.35” + 1.38” + 0.84” + 1.61” = 6.03”

Divide by 5 to get 1.21”. This is the mean radius (or average group radius) of the group!

Using the mean radius measurement to scribe a circle around the center of the group gives you a graphic representation of the mean radius. This shows the average accuracy of all the shots in the group. This demonstrates why the mean radius is much more useful than the extreme spread in evaluating the accuracy of our rifles and ammunition.



Over-laying the targets of at least three, 10-shot groups fired in a row and determining the mean radius of the composite group gives us a statistically powerful tool for evaluating the radial dispersion of a rifle/ammunition combination.



The table below will give you an idea of the relationship between the mean radius and extreme spread for 10-shot groups.



Here are some interesting quotes pertaining to the mean radius from old issues of American Rifleman:



“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 examples illustrate the sensitiveness of the extreme spread to number of shots in the group. Indeed, as the table indicates, the measures made to only the outside shots of the group, e.g. the extreme spread, are very sensitive to number of shots, while the measures made to all the shots, e.g. the mean radius are far less so. It may be added that the latter measures are also less variable in their representation of the group; they are more efficient. This explains why the target testing of U.S. military rifle ammunition is by mean radius."


....


As explained previously, 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.

Besides doing a 30-shot composite group formed from the ten, 3-shot groups fired in a row with XM193 as shown above, I also compiled a 30-shot composite group formed from the three, 10-shot groups fired in row. Here they are, side by side for comparison.



The 30-shot composite group formed from the ten, 3-shot groups has a mean radius of 0.45” (indicated by the inner blue circle.)

The 30-shot composite group formed from the three,10-shot groups has a mean radius of 0.42” (also indicated by the inner blue circle.)

Finally, I compiled a 60-shot composite group formed from all of the above groups.







The mean radius of the 60-shot composite group is 0.44”. This sixty-shot composite group gives us a fairly definitive idea of what we can expect from the rifle/ammunition combination in question when fired from 50 yards. Just as importantly, this demonstrates that the thirty-shot composite groups come quite close to the same results as the 60-shot composite group; differing by only a couple one-hundredths of an inch in mean radius from the 60-shot composite group.



....


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 above 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 above measure (from smallest to largest):

0.34”
0.39”
0.50”

The mean radii of 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. The mean radius of the 30-shot composite group formed from over-laying the three 10-shot groups on each other is even closer. Consistency and a high degree of predictability are what make the use of 10-shot groups (particularly three,10-shot groups fired in a row) far superior to 3-shot groups in evaluating the precision of our rifles and ammunition!



....


Here is a final demonstration that further illustrates and reinforces all the concepts previously presented. Using one of my AR-15s that has a free-floated Colt HBAR, I fired five, 10-shot groups from 100 yards using a hand-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 hand-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”

Those who espouse the use of 3-shot groups for evaluating the radial dispersion of a rifle/ammunition combination like to point to the smallest 3-shot groups for their accuracy claims and then pretend that all those large 3-shot groups don’t exist.

The average extreme spread for all sixteen of the 3-shot groups was 1.72”. Also, the statistical centers of many of the groups, (both large and small) were located at different locations on the target.

Pictured below is the first 3-shot group of the 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 is remarkably similar in radial dispersion to the 50 round composite group formed from the five 10-shot groups.






Here’s the only target from the above shooting session that the Internet Commando would have posted.




Remember, all the data for the above examples were obtained during live-fire testing from my bench-rest set-up, not from computed generated models that fail to demonstrate a correlation with actual real-world data.


....


Institutions and organizations that buy enormous amounts of ammunition and weapons are far more interested in facts, than sales hype and propaganda and most of them demand that accuracy/precision testing be conducted using 10-shot groups. This includes the Federal Bureau of Investigation, Crane Naval Surface Warfare Center, the US Army Marksmanship Unit and the US military’s acceptance testing of both 5.56mm ammunition and weapons. On the other hand, businesses that use 3-shot groups for making their accuracy claims are usually trying to sell something.

....

