What's a shot group?

Larger sample pool is more accurate, and a more consistent sampling process produces more accurate data.

I haz teereeZ.......

IMO unless your using a really solid machine rest, the human factor in the sampling process quickly becomes the weak link for most of us when shooting high number groups. Its HARD to concentrate on delivering a bunch of rounds exactly the same way. Especially if you start stepping upto the edges of recoil tolerance, and/or the point where the rifle gets kicked out of position.

Then you also have environmental factors that change with the delay between data points....even position of the sun can cause an effect.....so it comes back to the trigger nut making an adjustment to deliver the round to the same point of aim.......
So the longer you take to deliver your total shot group, the more likely there is to be an environmental or position change.

Soooo my theory is that a 25shot one sitting group by the most consistent shooter, is probably WAY more accurate a figure than a 5. But 5, 5 shot groups by a less consistent shooter is probably more accurate a figgure than a single 25.

Some people think stats are cool.
Of course they may not be observing of all inputs/variables.

IMHO just shoot 5 shots, letting things cool a little between shots (you and the rifle).
Repeat 2 or 3 times for verification.

If the same, good to go.

Unless you are in some long string match and have to learn where accuracy starts to degrade, it aint worth it.

Of course you should shoot for cold shot vs warm, and know if your rig needs a fouler or two.

I think a larger sample to be more accurate in data, if shot from a machine rest.
Think larger sample (non machine) could be influenced by shooter fatigue.

Think smaller sample, multiplied, probably better.

And in doing smaller samples, I would be so OCD as to do it from same bench, same temps, same time of day.
Like da woof says, lighting can be a biggie.

I shoot a curve as node confirmation very frequently to verify the health of my barrels. This test consists of shooting 10 rounds to warm the barrel followed by 8x three shot groups with varied charge weights.

What I am left with over time are dozens of targets using the same 9 charges fired on them - the 10 shot group plus 8 individual charge weights. The 10 shot group, with the exception of the first test of a new barrel, is typically my node load, usually between two of the test charge weights. Almost unilaterally, and by significant margin, superimposing 3 of the 3 shot groups using the same charge weight from 3 different tests will show a smaller aggregate group than any single 10 shot group. Shooting multiple small groups with low round counts is far easier than shooting a small high round count group.

Unlike another member on this thread recently, don’t let yourself be mislead into thinking statistical models referring to a cone of fire are ever apt. Examine Litz’s work for his Monte Carlo WEZ model against the common statistical model and you will immediately see the failing of typical single variable Gaussian statistics applied to group sizes and relative shot count influences.

If you shoot a 5 shot 1” group, statistically you will be 75% confident your next shot will also be in that 1” group.
If you only shoot 5 shot groups, statistic confidence level will never be above 75% for any one shot.

If you shoot a 32 shot 1” group, your confidence level will statistically be 95% for any single shot.

100% confidence, statistically, cannot be achieved. Math drives larger shot strings for some people.

But we as shooters have quite a bit more confidence than 75% shooting 5 shot groups, because of our experience. I can shoot a new to me gun a few times and be pretty confident (maybe close to 100%) I can either hit or miss with it.

Personally, I like 10 round 100 yard groups for scoped rifles for a bunch of reasons. But I have no objections to 3 or 5 shot groups, either. I combine chronograph data with tight 10 round groups to prove a good load to myself. I cannot tell you how many good chronograph loads and crappy 10 round groups I’ve shot, or vice versa. But, when both chronograph and groups are good, then I load up a bunch with confidence.

I tell people I have an MOA gun. What I don’t tell them is that it’s a 10 shot MOA gun, and in my experience (1) people assume a three shot group and (2) there is a big difference between a 3 shot and 10 shot MOA gun / shooter. So, I’m playing cards close to my chest.

I emphasize “shooter” in shooting 10 shot groups, because often that is what it comes down to.

Shooting fewer shots into groups will let you see the impact of each shot, whereas a single 25 shot group leaves such a large hole that each individual shot cannot be seen and measured. Each point must be determined for the data to be meaningful. The aforementioned Monte Carlo model utilizes random variables in each range of uncertainty (ranges such as velocity, wind, the precision ability of the rifle, etc.) to determine each data points, and then uses these points to calculate probability. It works well in theory. I taught statistics on a post-graduate level for a few years and know (if you ignore the terminology) it is just common sense. It would be very difficult to see anything meaningful on a target unless you could see where each shot landed. Thus five groups of five shots each should tell you much more than a single 25 shot group.

hardheart said:

In the Army I could group and zero in about a third of a magazine if I dialed in the sights beforehand (they didn't ever count the first 3 round group and then needed 5 of the last 6 shots in the circle), but did that really mean anything?

Click to expand...

I think it means you are a pretty good shooter.

Depending on what type of shooting you will do. Deer hunting with a cold barrel ,well a 5 shot group is fine. But if you are in competition and barrel will foul and heat up.25 shot group is your friend .MHO.

