Home Forums Reloading Big Game Rifles Group statistics

The fundamental issue is that all measures of dispersion are differences between data points. Data points behave as we have come to expect. Differences do not. They do not like to be cornered and made to tell the truth. Skewness and kurtosis are even worse. You need thousands of data to get a good grip on those parameters.

For an article I was doing, I created a 20000 shot simulation. With that, I got a very good estimate of the group size distribution. It looks a lot like the distribution of standard deviations: a normal distribution that has been pushed to the left.

Aside from massive reams of data, the shooter, especially with a sporting rifle is w/o a doubt the weakest link in the system..........doing as above mitigates much of that issue.

Statistics like this can drive a sane person mad if you let it.

Compromises have to be made & each shooter, more or less, has to come to grips with his system & what he is willing to do or accept.

I'm not a target shooter, so my needs are less stringent than what an F Class shooter's might be.

Jack Leuba is a honcho at KAC (Knight's Armament) who supplies a lot of ordnance to SF type people. This is an interesting article with a slightly different tack that some shooters might find interesting.

Let's Talk Accuracy

MM

The golden nugget award right there. Thanks

Out of curiosity, I just coded up a similar simulation using 100,000 shots divided into 5-shot groups. The individual shot POI was modelled using a Gaussian distribution. The group size, when defined as the maximum distance between two shots in a group, looked as you described with a skewness of ~0.41. Interestingly, when group size is defined as the mean distance between pairs of shots in a group, the distribution is more normal with skewness of ~0.28.

That was my point earlier, was this custom loaded ammo where the bullets were sorted by weight, diameter, length and brass sorted, etc or was this something like factory ammo, be it Lake City (since this was for the government) or off the shelf ammo like Remington or Winchester?
All of that plays into the data that the test produces. He did not say how they did it and maybe each round was produced to BR standards. I guess I would like to know a little more about how the test was done just to get a clearer picture.

I understand and agree with statistical deviations in group size with any given load, but I have seen some threads interpreting Bryan’s analysis as meaning load development is futile and they’ll all shoot the same with a big enough sample size. My own experience has shown me that that is not true. You CAN develop a load that averages better than another, but there will always be a range of group sizes with any given load.

John

I can tell you, I’m not.

Wearing barrels out shooting groups is a sport I just don’t understand. I shoot stuff, and a group only tells me where the center of my poa is when I leave the house…

You and me both. A colossal waste of time in my world.

John,

Agreed. Bryan mentioned a typical SD of 30% of the mean group size. The absolute mean and SD will vary with different loads and rifles. His point was definitely not that load development doesn’t matter.

Wow! Someone as curious as I am. Well, maybe more curious, since you took it to 100K, and I only did 20K.

Haha, well going from 20k to 100k was as simple as 3 key strokes, so I'm not sure it says much about the relative curiosity.

I'm seeing some very interesting results, however, and am now running a simulation using 1M shots for both 5-shot groups and 10-shot groups, using both definitions of group dispersion (distance between two furthest shots, and mean distance between all pairs of shots).

While you are at it, you might try running 3, 4 and 7 shot groups. That will let you compare average group sizes for different numbers of shots. I published my results a few years ago, and it would be cool to have the results duplicated.

The stats for group size are nasty. I couldn't see any way to do it except by simulation, as you have done. When the going gets tough, the tough resort to simulation.

That’s funny, true but funny. 👍

Haha, very true.

Where are your results published?

I'm already seeing some interesting results and will comment more later.

Varmint Hunter

Things are simpler if you simply worry about how far each shot is from the center of the group, but that is more complex than anyone is going to do in the field. For groups with 5 shots, group size has practically all the statistical strength of standard deviation.

The assumption that's being made here is that the cross hairs are, or were in the center of the group for each shot. What we're contending with here, as you know, are two systems of variation, or noise. There is the variation of the reticle about the target, and the variation of impacts about the reticle. Strangely we tend to blame both systems on the later while suffering from the inability to address the variation of the former. On the mentioned test platform above an 8x32 power Nikon scope is the sight. At 100 yards I can still see slight movements in the reticle about the target. I don't think it's fair to the ammunition to go ape crazy on gaussian distributions for load worthiness estimation when the launching pad is adding considerable noise. I also don't think 3 standard deviations, or 30% scatter is true for all guns and shooters. For a very accurate BR rifle I doubt the competitors would find that amount of variation acceptable.

Very informative video; thanks for posting Mathman!
One takeaway I found useful is that I may start testing primers earlier in my load development. Also the results of Bryan's testing of annealing wasn't what I would have suspected.

Earth to Jordan Smith: Come baaaaaaack, come baaaaaaaaaack !!!!


MM

Using 1M shots was taking too long for the simulation to run.

Using 100k shots (20k groups of 5 shots), a couple of interesting observations emerged:

- Using 30% standard deviation in individual shot POI, the mean group size is 0.92 MOA and the SD in group size using 5-shot groups is 0.25 MOA. Smallest group is 0.2 MOA, largest is 2.2 MOA. When sampling group size of 5-shot groups, the data distribution looks very close to a normal distribution (as if the CLT applied here *grin*), but with a slight offset to the left (skewness of 0.39) and a slightly prolonged right tail (kurtosis of 0.20). Interestingly, when group size is defined as the mean distance between pairs of shots within the group, and the group size sampled, the data is distributed much more normally, with skewness of only 0.30 and kurtosis of 0.06.

- Using 10-shot groups (10k groups of 10 shots each), the mean group size is 1.14 MOA and SD is 0.23 MOA. Smallest group is 0.40 MOA and the largest is 2.32 MOA. The distribution of group size using 10-shot groups shows a larger shift to the left and longer right tail, with skewness of 0.41 and kurtosis of 0.27. The sampled mean distance between pairs of shots using 10-shot groups follows a normal distribution very closely, with skewness of 0.15 and kurtosis of -0.07 (the longer tail is on the left side now). This implies that the mean distance between shots in a group does seem to follow a Gaussian distribution when sample size is large enough.

When Brian stated that his F Class rifle that he shoots .6 moa with won him number 3 in the world I new I was listening to one of few men who say it how it is! Its funny how many people never count fliers.

The fact is a rifle only shoots as well as it does on its worst day and that's how I have always approached it. The worst day is part of the statistical evidence. A true .6 moa rifle will shoot 6" groups at 1000 yards on a bad day! That's impressive IME. If more people were honest with themselves there abilities would for a certainty be inspired to improve.

That's basically what my takeaway was


Trystan