At the 1992 Barcelona Olympics, USA Shooting Team members Launi Meili and Robert Foth won the gold and silver medals in the three-position rifle events. The Olympians used the new Federal Gold Medal ammunition to aid them in obtaining their victories. This was the first time in more than 30 years that an American won an Olympic medal in one of the small bore shooting events while using American-made ammunition.

It’s interesting to note that pertaining to the accuracy/precision development and multifaceted testing of the Federal ammunition that helped the US Olympians win gold and silver medals in Barcelona, Federal’s Director of Product Engineering, Dave Longren, had this to say:

'The standard test string was three 10-shot groups, with the most attention paid to the 30-shot composite. "When you’re working at this level, the traditional five 5-shot group test simply doesn’t give you statistically valid results.”'*

* Hunnicutt, Robert. “Ammo Good as Gold.” American Rifleman Nov. 1992: 32-33, 72-73. Print.

.....



"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 from NUMB3RS


. . . and it helps us evaluate and improve our rifle-craft.

Molon



.........
Link Posted: 4/24/2006 11:07:13 PM EDT
[Last Edit: 8/21/2016 2:40:51 PM EDT by Molon]

Some additional information on the subject matter . . .









The Texas Sharpshooter


(Second Cousin of the Internet Commando)



Envious of all the attention his cousin, the Internet Commando, receives at the local tavern, as well as on the popular firearms forums on the Internet, our antagonist decides it is time for him to make his mark in the world. He decides he needs to perform some feat of marksmanship that surpasses even the accomplishments of his cousin, the Internet Commando.

But what can he possibly do that the Internet Commando hasn’t already done? Our antagonist recalls the tales of the Internet Commando. He remembers his cousin boasting of shooting sub-minute of angle groups using XM193. How could he possibly top that? Then, it dawns on him. The Internet Commando was using his sights when he fired those sub-minute of angle groups with XM193. “Anyone can shoot a small group using their sights,” he thinks to himself. “It would take real skill to shoot a good group without using the sights, say . . . as in shooting from the hip!”

Seeing his destiny laid out before him, our antagonist sets up his target at 25 yards and proceeds to fire on the target shooting from the hip. As our antagonist walks towards his target to examine his results he begins to grin from ear to ear. “Wait until my cousin sees this,” he actually speaks aloud.

That night at the local tavern our antagonist shows his target (pictured below) to those who have been hanging on every word that his cousin, the Internet Commando has been saying. The people are absolutely astonished that our antagonist was able shoot such an amazing group firing from the hip at 25 yards. Bewildered by the incredible skill demonstrated by our antagonist, the Internet Commando tells his cousin, “You’re quite the sharpshooter Tex!”










While the above fable is fictitious, it is based based on a real target that I fired from an AR-15. I actually fired that group pictured above from 25 yards while shooting from the hip. For those of you that haven’t already figured out how I was able to perform such a feat, here are the little details that Texas Sharpshooters fail to mention.

I actually fired 30 shots from the hip at the “target” which was a blank piece of paper measuring 36” X 24” (kind of like the broad side of a barn). I then found 3 shots that formed a cluster and “drew” the bulls-eye around the shots. Those 3 shots occurred randomly. Not from any outstanding shooting skills of mine, nor from any outstanding qualities of the rifle or ammunition I was using, but purely by chance. (The actual extreme spread of the 30-shot group was 31”; that's 2 feet, seven inches.)

The fallacy of the Texas Sharpshooter is based on the fact that clusters of data can occur randomly or by chance (the clustering illusion). “In making statistical observations, results will not be distributed with total uniformity but will naturally be sparser in some areas and denser in others, purely by chance.”* Human beings tend to want to discern patterns in random clusters where none actually exist. We try to assign significance where there isn’t any.

