Defensive Carry banner
1 - 10 of 10 Posts

Super Moderator
Joined
14,406 Posts
Discussion Starter · #1 ·
OK, I admit it, I'm a number cruncher. It would be difficult to tell which I like best, shooting or crunching. 馃

Fortunately, all the number crunching can reveal things that would be hard to see otherwise. So, here's kind of a summary of the results of the three statistical tests I did.

First, it really bothered that I was getting great 3-shot groups but the composites were not impressive as can be seen here...


3/10/2023 10 groups: 1.320 MOA / average size of the 10 groups: 0.587 MOA
3/15/2023 15 groups: 1.553 MOA / average size of the 15 groups: 0.562 MOA
3/16/2023 16 groups: 1.602 MOA / average size of the 15 groups: 0.536 MOA

Hmmm, near 0.5 MOA average group sizes and yet composites about 3 times that - is something going on I haven't caught? Let's look at plots of the groups versus vertical displacement. That is, how far is the group from the POA.







See anything common to all three? Yep, you got it - the vertical position of each set is trending downward. That would certainly strongly contribute to large composite groups!

This may be due to barrel heat from so much shooting. I thought I was shooting slowly enough that heat wouldn't be a problem. I could comfortably lay my hand on the barrel (near the muzzle) and it was warm, but not hot. I was shooting at a pace of about 1 round per 30 seconds. That may be too fast to prevent heat build up near the chamber.

How I see this is that the gun/load is shooting much better than the composites suggest. Let's look at some tables...



The tables have a lot of data in them but we only need to look at part of the data. I'll start with the +2 SD data. Why is the +2 SD important? In statistical analysis, the +/-2 SD points are where 95% of the data should fall. We really don't care about the -2 SD that would just indicate really small group sizes and what we're concerned with is BIG group sizes. Without getting into the math, I'll just say that there is only a 2.5% probability that a group will be large enough to fall outside the +2 SD point. Know why it's only 2.5% and not 5%? The other 2.5% is below the -2.5 SD point.

OK, there are three ways we can analyze group sizes, composite, average, and +2 SD. I was really big on the composite until I started to see problems with it. One problem is it addresses both group size and positional relationships of the groups.



I picked these groups because they are well under 0.5 MOA, but when you look at the composite of these three excellent groups, it suggest a different story. The composite shows a 1.052 group. The size isn't larger because the groups got larger, it's because the position of the groups varied.

While the composite is interesting, it is worst case and it does not give us any indication how likely (probability) it is that size group would occur. What if the reality was that composite only had a 1% probability of happening. Would you care? I wouldn't; I'd want to know more closely what I could expect consistently.

So I don't much like the composite analysis anymore.



So what about the average? Statistically, the average is where data will appear about 50% of the time. Some groups will be larger and some smaller and we still don't know how probable we are to get a larger group than average.

Which brings us to the +2 SD method. Where the composite deals with both the groups' size and position, and gives us a worst case, and no probability, the +2 SD method deals ONLY with group size and does give us probability of occurrence. Let's look at the tables above at the +2 SD column. As you can see, the +2 SDs are 0.944, 1.063, and 0.901 MOA. That means that there is a 97.5% probability that our groups will be equal to or less than those values.

So in essence, the +2 SD gives us precision, but not accuracy.

OK, let's nail this down. In the third table, we have a +2 SD of 0.901 MOA. Since this was a 45 shot group, we can expect 44 (97.5%) out of 45 shots to be less than or equal to 0.901 MOA. Here's the distribution chart - notice one group lies beyond the +2 SD line.



We do have to be careful here because that dot beyond the +2 SD line is a group, not a single shot. So, I looked at the group that generated that point and it has one shot that was low. The other two hits measured 0.443 MOA. So it was indeed one shot that caused the group to be larger than 0.901 MOA.

Whew! I'm tired - this was supposed to be a quick post - didn't work out to be so quick - or short. Gotta go eat now.
 

Registered
Joined
81 Posts
Whew! This is way, way to deep for me. Pray tell, what is +/-SD? Standard Deviation; a course which I flunked in colleg? It is Greek to me?
____
SD is the ratio of an object's mass to its cross sectional area with respect to a given axis. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis.

Still way to deep -

Dave Y -
 

Super Moderator
Joined
14,406 Posts
Discussion Starter · #4 ·
Whew! This is way, way to deep for me. Pray tell, what is +/-SD? Standard Deviation; a course which I flunked in colleg? It is Greek to me?
____
SD is the ratio of an object's mass to its cross sectional area with respect to a given axis. It conveys how well an object's mass is distributed (by its shape) to overcome resistance along that axis.