A group to me is a full magazine in whatever im shooting. Or 3-5 in a single shot. A group of five 5 shot groups is still a group...

It's a topic that is all over the place.

I know, personally, folks who fiver 9, 10, 12 shots, pick the three they like best, and call that their "three shot group."

I know some folks who get the digital calipers out every three shots and record the results to three decimal places.
Some of that group also has the ammo documented to similar standard, too. (The Venn Diagram of that seems to not bother that group as much as the math and database management bends mine.)

The longer range iron sight crowd leans a bit more to ten shot groups--which is probably a reflection on how they compete, 5 or 10 aimed, timed shots, and a tiny number of "spotters" or "sighters."

The math of it can be as complex or as simple as you are comfortable with, really.

The study of statistical math teaches that more data tends to even out minor, systemic variations. (And there's a huge pile of those with shooting, is it 68.0º or 68.5º; was the wind 035 at 4.2 kts or 033 as 4.5kts; did you pull in 1.8# or 1.6# and so on.) If you measure all those variables, and put them in a list, the amount of variation is smaller for 10 or 20 instances than for 3 or 5--that's just math.

But, we are talking about a practical situation, too. Are you going to "ladder" your handloads in batches ten at a time? (And, that's matching up projectile weights, charge weights and the like, too.) Is your chosen factory ammo consistent across batches of 10 or 20?

Personally I tend to the general rather than the specific. More minute of paper plate or dollar bill (8" paper is ±* MOA at 100; 32MOA at 25--so what a dollar bill covers at 25 yards might be a better measure).

Your Mileage, obviously, May Vary.

It depends on what you want to prove. IMO 3 shots are enough to prove the accuracy of the load. Five shots give a better indication of the rifle's accuracy, and 10 shots or more start to show the accuracy of the shooter. And I'd never put much faith in a single group, 3, 5, or even 10 shots. I've had quite a few 3 and even 5 shot groups in the .3's, even a couple in the .1's. Doesn't mean my rifles or I can do it consistently.

I've got better things to do with my time and money than shoot 5-10 round groups with expensive ammo. I'll do it with 22's, or even 223 which is, (or used to be), inexpensive. But my hunting loads, even handloads, work out to about 50 cents to $1+ every time I pull the trigger.

For what I do a series of 3 shot groups over a period of time tells me what I need to know. I'll fire several groups of 3 shots at different targets on each range visit. As said above, too many shots at the same target and you have no idea where each one is hitting. If you don't know what you're doing wrong, you can't fix it.

And to push that even farther I don't have complete confidence in the rifles accuracy until I've repeated this over multiple range trips spread over weeks, months or even years.

I have some go-to rifles that will keep 3 shots into an inch or less far more often than not. It is not unusual to see the 1/2" group, and in rare cases for some reasons I'll get a 1 1/2" group. Some people will argue, that even that 1 group in 100 that opens up to 1 1/2" makes the rifle a 1 1/2" rifle. Maybe so. But I'm more interested in knowing that 95% of the time any 3 shots that I fire will be within 1" or less of my aiming point.

And as primarily a hunter, knowing even 3 shots would be rare; I really worry much more about where the 1st shot goes, and is it within 1" of POA. And that happens near 100% of the time for me. Shooting long shot strings cause rifle barrels to heat up and group sizes to increase. It also forces the shooter to concentrate for a much longer period of time and even with light recoiling rifles the effects of recoil and muzzle blast do have a cumulative effect on accuracy. If you're a target shooter then you need to train for those conditions. If not a target shooter, then 3 is enough in my opinion. As long as you are consistent with those 3.

@hardheart

1) Yes, it is highly probable in fact that 5x 5 shot groups super-imposed to create one composite group will be smaller than one 25 shot group.

2) No, it isn’t ONLY due to shooter variables.

I shared my example above doing exactly that, shooting multiple 3 shot and 5 shot groups, superimposing these into a composite group, shot round robin against a 10 shot conventional group, I know I shoot smaller composite groups than I do actual groups.

Statistically in simulations, this is also supported because the likelihood of variable means to combine is greater than the likelihood of variable extremes. Multivariate systems aren’t so easy quantitatively, but understanding their qualities isn’t so difficult: Doing something a few times is easier than doing it a bunch of times, so much to the point that doing something a few times, a bunch of times is easier than doing something a whole lot of times, aka, it’s always easier to shoot 5x 5 shot groups smaller than one 25 shot group.

The maximum deviation would probably be nearly the same. Being able to track each hit would show how much and how often your shots are out of the center of your aggregate 25 round group. All a fellow can do is to reduce the range of each of the many variables and hope for the best.

hardheart said:

I've been doing three shot groups of different powder charges in 0.3 gr increments to see where POI is most consistent and where the rounds aren't too far apart for a load window. But now I don't know exactly how to go about shooting 5, 10, or more rounds to verify.

Click to expand...

A good test is to put up a target at 100 yards with 10 1" dots and then put one round in each dot. This tests both accuracy and precision. If you can do that, put up a target with 10 1/2" dots and repeat. I've noticed that many shooters are better at shooting small groups away from the point of aim than at the point of aim.