In the case of the Texas Sharpshooter “information that has no relationship is interpreted or manipulated until it appears to have meaning.”* More specifically, “although the shots were random, the Texas Sharpshooter makes it appear as though he has performed a highly non-random act. In normal target practice, the bulls-eye defines a region of significance, and there's a low probability of hitting it by firing at random. However, when the region of significance is determined after the event has occurred, any outcome at all can be made to appear spectacular.”*

If you had not known that the Texas Sharpshooter had drawn the bulls-eye after the shots were fired, you would “falsely assume he's an excellent marksman by reasoning from effect (bullet holes in the bulls-eye) to cause (he fired the bullets).”* The fatal flaw is “assigning significance to the outcome of a random event after it has occurred.”* The danger is in “jumping to a conclusion that a random cluster is a causal pattern.”* The Texas Sharpshooter “takes a random cluster, and by drawing a bulls-eye onto it makes it appear to be causally determined.”*



Here is a pic of the target before the bulls-eye was drawn on it, shown with a yardstick on the left border.








Here is the target in negative.








Lastly, the target in negative with the random cluster (actually two random clusters) highlighted.








*Sentences in quotation marks are from multiple unknown authors.



….


Two schools of thought pertaining to the Texas Sharpshooter:


“We are Texas Sharpshooter.” The Borg Collective model.


“There can be only one!” The Highlander construct.


....





The Internet Commando’s Nephew


The scene opens with Billy rushing into his house to tell his mother of his accomplishments while at the shooting range with his uncle that afternoon.


Billy: Guess what, Mom! I can shoot sub-MOA groups all day long with my chrome-lined, NATO chambered AR-15 using XM193 ammunition. I’m a real Internet Commando now!

Mother: Billy, how many shots were in those groups?

Billy: Aw, gee Mom. They were only 3-shot groups, but all the other kids are shooting 3-shot groups.

Mother: And if all the other kids jumped off a bridge, would you do that too?

Billy: No, Mom

Mother: Billy, you know that 3-shot groups aren’t good for you. What have your father and I told you about 3-shot groups?

Billy: 3-shot groups don’t mean jack-shit?

Mother: That’s right, Billy. So how many of those 3-shot groups of yours were actually sub-MOA.?

Billy: Well . . . only two.

Mother: And how many groups did you actually fire?

Billy: Five.

Mother: Billy . . .?

Billy: Ok, it was ten groups. You happy now?


Mother: So you fired ten, 3-shot groups and CHERRY- PICKED two groups to brag about? Your father and I raised you better than this, Billy.

Billy: Sorry, Mom.

Mother: Sorry doesn’t cut it, young man. I’m going to have a long talk with your uncle and you’re no longer allowed to log-on to glock-gab.com. That site is rotting your brain.

Billy: But Mom!

Mother: No buts, Billy. And the only reason that I haven’t grounded you is because you haven’t used the “F” word.

Billy: You mean f . . . l . . .

Mother: Watch it, Billy.

Billy: Flier!

(Billy turns and runs to his bedroom as fast as he can.)

Mother: That’s it! You’re grounded, and just wait until your father gets home! This is all because of that uncle of yours!”


After Billy finished his week of being grounded, his parents decided to supervise an experiment at the shooting range with him to reinforce the folly of using 3-shot groups to evaluate the accuracy of an AR-15 rifle/ammunition combination. Shooting from a bench-rest at a distance of 100 yards using his father’s Krieger barreled, semi-automatic AR-15 (Billy’s actually a pretty good shot for his age) and using his father’s hand-loads topped with Hornady 55 grain FMJ projectiles, they had Billy shoot thirty shots in a row (each round was single-loaded) on thirty different targets; one shot per target (all while monitoring the wind conditions on the range using a Wind Probe). (Prior to Billy shooting his thirty shots, Billy’s father fired a sub-MOA 10-shot control group from the same rifle.) They then collected their targets and headed home to continue the experiment.

Once at home, they entered each of the thirty individual targets into the computer using the software program RSI Shootng Lab. Next, they used the software program to form ten, 3-shot groups from the thirty individual shots. (The first 3-shot group was formed from shots 1-3, the second 3-shot group was formed form shots 4-6 and so on.) The results are pictured below. (The point-of-aim for the groups shown below is the double white circle.)








The ten, 3-shot groups.







Billy’s parents pointed out to him that the 3-shot groups had wide variations in their extreme spreads from shot-group to shot-group. The extreme spread of the largest group (group number 8) was five times as large as the smallest group (group number 2). They also pointed out the centers of the various 3-shot groups varied quite a bit in their location from the point-of-aim. For example, all three shots from group number 3 where higher than the point-of-aim, while all three shots from group number 4 where lower than the point-of-aim. Also, the center of group number 3 was to the left of the point-of-aim, while the center of group number 4 was to the right of the point-of-aim.


