Why 3 shot groups are not useful.

[SFCat66]

I think some topic creep has occurred in this thread.

In the original ARF post, my understanding of the point of the article, and Robert's posts, are to obtain a better statistical picture of what a given round/weapon/shooter/etc. is able to perform repeatedly.

The article does not differentiate between zeroing sights, and round performance, and I believe that's what has led to some misunderstanding.

Most sight zeroing is done with three shot groups, as it's a easy way to visually guage and "triangulate" a center zero point to move the shot group.

While I agree that one has a better chance to refine zero by shooting a larger quantity of rounds, given the inherent accuracy(or lack therof) of any weapon system, does it really matter for the majority of hunting/military rifles out there?

If you are trying to define round performance, in the development of new loadings, or to confirm existing recipes, then I would conduct the higher round count testing for accuracy data, and not the ability to gauge the accuracy of the weapons sights.

[silencertalk]

http://www.shootersjournal.com/Features/WHICHONE.pdf

Update: http://web.archive.org/web/200608131417 ... ICHONE.pdf

[Ben B.]

Radial std dev. Cool. Nice find.

It's still a pain to work with. Would have to shoot on graph paper to facilitate transfer of each shot's location into the spreadsheet or whatever for running the numbers. Excel could do easily do the calculations.

[silencertalk]

You can use RSI Shooting Lab or this program:

http://www.rawilson.net/shareware/Gsc/index.html

Or someone could write an iPhone app which takes a picture and does it automatically.

I talked to the RSI Shooting Lab guy and he thinks mean radius is the way to go. It is more human readable as the output is the average radius rather than an abstract value. Also it is only in really large samples where there is any meaningful difference. Even after 30 shots it only has about a 2% advantage.

[TROOPER]

The 3-shot group still has a tremendous value when shooting with scopes. Assuming your scope is set so that the POI and POA are nearly identical, then the 3-shot group becomes a good indicator since the first shot is not 'free'.

In the "Texas Sharp-Shooter" argument, the shooter fires, and then paints a target around the bullet-hole. It then it appears that the shot was dead-accurate since where ever he hit is where he intended to hit.

With a scope, this is different situation since the first shot had a specific intent as opposed to simply being a freebie. After all, since most 3-shot-groups are taken as a measurement of a gun's consistency versus its accuracy, then that means that if the first shot misses the bulls-eye, that's fine, provided the remaining two shots still come close to the first one.

When shooting with a scope and the intent to hit a specific target, then the first shot is not free and the size of the group is irrelevant since only 'hits' are measured.

I have no idea what I'm trying to say. I do know that at 50 yards it is absolute child's play to keep my .17 HMR in the one-inch bullseye. This is further exasperated by the fact that I've got the scope dialed up to 14.5 magnification. I know that a 50 yard shot is not anything to write home about, so don't lampoon me for being a 'mall-sniper'. I'm only pointing out that measuring the shot-consistency - which is the crux of this whole discussion - is slightly more meaningful when accuracy is also being measured. Again, the reason for this is that the first shot is not 'free'. Or to put it a different way, when doing a 3-shot-group without attempting to hit any particular target, then the first shot, regardless of where it hits, is still exactly where it was meant to be. So the only thing being really measured is if the next two shots come close to the first free one.

Now assuming that I was selling my gun on E-bay and in the description I put that in a supermajority of the time a 5-shot magazine will bullseye at 50 yards - do you think this description would be misleading or dishonest? Just to keep it in perspective, its relatively easy to shoot a quarter at the 50 yardline using this gun.

[silencertalk]

http://www.rawilson.net/shareware/Gsc/howtogsc.html

In 60 dpi I scanned a ruler and clicked on 4 inches apart and it said my group size was 4.020 inches. I tried it at 600dpi and clicked 1 inch apart and it said 9.972 (0.997). So I went from 20 thousands off to 3 thousanths off. I guess I would use 600 dpi for benchrest and 60 dpi for less accurate rifles.

Use this program for at least 10 and ideally 30 shots, and take the "Radius Standard Deviation" and multiply by 6 (3 standard deviations along the radius). The resulting number will be the expected groups size diamater with about 99% certainty.

