Obtaining more information from your groups - overlaying groups

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Originally Posted by gimp

The sample size required to have the power to detect whether a load is "better" confidently depends on how much better. If you're trying to detect a 10% improvement, you'd need a very large sample size. 300 rounds? A 25-50% improvement should be visible with 10-20 shots. I'd recommend doing your testing at 100m to remove the variable of wind as much as possible, you'll note your 20rd group is slightly wider than tall - maybe wind, maybe recoil, maybe trigger control, maybe random chance.

It is more sensible to identify your requirements first - then simply select a load that meets those and move on.

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If you do decide to try identify a load that is "better", you'll notice that looking at the mean radius rather than the group size will be much more helpful. With the same load you have a 40% variation in group size between your 2 groups. The mean radius measurements are within 5% of each other.

With that kind of variability group-to-group, even with 10rd groups which is much better than most people use, group extreme spread (size) is clearly next-to-useless for informing any decisions about whether a particular load is better than another - unless there's an absolutely massive difference. Like a factor of 4 or more

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Originally Posted by gimp

If you do decide to try identity a load that is "better", you'll notice that looking at the mean radius rather than the group size will be much more helpful. With the same load you have a 40% variation in group size between your 2 groups. The mean radius measurements are within 5% of each other.

With that kind of variability group-to-group, even with 10rd groups which is much better than most people use, group extreme spread (size) is clearly next-to-useless for informing any decisions about whether a particular load is better than another - unless there's an absolutely massive difference. Like a factor of 4 or more

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That's helpful to know. Makes sense of some folk suggesting larger rather than smaller changes (to a load), which I guess gives you greater 'signal to noise' in a smaller sample size.

Precisely

I had a quick play adding some fields to auto-calculate the total overlaid group size and use the observed MR to generate the predicted true cone of fire. Will properly update the template with these if anyone wants it.

You'll see that the 10rd mean radius predicts the actual 30rd group ES really closely in this example from a real dataset


Attachment 268261

Still at the beginning with Hornady app, will keep shooting at this target, as you can see this Savage storm shoots the first 2 well from a cold clean barrel then goes off, annoying. Done this often & I give barrel time to cool. First shots being the most important I guess.
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Originally Posted by flock

Still at the beginning with Hornady app, will keep shooting at this target, as you can see this Savage storm shoots the first 2 well from a cold clean barrel then goes off, annoying. Done this often & I give barrel time to cool. First shots being the most important I guess.
Attachment 268312

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I'll be really interested to see more data and what the overall group fills out like - I have not yet seen a rifle where "opening up with heat" is actually a real phenomenon rather than just an impression given by the general dispersion being relatively larger than understood

Clean being a bit of a confounding variable

Here is my effort at a ten shot group. It’s a tikka 22-204 shooting 80g eldm with 2208.Attachment 268441

In the interests of science, I went and did some shooting today.

I was curious to test the idea that shooter error, barrel heat, or other factors may result in relatively bigger groups over 10rd groups than you'd get shooting 3 shot groups - the idea that "only the first shots matter". Well, how different are the first shots really from any others fired subsequently? Do they behave any differently, or can a 10rd group (or larger) predict more accurately what you can expect from any future first shot?

I shot 10x 3-shot groups, and 3x 10 shot groups - with PMC Bronze 55gr FMJ .223 at 105 metres. Rifle Remington M7, scope March F 3-24x, parallax dialled out, rear bag & atlas bipod shot prone, the usual drill. Light wind. Barrel cooled pretty completely between 3 shot groups, less so between 10 shot groups as I was running out of time and patience.
Note that I selected this ammunition because:
1) I have a lot of it left over from when we had ARs
2) I expected relatively poor precision from it, and that is necessary to amplify any effects - I couldn't use a really precise load e.g. the 73gr ELDM - it already shoots extremely precisely with 10rd groups. Trying to see any difference is futile. Using a load this imprecise however does introduce a heap of variance that makes even the more efficient 10shot groups and Mean Radius more variable.



So how different is precision and accuracy when measured with multiple cold 3-rd groups vs 10-rd groups?

Let's start with precision.

The average 3-shot group size was 1.25MOA; the smallest .4 and the largest 2.1. This gives a 70% variance either way from the average.
The average 10-shot group size was 2.1MOA; the smallest 1.6 and the largest 2.7. This gives about a 25% variance either way from the average.

The 10x 3rd groups look like this, overlaid (and centred around mean point of impact)

3 shot sample - scatterplot
Attachment 268529


The overall 30-rd composite group was 1.0MRAD, or 3.6MOA. The mean radius values are:
At 10RD: 2.4CM
At 20RD: 2.3CM
At 30RD: 2.0CM

What cone of fire do these mean radius values predict?
Using the mean radius from the first 10 rounds, the predicted O95 is 1 MRAD
Using the mean radius from the first 20 rounds, the predicted O95 is .96 MRAD
Using the mean radius from the full 30 rounds, the predicted O95 is .83 MRAD

This is actually interesting - there is a significant outlier in the first 10 rounds - now whether this is "really" an outlier, or I simply picked up a shot from the extreme ends of the distribution - isn't clear. However it falls outside the O95 predicted by the more precise 30rd mean radius figure, and outside the full group of the other 59 rounds fired.