(If Billy’s uncle had fired those ten, 3-shot groups, he would have cherry-picked group number 2 and group number 5 to represent the accuracy/precision of his AR-15 rifle and ammunition and pretended that the other eight groups didn’t exist.)


Next, Billy’s parents had him form three, 10-shot groups from the thirty individual shots using the software program. (The first 10-shot group was formed from shots 1-10, the second 10-shot group was formed from shots 11-20 and the third 10-shot group was formed from shots 21-30.) The results are pictured below.









Upon seeing the 10-shot groups pictured above, Billy immediately noticed how much smaller the variations in extreme spreads were from shot-group to shot-group. In fact, the extreme spread of the largest 10-shot group (group number 3) was only 1.5 times as large as the extreme spread of the smallest 10-shot group (group number 1). Billy even pointed out to his parents that the centers of the three 10-shot groups were all located very similarly from the point-of-aim.

“That’s my boy,” cheered Billy’s mother.

Billy’s father proudly remarked to Billy, “So now you see why 10-shot groups give us a much better picture of the actual radial dispersion of the shots fired from a rifle/ammunition combination.”

Billy’s father went on to explain, “And if we over-lay three 10-shot groups that were fired in a row on each other and use the mean radius of the 30-shot composite group that is formed, we get a very good indication of the radial dispersion produced by a rifle/ammunition combination.”








Billy then asked his parents, “Should I try to explain this stuff to Uncle?”

His father replied, “You can try . . .”




....


The shot-groups depicted in the above fable are from my actual targets obtained during live-fire testing.



....
Link Posted: 4/24/2006 11:19:40 PM EDT
Cool.
Link Posted: 4/25/2006 12:14:56 AM EDT
Excellent.
Link Posted: 4/25/2006 12:59:05 AM EDT
Excellent post!
Link Posted: 4/25/2006 1:30:57 AM EDT
Ahhhhhh......the truth shall set U free!

Good post!
Link Posted: 4/25/2006 1:45:27 AM EDT
Oh come on. Shoot one shot groups. Outside edge to outside edge will be around .224. Top that!




Woody
Link Posted: 4/25/2006 1:45:28 AM EDT
[Last Edit: 4/25/2006 1:46:19 AM EDT by DK-Prof]

Originally Posted By Molon:

Dedicated to DK-Prof for his shining example of "truth in accuracy reporting" in these two threads:

How Accurate is XM193?

Apparently, I suck at shooting.





Yay - I'm famous!



I was actually thinking about this EXACT thing when I was on the range about a week and a half ago.

When I'm shooting a 10-shot group, I'm sometimes struck how "nice" it looks when I'm only 3 shots into it, so I stopped at 3 shots at a particularly nice-looking one when I was at the range, and then shot a regular 10-shot group after that.

Here's the pic: The 3-shot group is on the main (large) ring and measures about 3/8 of an inch (i.e. less than 1/2 MOA) - but when I fired 10 shots on the top right ring, the group is about 1 3/4 inch.



It illustrates Molon's point really nicely. When I shoot a bunch of 10-shot groups, I'm lucky to average about 1 1/2 inch groups - but if I stopped at 3 round, and SELECTED which groups to measure, I could easily claim to shoot 1/2 groups.
Link Posted: 4/25/2006 1:54:27 AM EDT
[Last Edit: 4/25/2006 1:55:16 AM EDT by jls7]
Excuse me sir. I dont know who you think you are but I am the one and only true internet commando and my AK-15 will shoot sub .5 moa all day long, the trick is using the top of my laptop as a benchrest.
-jls7
Link Posted: 4/25/2006 3:41:03 AM EDT
Great info! I have always taken 7 shot groups and up since I always tell myself that 3 shots cant be a measure of accuracy.
Link Posted: 4/25/2006 8:12:55 AM EDT
20 round groups in less than 30 seconds, as 20 conveniently fit in my old M16 range mag, and tend to take most of the variables out of the equation. Plus since you have 20 to fire, you can squeeze them off pretty fast since we are only talking a short 100 yards here.