[silencertalk]

Someone who has a sub-moa rifle - fire at least 10 but ideally 30 shots and scan the target at 60dpi and email it to me and I will give you statistics on it.

[silencertalk]

Now assuming that I was selling my gun on E-bay and in the description I put that in a supermajority of the time a 5-shot magazine will bullseye at 50 yards - do you think this description would be misleading or dishonest? Just to keep it in perspective, its relatively easy to shoot a quarter at the 50 yardline using this gun.

When gun makers like Les Bear give a 1/4 MOA guarantee I am pretty sure they mean 3 shot groups. I don't find it misleading or dishonest so much as common practice due to widespread ignorance that it is meaningful. If a maker reported 6RSD like I propose, their guns would look much worse than the rest of the industry which is reporting 3 shot extreme spread.

It is one thing for marketing, but what I don't understand are people who do 3 or 5 shot extreme spread for their own info. What is the advantage of doing that for yourself?

[TROOPER]

When gun makers like Les Bear give a 1/4 MOA guarantee I am pretty sure they mean 3 shot groups. I don't find it misleading or dishonest so much as common practice due to widespread ignorance that it is meaningful. If a maker reported 6RSD like I propose, their guns would look much worse than the rest of the industry which is reporting 3 shot extreme spread.

It is one thing for marketing, but what I don't understand are people who do 3 or 5 shot extreme spread for their own info. What is the advantage of doing that for yourself?

I don't know that there is a significant advantage, only that there isn't a disadvantage if the shooter understands "the whole picture".

Hypthothetical situation: I have a gun that shoots 1-inch, 3-shot groups at 100 yards 1 out of 5 attempts. So I shoot 10 targets, three times each. Out of those 10 targetrs 2 of them will have sub-MOA groups. As long as I understand that my chances of achieving my stated accuracy are only 20%, then there isn't a problem with my expectations, and I am now dealing with statistical fact.

This is pretty much the same with confidence intervals in statitistics. The common spreads are the 90%, 95%, and 99% CI. Most of the pollsters use the 95% by default, because statistically speaking, if you want me to give a 100% quote on my guns accuracy, then I can give you some outrageous spread like, "I am confident that 100% of the time I can produce less than a 24-inch grouping of three shots at 100 yards."

I can statistically shrink my groupings if I lower my confidence level. "I am confident that 20% of the time I can produce a 1-inch grouping of three shots at 100 yards."

The problem with individual shooters is that they fail to tack on that coefficient to their data. My fictictious gun, for example, is a 0.2*1-MOA shooter, since it only performs this feat 20% of the time.


A man won the lottery, and now makes the claim, "I am able to win the lottery", which while true, fails to account for his failed attempts.

Or how about if at the next silencer shoot everyone brings a 10/22 and as a group, all fire at a dime 200 yards away in the middle of a target. Eventually someone will hit it, and then that person will make the claim, "I can hit a dime at 200 yards with my Ruger 10/22."

I see exactly what your point is; and I agree that if we all used only 30-shot groups, we could systematically avoid the mistake made when individual shooters fail to mention their confidence level, or coeffecient, or whatever you want to call it. Its just that on a personal level, I feel that after putting 100 or 200 rounds through my gun, I am able to use a 3-shot-average to express to myself what my gun is capable of, because I have an inherent understanding of the context in which that group was arrived upon.



I also have a general complaint with manufacturers who make broad-brush claims such as a 1/4 MOA; and especially when they say, "with the right ammunition". What does that even mean? If a manufacturer stated that firearm "X" would, with Brand "Y" in "Z" grains, print a 3 shot group of 0.75 inches 90% of the time, that would be a different story. Because you'd have every variable accounted for and the experiment could be duplicated with similar/identical results.

I also see why they wouldn't want to do this. Differences in skill levels of the shooters first of all, nevermind the dozen other variables such as wind, temperature, humidty, elevation, quality of the scope rings, bench-rested or standing, blah, blah, blah.