The 30rd scatterplot from the 3x 10 round groups looks like this:
Attachment 268530

he overall 30-rd composite group was 0.83MRAD, or 2.9MOA The mean radius values are:
At 10RD: 1.5
At 20RD: 2.3CM
At 30RD: 2.1CM

What cone of fire do these mean radius values predict?
Using the mean radius from the first 10 rounds, the predicted O95 is 0.6 MRAD
Using the mean radius from the first 20 rounds, the predicted O95 is .93 MRAD
Using the mean radius from the full 30 rounds, the predicted O95 is .89 MRAD

Note that the actual 30rd group size from the 3x 10rd groups overlaid measures pretty much exactly what the O95 prediction from the 30rd mean radius from the 3rd groups predicts ! and within a couple of mm of what the 30rd mean radius from the 10rd groups predicts. Note that overall the 10x 3rd groups did produce a very slightly smaller mean radius than the 3x 10rd groups - but with the variance in the samples, it is functionally identical.

The 10rd groups overall group overlaid is smaller (2.9MOA) than the 3rd groups overlaid (3.5MOA) - however if we look at the total 60 round group, you can see that one "outlier" really is outside the total group. If it's ignored, they are both about the same size and don't really look any different. I however think it shouldn't be ignored, it's just part of the 5% of the cone of fire that you're really unlikely to capture and it happened today.

Attachment 268531

So: I see no evidence that firing 3 shot groups gives you any better information about precision that just firing 10 shot groups and being done with it - with this combination. There's no evidence for any effect of barrel heat or shooter fatigue within the larger groups.

How about accuracy? How well zeroed can you get using 3 vs 10 round groups?

The mean point of impact of the 30 rounds total fired in 3rd groups is 1.17CM Left, 1.84CM high. 6 out of 10 3rd groups gave a group centre location error from that measurement of 1 or more .1MRAD clicks in one or both directions. That's actually better than I've seen in the past.
Attachment 268532

The mean point of impact of the 30 rounds total fired in 10rd groups is 1CM Left, 1.6CM high. None of the 3 10rd groups were more than 1 click away from this.
Attachment 268533

Of course, you should really be able to zero within 0.5 of 1 click value in both directions - all of the 3rd groups were more than 0.5 away from the true MPOI in at least 1 direction. 1 of the 3 10rd groups was just over 0.5 click away.


Do 3 round groups give you an adequate zero for hunting? Absolutely. However if you'd like a more precise zero that you can have confidence in, and that doesn't seem to shift day-to-day - consider using at least 10rd to establish your mean point of impact. There really isn't any downside.


Targets - there are plenty of 3 shot groups where it would be difficult to be certain whether a shot was really "a flier" or not if you did not have confidence in your shooting and your system. These kinds of groups cause all kinds of confidence issues and confusion.

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Attachment 268561

Maybe all the error is me, and I just can't shoot consistently enough to see other effects - it's all just shotgun groups from bad shooting.

Maybe not.

Attachment 268534

It doesn't seem to be a problem with more consistent ammunition.

So what is the problem I really see?

Essentially, it's that the average hunter/shooter and the hunting/shooting culture has picked up the language and the concepts of precision shooting, and people are applying these to their results without really understanding them. It creates an environment of misinformation, drives people to waste a lot of time and ammunition or components chasing results that don't matter and aren't real because other people claim them on the internet, and leads to variously, both poor confidence in equipment when results are inconsistent - or unjustified overconfidence that then falls apart when taken out a bit further.

I really see very little downside to applying a bit more specificity in terms and collecting more data. It allows absolute confidence, tied to real expectations - and frees up energy to focus on things that matter more.

I guess a couple of other theoretical checks you could do, Is choose a rifle know to group poorly, and see what percentage of good 3 shot groups come from it.

And in another vein. Choose a relatively inexperienced shooter with a proven accurate rifle/ammo combo, and see if there is any fatigue over the course of a 10 shot group.

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Originally Posted by whanahuia

I guess a couple of other theoretical checks you could do, Is choose a rifle know to group poorly, and see what percentage of good 3 shot groups come from it.

And in another vein. Choose a relatively inexperienced shooter with a proven accurate rifle/ammo combo, and see if there is any fatigue over the course of a 10 shot group.

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The former is more or less what I viewed I was doing here - this rifle with this ammo is a pretty poor shooting system. I unfortunately don't own any terribly imprecise rifles ! but this imprecise combination produced 4 out of 10 3rd groups under 1MOA, and 2 out of 10 at or under 0.5MOA.


I'll try find an inexperienced shooter and see what results look like. Of course, others can contribute too!

I guess what you might find with a rifle/ammunition combination known to produce consistently poor 3-shot groups is that it's actually more like a 5-6MOA combination rather than 3-3.5 MOA like this one.

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Originally Posted by gimp

The former is more or less what I viewed I was doing here - this rifle with this ammo is a pretty poor shooting system. I unfortunately don't own any terribly imprecise rifles ! but this imprecise combination produced 4 out of 10 3rd groups under 1MOA, and 2 out of 10 at or under 0.5MOA.


I'll try find an inexperienced shooter and see what results look like. Of course, others can contribute too!

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You are probably right. It's just that I thought about trying the same experiment you did, by introducing poor performing ammo, or a mix of ammos, to a rifle that performs well. And was unsure of what accurate info that would gain me. I just felt it would be better info to be keeping such variables as ammunition quality etc to the same standard so that you can judge the performance of the rifle.

IE, rather than trying to induce poor performance in a good system, still be trying to produce the best performance in a system that docent historically perform well.

I appreciate your thorough efforts in the name of science. Shooter experience would be another interesting variable, but much harder to quantify I imagine.

It's slightly amusing to reflect on my early days of shooting, where 'sighting in' would involve taking one shot, adjusting scope, then taking another. Often I'd be halfway through a box of ammo, and still chasing the zero around the page! Blamed it all on the scope back then.