Along those lines I usually put 5 or 6 target dots on 1 large target and shoot 3 to 5 rounds at each one. I want to know what my poi is and how close I put each shot on it. Usually I am looking at hunting accuracy. Load testing and target training is similar but may involve a lot more shooting. Also rate of fire makes a difference too. For instance if you want cold bore poi or first 3 shots only. I guess it depends on what you are trying to accomplish.

Sorry to say, but this another discussion of the chicken or the egg. Some people believe shooting 10 shots or more will show more consistency than shooting only 3. The answer may be shooting at 5 targets. Each target gets on shot each in a row of 5 and then repeat shooting each target again, one at a time for the 2nd shot etc. After shooting 15 shots compare the targets for accuracy. A good shooter shooting the 5 targets will eliminate, flinching, tension, heart beats and a hot barrel(vs a cold barrel) etc. All too many times variation in shooting 25 at one target doesn't really eliminate variables that we all have.

This thread got me thinking. Typically we measure groups by the distance between the two shots that are farthest apart. And nothing else.

Perhaps a better way to do it would be to measure the distance from POA for each shots, and then work out the average of those numbers.

5 groups of 5 shots implies different conditions between groups. distance, heat, time, built-up fouling, wind, sun, birds chirping, something. if there is no difference whatsoever then they should be considered all of the same group.

statistically, for a sampling of anything, three gives you a a good ballpark figure, four gives you a good estimate, and five is pretty solid. more than five is diminishing returns and more than 20 is statistically pointless.

when you have multiple groups (such as 5 groups of shots) they are not treated as one large group. you take the standard deviation of each one seperately, then use a mathematical routine that discards 1 degree of freedom per group and then lumps them together. that is called a pooled standard deviation.

so a group of 25 shots is statistically pointless. however, divided into 5 groups of 5 shots, it could serve the purpose of determing what conditions affect accuracy by examining a change in the statistics. for example if the pooled SD is unchanged from some previously established value, you know whatever changed between groups had no effect. or, if it did change, you can gauge how much of an effect it had.

It's a complicated topic. I've done practical statistics professionally for 25 years, and some aspects of it still frustrate me. The following may be helpful:

1. Analysis requires that all "special cause" has been removed from the system. That is, no barrel rubs, no shooter flinch, no loose hardware, etc.

2. The distribution for shot standard deviation and for group size is not normally distributed. Litz assumed a normal distribution, and that is a serious error.

3. There is no Central Limit Theorem for any measre of dispersion, i.e. range, variance, standard deviation, group size, etc. That complicates matters.

4. A rifle that, over the very long term, shoots 5 shot grouips that average 1" will routinely print 5 shot groups as small as 1/2" and as large as 1 1/2".

5. An average of three 5 shot groups will give you your long term average group size within about plus or minus 25%. Creighton Audette worked that out quite a while back, and not knowing that, I duplicated his work a few years ago. His work and mine agree.

5. As the number of shots in a group increases, so also does the long term average of group size. This is because no group ever gets smaller as shots are added. The conversion factors between group sizes are known, and I'll post those shortly.

So many statements about statistical validity made in this thread, and frankly, they all imply the one making the claim fails to understand statistics.

Hint: confidence interval is dependent upon the population. Saying 4 is good enough or 10 is good enough might be wholly meaningless. We have empirical results based on VERY specific rifle types and conditions (benchrest rifle results, as an example) and we have mathematical simulation results, but we don’t truly have a consistent system of multivariate boundaries which universally apply to all shooters with all rifles. I can know, based on literally hundreds of repetitions of groups fired with the same rifle at the same targets under the same conditions, any given 3 shot group has never demonstrated, and in all reasonable probability WILL NEVER demonstrate the extreme size of any given single 10 shot group, and equally, have never and will never see any of these 10 shot groups fall smaller than the average - let alone the raw smallest of the 3 shot groups. Possibilities and probabilities are very different things.

I have been working a load ladder for a 223 Rem. using a 62gr bullet and one powder. My ladder was 21.7gr powder up .3gr increments to 22.9 found nothing special. These were shot at 50yds. and was informed that to be more true I should be testing at 100yds. Next group of loads were then fired to 100yds.

Each of these tests I am using a target with 5 sighting bulls, one for each load. With this I am firing 3 shots with each load through the cycle and then repeating this on the same target so that there are 6 shots on each bull with each 3 shot group marked together with a Sharpie. I have then repeated that exercise again on a fresh target so I have a total of 12 rounds shot during this session.

Once at home I have a lamp with a small spot light bulb in it and I am able to overlay the two targets and superimpose them. Very telling in my mind. Easily shows which loads have potential or are just junk.

I am not locking my gun in a machine on a bench so there will always be the human factor involved. I am not a machine and I do not expect my shooting to be machine like. But I do repeat my tests on different session to prove repeatability. If the test results can't be repeated then just what value do the tests have?