But yes, a claim as bold as 1/4 MOA leads one to believe that the rifle could be removed from the box, loaded, and then fired into 1/4 MOA.

Either way, we still come back to the same conclusion. For your own references, almost any size group is telling if you do enough of them, because then you'll know what to expect from the individual firearm.

[silencertalk]

The only possible way that a production AR15 is 1/4 MOA is, as you say, with X% confidence (where X <= 20%).

If it can only make the claim a small percentage of the time, was it fair to make the claim to begin with? Maybe. It is like saying I can score under par in golf. Sure, 6% of the time, but I will leave that part out.

So a customer complains and the maker shoots the gun a few times, produces a 3-shot 1/4 MOA group, and says the gun passed. That does not make it a 1/4 MOA gun (in my opinion) and more than I am a par golfer. What matters in golf is long-term statistics. I would argue that also applies to a rifle.A 1/4 MOA gun, I feel, is one which can put all shots into 1/4 MOA with a high degree of confidence. Only some bench rest rifles can do that.

95% is 2-stdev. 99% is 3-stdev. Maybe 95% is the way to go, I am not sure but I am thinking 99% is the way to go. You want the gun to be at least 99% reliable and 95% reliable is not good enough, so why not demand the same for your knowledge of its accuracy performance? Besides, what is the harm in the 99% groups being larger than 95% groups? As long as you only compare them to other 99% groups, everything is fine.

When the military assesses rifles or ammo, they do the types of tests I am talking about.

Get one of the finest tactical rifles and predict what it can shoot 99.7% of the time and I bet it is over 1 MOA.

[Meche_03]

link to a US Army Research paper on part of the topic of discussion. Not very long and has the math so on could make their own program or excel sheet.

http://handle.dtic.mil/100.2/ADA387108

Now, need to find the paper on the statistical importance on the number of shots in a group. Off the top of my head 4 shots are required to be 75% confident that the remaining shots will be within a circle shaped area defined by the 4 shots.

http://www.bobwheeler.com/guns/GroupStat.pdf

Still not the one I'm thinking of but it does help. More of an egghead view of the problem.

[silencertalk]

Thanks.

The paper says RSD is a very good method but difficult to communicate to the rifleman. I agree but 6*RSD is easy to communicate. I have not seen any mention of that in any paper.

You need 25 shots to be 75% certain whil using extreme spread (or 10 shots using mean radius).

[renegade]

A neat feature might be to make targets with built in rulers. That way you can scan and then (manually) calibrate it easily by clicking the endpoints of the ruler and entering the known distance.

So many projects, so little time.

[silencertalk]

That free software works fine and you can scan at 60dpi (or 600dpi and divide the results by 10).

[TROOPER]

The only possible way that a production AR15 is 1/4 MOA is, as you say, with X% confidence (where X <= 20%).

If it can only make the claim a small percentage of the time, was it fair to make the claim to begin with? Maybe. It is like saying I can score under par in golf. Sure, 6% of the time, but I will leave that part out.

I absolutely agree with all of the above.

So a customer complains and the maker shoots the gun a few times, produces a 3-shot 1/4 MOA group, and says the gun passed. That does not make it a 1/4 MOA gun (in my opinion) and more than I am a par golfer. What matters in golf is long-term statistics. I would argue that also applies to a rifle.A 1/4 MOA gun, I feel, is one which can put all shots into 1/4 MOA with a high degree of confidence. Only some bench rest rifles can do that.

95% is 2-stdev. 99% is 3-stdev. Maybe 95% is the way to go, I am not sure but I am thinking 99% is the way to go. You want the gun to be at least 99% reliable and 95% reliable is not good enough, so why not demand the same for your knowledge of its accuracy performance? Besides, what is the harm in the 99% groups being larger than 95% groups? As long as you only compare them to other 99% groups, everything is fine.

95% CI is probably sufficient for most applications including firearms. However, in a military setting a 99% CI should be used due to the imbalance between stakes and probablity.

When the military assesses rifles or ammo, they do the types of tests I am talking about.