Now this was with blue box BH 75 grain, and a JTAC built 18" Krieger barreled SPR in about 27-30 seconds.
The only time I did better in this "exercise" was with my Bushmaster Varminter, which was about 3/4" with 55gr Winchester Silvertips, but that is discounting the single flier which opened the group up to 1.5".
Link Posted: 4/25/2006 10:02:24 AM EDT
LOL! Great post, funny and informative.

You deserve a beer
Link Posted: 4/25/2006 10:15:19 AM EDT
It's a great shame Rick is no longer writing for Shooting Times...

his articles will still appear for some time, until they run out of pieces they have on hand from him already.....

good info.......
Link Posted: 4/25/2006 10:41:43 AM EDT
5 shot groups

100 yds 20" Bushy (20th anniv model) My handloads





TXL
Link Posted: 4/25/2006 10:50:52 AM EDT
yup three shot groups suck. For testing reloads I switched to 5 shot groups a long time ago. If you muff one shot you have no idea if that load is great or crap. True accuracy testing starts with 10 shot groups.
Link Posted: 4/25/2006 11:16:44 AM EDT
great info, thanks Molon!
Link Posted: 4/25/2006 12:11:55 PM EDT
Great post. I learned years ago to never shoot less than 5 unless I am sighting in. When I get a load I like and want to test it I do the 10 shot group thing.
JRandyH
Link Posted: 4/25/2006 12:41:24 PM EDT
Great post! The only time I shoot three shot groups is if I've just installed an optic or re-zeroing an optic and I'm trying to get an idea of where the bullets are hitting.
Link Posted: 4/25/2006 1:52:33 PM EDT
Cool post.
Link Posted: 4/25/2006 4:11:40 PM EDT

Originally Posted By JRandyH:
Great post. I learned years ago to never shoot less than 5 unless I am sighting in. When I get a load I like and want to test it I do the 10 shot group thing.
JRandyH
www.pbase.com/jrandyh/image/56762417.jpg




ACtually, when I developed that load above, I used 5 shot groups, and incremented powder by .2 grains. It was cool to see the group get smaller, then progressively bigger.

Found my sweet spot, and voila, I be happy.

TXL
Link Posted: 4/25/2006 5:06:27 PM EDT
Cool,
And my gun likes 52 grain black hills thats 10 years old LOL.
JR.

Link Posted: 4/25/2006 5:22:34 PM EDT
Basic statistics, nothing more.


I wound up shooting 10 shot groups, actually multiple 10 shot groups and doing an average of several, because of experiences that relate closely to the troubles exibited by low shot count groups as illustrated in the first post.


My accurized AR15 would occasionally turn in a couple of real winners with 5 shot groups hovering between 3/8-1/2 inch at 100 yards. But then, unexplicably the groups would occasionally come in at 3/4 of an inch with no apparent explanation for it. Maybe 3 out of 5 groups would be rediculously small while the rest would come in at 3/4s of an inch.

After taking a statistics course in college I decided to increase my sample size. What I found was that the 10 shot group was much more represenative of the standard distribution curve. Out of 10 shots, 60-70% would fall within the 1/2 inches I often saw with 5 shot groups while a remaining 3-4 shots would be responsible for pushing the group to 3/4 of an inch.


The higher shot count/sample size gave me a much better indication of what was going on, a very clear and obvious visual representation. Something that might not be readily apparent with a 3 shot group, even if you take multiple 3 shot groups and average them together. 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.


10 shot group from my varmint AR, something that could be backed up with multiple groups fired.

Link Posted: 4/27/2006 10:12:45 AM EDT
That's an outstanding group!
Link Posted: 4/27/2006 10:21:01 AM EDT
GREAT post Molon.

