Group size goes small to large and back to small

[Rio Precision Gunworks]

I shot my first 600yrd Fclass competition about 3 years ago. (Only been to 2) I went with a stock gun and stock ammo and was WAY out classed in equipment. After the shoot, several of the shooters came to me offering suggestions and recommendations. I was impressed that the gentleman i was in competition with was offering to help me get better. That was my first impression of this sport and the people involved in it. The after years of trying to learn the techniques of reloading and LR shooting on my own, i signed up for SH and quickly learned that not everyone in this sport is a gentleman. After this experience, id rather go back to learning on my own. I spend 2 day reading a couple of good resourceful information buried in 20x's the amount of garbage and chest beating.

You're going to need realistic expectations. You basically did the rifle equivalent of saying the earth might be flat. People aren't going to respond well to this.

Especially when there's mountains of data and books on the subject. I'd suggest reading all of the applied ballistics literature. That will hopefully eliminate any future instances of a less than warm welcome.

Keep in mind, "learning on my own" resulted in this thread being started with almost no data to support a theory that's been debunked countless times.

 

[Dead Eye Dick]

I have to do it, I have to….

 

[MR&R]

You're going to need realistic expectations. You basically did the rifle equivalent of saying the earth might be flat. People aren't going to respond well to this.

Especially when there's mountains of data and books on the subject. I'd suggest reading all of the applied ballistics literature. That will hopefully eliminate any future instances of a less than warm welcome.

Keep in mind, "learning on my own" resulted in this thread being started with almost no data to support a theory that's been debunked countless times.

I respect that. I also respect the greater education/experience that others have over me and thats why i came to this sight. If you read my opening statement, i said "I have a theory but I'm not sure what's going on." I ended with "any ideas?". I never claimed to have an answer, only a thought (which is what a theory is), and was looking for more educated answers. I will admit that, hide site, maybe i should have said "I have a theory" because some took that as me saying i have the answer.
Whats baffling to me is the number of people who attacked my clain to shoot 1/4moa at 1000 saying its nearly impossible, then get several saying they consistently shoot 1/4moa at 700, 800, and 1000.
By the way, the picture i posted earlier, some assumed i was showing my 1/4 group at 1000. It was 1 out of 3 of my 17yr old daughters 3 shot group at 1000 using my gun and my loads. I dont routinely take photos of my groups cause im not into "show and tell". However, i was impressed and proud of my daughter and i took the picture to send to the rest of my family.

 

[Macht]

Here's a 3D representation of the probability distribution of the shots from a 100-shot sample. Basically the total volume of the solid (cut in half here) is 100% of the shots, and as you slide radially you can enclose more or less of the probability a single particular shot will land within said radius/diameter (whatever reference frame you want to use, you can look at it purely radially in 2D and ignore the revolved volume).

The distribution is very similar to a normal distribution with the exception that you cannot have a negative radius for a given shot. What would be a "negative radius" shot just pops out as a positive radius on the other side of the MPOI. The mean radius isn't far enough away from the MPOI, and the bell curve tails cross over the MPOI (this is more and more true the better the dispersion is). So if you could imagine where ever the tail crosses the MPOI, the effective distribution % remaining flips back over the MPOI and skews the peak of the curve inwards towards the MPOI.

View attachment 8277153

Assuming a circular group (generally true)... Functionally, your radius of any given shot is a random event and follows a (mostly) normal distribution. If you think you can define the PDF at various ranges with 3 or 4 4-shot groups, I've got bad news for you.

That's the best representation of dispersion I've seen posted on the Hide. Did you fit a Rayleigh distribution to test data and then revolve it into a solid?

 

[Tokay444]

I respect that. I also respect the greater education/experience that others have over me and thats why i came to this sight. If you read my opening statement, i said "I have a theory but I'm not sure what's going on." I ended with "any ideas?". I never claimed to have an answer, only a thought (which is what a theory is), and was looking for more educated answers. I will admit that, hide site, maybe i should have said "I have a theory" because some took that as me saying i have the answer.
Whats baffling to me is the number of people who attacked my clain to shoot 1/4moa at 1000 saying its nearly impossible, then get several saying they consistently shoot 1/4moa at 700, 800, and 1000.
By the way, the picture i posted earlier, some assumed i was showing my 1/4 group at 1000. It was 1 out of 3 of my 17yr old daughters 3 shot group at 1000 using my gun and my loads. I dont routinely take photos of my groups cause im not into "show and tell". However, i was impressed and proud of my daughter and i took the picture to send to the rest of my family.

It was the 2 SD for me dawg.

 

[Ledzep]

That's the best representation of dispersion I've seen posted on the Hide. Did you fit a Rayleigh distribution to test data and then revolve it into a solid?

I made that about 2 years ago. If I remember Monday I'll take a gander at the profile to see how I created it but I seem to remember plotting a bunch of points and fitting curves to the 100-shot group data.

 

[Ledzep]

@Macht Just checked the model and yeah it has a hidden sketch (this was done in SolidWorks) with the histogram data points then the revolved surface is a series of splines that are a fit to those points.

I'm going to talk to a couple of people (Excel nerds) today to see if I can do something in Excel to replicate the behavior we see with these large sample distributions. Basically something you can input mean radius and SD of radii and have it convert to a hit probability distribution like the picture I posted. Might be able to do a simplified version that makes assumptions on SD and you just input Mean Radius to make a little more in-depth hit probability tool.

 

[Macht]

@Macht Just checked the model and yeah it has a hidden sketch (this was done in SolidWorks) with the histogram data points then the revolved surface is a series of splines that are a fit to those points.

I'm going to talk to a couple of people (Excel nerds) today to see if I can do something in Excel to replicate the behavior we see with these large sample distributions. Basically something you can input mean radius and SD of radii and have it convert to a hit probability distribution like the picture I posted. Might be able to do a simplified version that makes assumptions on SD and you just input Mean Radius to make a little more in-depth hit probability tool.

Haha, thought that looked like SolidWorks.

Just a thought: I've been screwing around in MATLAB with different ways to manipulate dispersion data in similar ways to what you're suggesting. If you assume your coordinates are normal and IID in the x and y axes then you can describe the distribution of radii using a Rayleigh distribution. You can develop that directly from your SD/variance only and then use the Rayleigh CDF to spit out your hit probabilities.

 

[Macht]

Thorough derailing of the thread, but I got curious. Knocked together some quick code that can do what I mentioned above. I generate some phony shot group data, calculate the sample standard deviation and feed it into the Rayleigh. I can get predicted group radii for given hit probabilities, or just output the graphs. Is that similar to what you had in mind @Ledzep ? I'd be curious to see how close to normal your large sample data is.

 

[Ledzep]

The large sample stuff definitely matches the Rayleigh better than normal, but normal is not incredibly far off. A year or two back myself and Jayden tried to get Excel to do a Rayleigh or skew a normal distribution to fit real data but couldn't figure it out and got distracted with other stuff. I'm going to pursue a MatLab seat this week. We've been talking about getting it for a while-- we've been pushing the limits of what Excel can provide for a few years now lol...

For example, you can use a normal distribution, take the mean radius + 2 SD's (SD in this reference is SD of individual shot radii) in either direction (double that) and approximate 20-shot average group sizes pretty accurately. I need to dig into the Rayleigh again to see the difference in SD vs. normal.

 

[Macht]

Matlab is awesome, definitely recommend. You could also test drive it with Octave (which is free) and if you decided to spring for a Matlab license most of your code would port straight over.

If you'd mostly be doing it for stats purposes R is also free, and I recently discovered a pretty robust dispersion analysis package for it (shotGroups).