Get one of the finest tactical rifles and predict what it can shoot 99.7% of the time and I bet it is over 1 MOA.

*ETA - "the imbalance between stakes and probability." There is a stretch of road between Austin and San Antonio that is ~70 miles long. It is just short enough for people to work in one city and live in the other, but just long enough to make speeding a true benefit (doesn't usually pay off in a city because of the random nature of traffic lights). As a result, there is a constant problem with speeders on this stretch of road. The police can alter this behavior by either changing the odds of getting caught, or by changing the stakes.

If they triple their presence, then the odds of getting pulled over are three times higher, and a number of people will stop speeding at that point.

If they didn't triple their presence, but instead just executed people after pulling them over for speeding, then a number of people will stop speeding at that point.

This applies to the 95% CI vs. 99% CI only insofar as the stakes are big enough to warrant this. If a person's life hangs on the 4% chance that the bullet will be a quarter-of-an-inch wide, then it would be more beneficial to use the 99% CI (That is a mathematical faux pas, but it is more about illustrating the point than giving a finite number). Otherwise, I'm certain that for paper-punchers, the 95% CI is more than adequeate; and especially if the individual shooters understand that their quoted accuracy is only at 95% and what that means.

[silencertalk]

True, but what is the downside of using 3x stdev for the 99.7% vs 2x stdev for the 95%?

To be satisfied with that is to be satisfied that you are only correct for 19 out of every 20 shots.

I think I said it, but one of the best things about that ShareWare PC program is that it will find the center of your group and you can then adjust your scope very well.

Has any paper mentioned 4 * RSD or 6 * RSD? I cannot find one.

[silverbulletexpress]

I certainly agree that 3 or 5 shot groups are meaningless, add in that those shooters are usually only counting that one or two great groups they got and forget the other 20 crappy groups they shot.

The problem is separating what the rifle is capable of from what the ammo is capable of from what the shooter is capable of from what the conditions will allow. Sorry for the run on sentence but that is what we are facing when we try to prove accuracy. So what do you want to know?

If you want to check your rifle for 500yd accuracy you have to take the wind out of the equation or the results are meaningless. How do you do that? Extrapolating short range results isn't acceptable. I know Sierra has an underground tube of at least 200 if not 300 yds to test bullets with from a machine rest.

Not being negative just trying to bring up a few points about how difficult it is to test for accuracy. I have to mention one of my pet peeves, gunwriters who report the 25 ft offhand accuracy of the pistol they are testing, talk about useless. If anything won't put them in one hole at 25 feet it's a pretty crappy POS.

I remember an article by Jeff Cooper years ago were he commented that the only accuracy that matters is whether you can hit with the first shot, in other words a one shot accuracy test. I thought he was nutty at the time but I'm tending to agree with him now.

[silencertalk]

I remember an article by Jeff Cooper years ago were he commented that the only accuracy that matters is whether you can hit with the first shot, in other words a one shot accuracy test. I thought he was nutty at the time but I'm tending to agree with him now.

Well that is accuracy but I am really talking about precision. You cannot test precision with one shot. If precision is high, accuracy is easy to correct by adjusting the scope.

[TROOPER]

I remember an article by Jeff Cooper years ago were he commented that the only accuracy that matters is whether you can hit with the first shot, in other words a one shot accuracy test. I thought he was nutty at the time but I'm tending to agree with him now.

Well that is accuracy but I am really talking about precision. You cannot test precision with one shot. If precision is high, accuracy is easy to correct by adjusting the scope.

If the gun always, always misses two inches to the left and one inch down at 100 yards, then it isn't the gun, its the scope. Precise is accurate, and a properly mounted and sighted scope on an inconsistent gun is inaccurate.

[silencertalk]

If the bullet is always 2 inches to the left and 3 inches down, then the gun is extremely precise but not very accurate.

[silencertalk]

http://www.ontargetshooting.com/index.html This is promising but does not seem to do RSD or MR.

[JohnInNH]

Geez... OK Rifle X shoots a 1/3 MOA group 3 shots... Switch ammo and shoot another 1/3 MOA group Off an inch.