This should be tacked.... if not for a just a while.
Link Posted: 4/27/2006 11:11:06 AM EDT
KISS
Link Posted: 4/27/2006 11:23:40 AM EDT
Link Posted: 4/27/2006 11:58:23 AM EDT
Link Posted: 4/27/2006 3:19:41 PM EDT
[Last Edit: 4/27/2006 3:23:08 PM EDT by DevL]
Because they are testing for rifle accuracy not the ability to read wind or dial in zeros for different ammo types. If they rezero for a 5mph cross wind what does that prove? Nothing. It only allows them to tak a picture with rounds in the bull and that has no real value or meaning. It s wasted time that could be used to test the next load. Rezeroing for each load you are testing is silly IMO. I see no reason to do it. I would find the most accurate group then rezero for that one. What you suggest just creates a lot of unneeded work and wastes time.

You are suggesting that you would fire 5 types of ammo and the one that was sloopy group but dead center would be your choice? Makes little sense. Find the smallest group then rezero that one and none of the others.
Link Posted: 4/27/2006 3:37:55 PM EDT
.
Link Posted: 4/27/2006 5:42:16 PM EDT
[Last Edit: 4/27/2006 5:43:02 PM EDT by DK-Prof]
I went to the shooting range today, and when I was almost done shooting, decided to just shoot two 10-shot groups and two 3-shot groups, just for fun. Same rifle, same conditions, relatively rapid fire (maybe 3-4 second between shots). This was at 100 yards, of course.

Here's what it looked like, beautifully demonstrating Molon's point.

The 3-shot groups look like they are close to 1/2 MOA, but the 10-shot groups are around 1 1/2 MOA.



Link Posted: 4/27/2006 7:26:55 PM EDT

Originally Posted By DK-Prof:
I went to the shooting range today, and when I was almost done shooting, decided to just shoot two 10-shot groups and two 3-shot groups, just for fun. Same rifle, same conditions, relatively rapid fire (maybe 3-4 second between shots). This was at 100 yards, of course.

Here's what it looked like, beautifully demonstrating Molon's point.

The 3-shot groups look like they are close to 1/2 MOA, but the 10-shot groups are around 1 1/2 MOA.

photos.ar15.com/ImageGallery/Attachments/DownloadAttach.asp?iImageUnq=46698


What ammo/gun is that you used?




Link Posted: 4/27/2006 7:30:25 PM EDT

Originally Posted By FALARAK:

What ammo/gun is that you used?





It's a 20" WOA barrel w. free float & bipod on an Armalite/Eagle lower - shooting Black Hills 69gr blue box.

My shooting isn't great or anything but I just thought the four groups really illustrated Molon's point perfectly.
Link Posted: 4/27/2006 7:54:41 PM EDT
Link Posted: 4/27/2006 7:58:59 PM EDT
I want to know more about that machine rest. How about more pictures, a web site, anything!
Link Posted: 4/27/2006 8:14:37 PM EDT
These shots are all with iron sights, right?
Link Posted: 4/27/2006 9:26:36 PM EDT
Great topic, my next visit to the range will definitely involve shooting 10 shot groups.

regards,

Luis Leon
Link Posted: 4/27/2006 9:27:44 PM EDT

Originally Posted By Mazeman:
These shots are all with iron sights, right?



Mine were with a Leupold VARI-X III.
Link Posted: 4/27/2006 9:38:43 PM EDT
This is the best I have ever shot, granted I am pretty new to the AR world. But anyway.... 5 shot group from a 20" bushmaster gov profile w/ Nightforce @15x. BHBB 75g MHP at 100 yards. Using bipod and one bag in the rear.

Link Posted: 4/27/2006 10:15:33 PM EDT

Originally Posted By jackal2001:
This is the best I have ever shot, granted I am pretty new to the AR world. But anyway.... 5 shot group from a 20" bushmaster gov profile w/ Nightforce @15x. BHBB 75g MHP at 100 yards. Using bipod and one bag in the rear.

users.rcn.com/thejackal/guns/75g.jpg



Feels GREAT dont it?