Still way to deep -

Dave Y -
In this case, SD is Standard Deviation. SD also stands for other things in other contexts, like sectional density.
 

Super Moderator
Joined
14,406 Posts
Discussion Starter · #6 · (Edited)
Minitab?

Based on your analysis, how should Defense Carry members apply your findings?
Excellent question!

I think at this point we should be in a "discovery" mode. That is, we see a new approach to load development, but before we discard the older approaches, we need to be sure what we replace those older methods with (if we intend to replace them) works better and more reliably than what we've been using.

Essentially where we are right now is pitting the 3-5 shot incremental charges against "pick a safe charge and go with it". It was Brian Litz that first put me on to this. In an interview, he was asked how he did load development and his answer was that he increases the charge until he sees pressure signs and then backs his charge off by 1 gr and that's the charge he goes with.

Then Hornady, in a podcast, kind of corroborated his method when they said if you shoot a large number of shots per charge (as they did to test this) you'll find that all the charges shoot about the same as far as accuracy goes. So for load development, pick a safe charge and go with it. Maybe we no longer need to invest time and money shooting 3 & 5 shot groups with incremental charges thinking one charge will work better in our guns.

So I'm testing this newer approach. In fact, I just got back from the range. I picked a third gun to test, a bolt gun and I chose to use H4895 powder because my software reloading tool indicated that powder would produce the fastest velocity at a safe pressure. The bullet was a 77 gr Sierra Match King. I picked the "safe" pressure from the software tool and loaded up 30 rounds at 22.8 gr. I would shoot ten, 3-shot groups to evaluate the load in the gun. So, there was no load development per se. I just picked a charge, much like Brian Litz did and went with it.

Here's the target I just shot at 50 yards...


So, essentially picking a charge at random shot super in this gun! Would another charge do as well? Don't know yet.

But here are some interesting stats...
60% (6 groups) of the 10 groups were less than 0.400 MOA
70% (7 groups) of the 10 groups were less than 0.500 MOA
All groups i.e. 100% of the 10 groups were less than 0.800 MOA.

I'll try the same test with a different charge tomorrow to see how it compares. I'm a little apprehensive about this next test, as this one is so good (for me) it's almost too good to be true.

Awww shoot, I left this out. You see that one low shot on the lower leftmost dot? That's one of those unexplainable outliers. I am certain that I did NOT cause that, nor did a velocity variation. The velocity for that shot was very close to the average velocity. I see that from time to time. I suspect it was a bullet problem, perhaps the bullet's balance was offset from the centerline and it was spiraling. Hornady actually addresses this in the podcast.

The bottom line is - I didn't include it in the group.
 

Super Moderator
Joined
14,406 Posts
Discussion Starter · #7 ·
Not to make too fine a point of it, but you mischaracterized 鈥渁verage鈥. Look at what you said, and I am sure you will catch it.

If one has a total of ten boxes with eight pounds of lead in five boxes and two pounds of lead in five boxes for a total of fifty pounds, the boxes have an average weight of five pounds each, yet no box weighs five pounds.
Yeah, I probably should have said, "The average is where there's a 50% probability of a data point falling." Or, "There's a 50% chance that a data point will fall close to the average value."

Good catch!
 

Registered
Joined
79 Posts
At 50 yards? Damn good shooting.

Just a question, all of your groups in the last picture are a bit low. Adjust or change the sights so you shoot a little higher should improve your overall groups. Interesting how they go lower.
 

Super Moderator
Joined
14,406 Posts
Discussion Starter · #9 ·
At 50 yards? Damn good shooting.

Just a question, all of your groups in the last picture are a bit low. Adjust or change the sights so you shoot a little higher should improve your overall groups. Interesting how they go lower.
When I got to the range, I discovered the scope was set for 100 yards (parallax turret). It was rainy and gusty so I wanted to shoot at 50 yards, so I'd have to adjust the scope for 50 yards. I did adjust the scope and shot two factory rounds and they were right on. But when I shot my first reload, I saw it hit a bit low. At that point I had to decide whether to adjust the scope which would open up the group, or shoot as is and preserve the first group.

Since I was more concerned about precision (group size) than accuracy (center of group from POA) I just left the scope where it was. But typically I set my scope for about an POI about an inch above the POA to preserve my sight picture. It's not so critical with 3/4" dots I was using this time, but when I use 1/2" dots a few hits can pretty much eliminate the dot. Then I don't have anything to aim at.
 
1 - 10 of 10 Posts
Top