Shoot 25 rounds and shoot a 3/4 -7/8th moa group.

Swap rifles.. shoot 3 rounds and it's a 2.5 moa. That 3 shot group IS useful.

If a shooter CAN shoot a 1/4 MOA group which is HARD to do even with a consistent 1/4 moa rifle. So many factors are the shooter.

But if a shooter who can consistently shoot sub MOA groups gets a rifle that shoots a 2 or 3 MOA group you KNOW it's the rifle/ammo. NOT the shooter.

I have very rarely met people who can shoot bug holes off the bench. It takes trigger time.

I DO think a 3 round group is useful in establishing at least the rifle and shooter are doing something right... more shots just will see if the shooter tires or makes a mistake. AND if the rifle is consistent as it heats up and becomes fouled slightly.

If the fist round is from a raw cleaned barrel and not from a once fired bore the chance of the real group and the first shot being in the group are reduced. This is why a log brook is important so you can map where that rifle's clean CBS is.

I have some rifles that should shoot bug holes and don't .. No matter how hard I try.. then I have 2 magic rifles that are more accurate than I am. And every time I shoot them they amaze me.

Take a five spot target and shoot 5 5 shot groups... then measure the changes. the Group may open or even tighten up. The group may drift.

My FNSPR with factory FED Gold Medal will shoot a 3 shot one hole group every time I take it to the range if there is no wind. ... I ONLY shoot 3 shots because that is what I want it for. The CBS and 2 follow up shots. I do not want it to get hot or care. it is Not my tactical match rifle it is the rifle I want to hit the X (or T Zone) with the FIRST SHOT. I can care less where shots 4-25 go since it is not for competition. It's the first and hopefully last shot.

My GAP rifles on the other hand I do want to know where the shots go when it heats up. Just like my "target rifle". The first 3 shots are sighters anyway and help to warm it up. it is shots 5-100 that count with that rifle.

My target rifle actually tightens up from a CLEAN bore. It just will settle in after fouling and shoots well for quite a while.

But if I am going to drag a rifle to a "hide" and wait for the shot of opportunity shot 5-100 mean s--t. Your rifle may "settle" into a place an inch over and an inch down after the first 3. hopefully your CBS and the following 2 shots are in the same 1/3 MOA hole.

Some people store the rifle clean and fire one fouling shot before deploying on the mission. So that they KNOW they will have the best chance of having shots 1-3 all go into the same hole.

Putting on a silencer can change your POI. You need to log that POI change as well as your clean CBS.

I use "RSI shooting lab" to analyze my groups.

[GlockandRoll]

I have a question, and apologies if it has been asked and I missed it.

What are the odds, if we had to guesstimate, that a gun that shoots a good 3 shot group will shoot a better 10-shot group also?

It may seem like a silly question, but think about it - I mean if I took a gun that shot a .5MOA group... then it's 10shot group should, by comparison, be larger.

[JohnInNH]

If I shoot a 10 round group with some of my rifles you might not see more than 4-5 bullet holes. This is why a 5 spot target is used in archery... you destroy arrows if they keep hitting in the same place...

Same principle here.

I like to shoot .. 3 round groups but more than one of them at a time. IF I dump them all in one target you cant see where they are going...

Also called fliers are easier to keep track of. I have posted my 5 shot groups using my "Cyclone" .4" If I put 5 more in the same hole how would you know it? Fliers (shooter error) would obviously open the hole.

So I DO see a reason to shoot 3 round groups... 3 to five per target.

But still for a call out rifle where one shot may/is the only shot you shoot. You NEED to know where your CBS (cold bore shot) will go.

Clean or fouled is also of importance. (see "Smack the Smiley" a true test of your shooting and log book data.)

[Wahoo95]

My issue with the original article is that the aiming point changed for the 3 different groups, so it's a bit unfair to lay them over each other for the basis of saying the actual 9 shot string would have been larger. Mabe I'm dense, but it seems to me that the shooter would have had better grouping if they shot a 10 shot group rather than 3 since the aiming spot would have been the same. Am I missing something?