I love shooting for groups. I can totally see how people get hooked on the BR crowd.
Link Posted: 4/27/2006 10:16:50 PM EDT
Great write up! I was never really under the impression that you should shoot 3 or 5 shot groups for anything other than sighting in. I hate having to disrupt the line to go replace a target when I have plenty of mags loaded up and ready to shoot. I just change them out after someone calls a cease fire. I don't really save targets unless they are better than my average shooting and show definite progress in my abilities. Then I hang them on my fridge to motivate me to out do my previous best. So far the best I've done was with WWB at about 70 yards, it was also 120 rounds so it looks like a big hole in the paper, but it's consistent.
Link Posted: 4/27/2006 10:17:31 PM EDT

Originally Posted By DK-Prof:

Originally Posted By FALARAK:

What ammo/gun is that you used?





It's a 20" WOA barrel w. free float & bipod on an Armalite/Eagle lower - shooting Black Hills 69gr blue box.

My shooting isn't great or anything but I just thought the four groups really illustrated Molon's point perfectly.



You are a good shooter.
Link Posted: 4/27/2006 10:18:11 PM EDT

Originally Posted By excist_and_reflect:
Great write up! I was never really under the impression that you should shoot 3 or 5 shot groups for anything other than sighting in. I hate having to disrupt the line to go replace a target when I have plenty of mags loaded up and ready to shoot. I just change them out after someone calls a cease fire. I don't really save targets unless they are better than my average shooting and show definite progress in my abilities. Then I hang them on my fridge to motivate me to out do my previous best. So far the best I've done was with WWB at about 70 yards, it was also 120 rounds so it looks like a big hole in the paper, but it's consistent.
i39.photobucket.com/albums/e180/excist_and_reflect/1c716a3c.jpg



NICE!
Link Posted: 4/28/2006 2:15:22 AM EDT
When I'm adjusting, I usually shoot 3-shot groups, but once I'm satisfied with the zero I always shoot a few 10-shots for "confirmation". Now that my carbine's complete (for now, you know how it is), the first thing I do when I get set up, is shoot a couple of 10-rd groups, just to verify the zero.
Link Posted: 4/28/2006 11:54:26 AM EDT

Originally Posted By FALARAK:

Originally Posted By jackal2001:
This is the best I have ever shot, granted I am pretty new to the AR world. But anyway.... 5 shot group from a 20" bushmaster gov profile w/ Nightforce @15x. BHBB 75g MHP at 100 yards. Using bipod and one bag in the rear.

users.rcn.com/thejackal/guns/75g.jpg



Feels GREAT dont it?

I love shooting for groups. I can totally see how people get hooked on the BR crowd.



I wanted to see what the rifle can actually do since I put a $1200 scope on the thing. I was very happy to shoot that group. Especially since I didn't have a match barrel on it.

I have a problem because I like to try and shoot tight groups, but I don't want to pay for the expensive match ammo. In either case I am happy with my rifle but it needs a PRS soon.
Link Posted: 4/29/2006 11:18:12 AM EDT

I want to know more about that machine rest. How about more pictures, a web site, anything!


I've looked through more than 30 back issues of Shooting Times so far trying to find a better picture of the machine rest but still no luck. Anyone with back issues of Shooting Times can try checking the "Precision Reloading" column to see if they can find a better picture.
Link Posted: 4/29/2006 11:31:34 AM EDT
Link Posted: 4/29/2006 3:01:02 PM EDT

Originally Posted By jackal2001:
I have a problem because I like to try and shoot tight groups, but I don't want to pay for the expensive match ammo.



I am the same, hence, I started reloading.
Link Posted: 4/29/2006 3:35:08 PM EDT
[Last Edit: 7/20/2006 2:24:26 PM EDT by AR15_Fanatic]
Well you guys ruined my 3-shot fantasies with all these inconvenient facts. Here are the best 10-shot groups I could produce yesterday at 100 yards.

www.hunt101.com/img/400953.jpg


Edit - old photo server down
Link Posted: 4/29/2006 3:57:32 PM EDT
Assuming the lines on your target form a 1" grid, your groups measure 1.62" and 1.69". Good shooting!
Link Posted: 4/29/2006 4:25:29 PM EDT
Thanks, but not as good as my nickel and dime sized 3-shot groups.
Link Posted: 4/29/2006 4:49:25 PM EDT

Originally Posted By AR15_Fanatic:
Thanks, but not as good as my nickel and dime sized 3-shot groups.




Welcome to my world!

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