Honestly Evaluating Load Accuracy

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It is a mistake to use the methodology or techniques of in print periodicals to determine accuracy measurement. In print periodicals only write articles so you will look at the ads. The periodical sells you a subscription that barely, if even, pays the postage, their profits come from advertisers. (a business model that has been inplace since the Ladies Home Journal of the 1880's) So what you read, is an infomercial, designed to prick you to run to the local gun store and buy, buy, buy. You will never read anything negative on any current production firearms.

As D.Pris said here, the purpose of articles is to give the reader "a taste". One of the techniques is using low shot counts, such as three shot groups, or, the current in print gold standard, five shot groups, as measures of accuracy. Readers assume in print writers are experts, honestly evaluating the article under test, and nothing could be further from the truth. The in print writer is given about $400 (per D.Pris) per article and he has an economic incentive not to spend too much ammunition or time evaluating the latest boom stick. Plus, you are not going to read about the weapon being a blunderbuss. It won't go in print, or the test will be altered to make the weapon look good. No article goes into print without three or more levels of management reviews. In terms of making turkeys look like eagles, there have been hundreds, if not thousands of articles on 45 LC Colt SAA's which have 0458" chamber mouths. Apparently all 45 LC Colts have 0.458" chamber mouths since the second generation issue, but when did you ever read an article about the things shooting 5 to 6 inch groups at 25 yards with anything but hollow base bullets? If there were "accuracy" tests, it was with the only ammunition that would shoot acceptably. It is as Noam Chomsky said "Advertising is designed to create ill informed consumers who make irrational decisions".

It takes a lot of ammunition down range to really have confidence in the true accuracy of a load. And the true reliability. Loads in the 308 Win and 30-06 that were tried and true across the course loads turned out to be, great. However, developing new loads, almost all that were accurate stayed accurate, but very often, they were too high pressure, which only revealed itself with continued use.

If you want to know how good your load is, take the rifle to a mid range match and see what your score is after 60 rounds. Then, shoot it in a couple of more matches. Eventually you will abandon the load for "better". Then a couple of years of competition later, as your marksmanship improves, try the old load, and you will find, it was actually pretty good: It was you who were awful.

I did ask the second place shooter at the Smallbore prone Nationals how many rounds it took before he had confidence in a lot of 22lr match, and he said about a brick (500 rounds). I can attest to making early decisions about the quality of match 22lr, both good and bad, only to find, a brick or two later that my initial estimate was 180 degrees wrong.
 
to the OP:

there are lots of different ways to measure groups. what we typically do on the internet and benchrest matches could be called "extreme spread". basically, we measure the two farthest holes in the group. then we assume that all future rounds will be somewhere in between those two. this leads to issues around sample size as you describe.

an alternative way of measuring it is what the military uses, which is called AGR or Average Group Radius. they take all the shots, and add up the distance from center and divide by the number of shots. this is good because it takes into account information from all the shots in the group, as opposed to just the two worst ones. however, what it doesn't do a good job of telling you how far out your worst shot could be.

Making some hand-wavy simplifications and assuptions... The Mean Radius is equal to 50% Circular Error Probability. You can expect half you shots to be inside and half outside Mean Radius. With the assumption that the POA and POI are the same then a 95% Circular Error Probability can then be estimated as 2.08 times the Mean Radius (50% CEP). So a Mean Radius of X you would expect 95% of your rounds to fall into a circle of radius 2.08X.

I have been using an app called Range Buddy. Take a picture of your target with something on the target you can use for scale (like a 1-inch grid) and enter a bit of data (range, caliber, etc) and click on the bullet holes and it calculates all the data for you. It calculates Extreme Spread (group size), Mean Radius, Group Area and POI vs POA shifts. I like it.

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mean != median

e.g. if you shoot 4 rounds into the same hole, and jerk the 5th one an inch away, your mean radius is .2" and 4 of the 5 will be inside it
 
mean != median

e.g. if you shoot 4 rounds into the same hole, and jerk the 5th one an inch away, your mean radius is .2" and 4 of the 5 will be inside it

So if you jerk the 5th round that is not a valid data point.

This is statistics so the expectation is large data sets but we then try to apply to much smaller sample sets and hope they still work. They usually do but our confidence in the results is less the smaller our data set is. So even if you did't jerk that 5th shot that .2-inch mean radius may not be the true mean radius of that weapon/ammo if we collect more data. A single 5-shot group's mean radius has a much bigger error range than say the mean radius of a 50-shot group. As shooters we don't typically calculate that or think about that next layer to the math much since we can't do anything about it without collecting more data.

On the other hand if it turns out that the .2 mean radius of that first group truly is correct one for that weapon/ammo that group would be an outlier and would would expect if you shot 50 5-shot groups for every 4-in 1-out group you shoot we would expect a 1-in 4-out group to appear somewhere in that much larger data set. It's all statistics that can appear to be violated by the occasional outlier but get a big enough sample set and it will all make sense.

We have now exhausted my statistics expertise. One of the few math classes I never took since I hated statistics. Would much rather tackle nasty partial differential equations than calculate statistics on data. I learned just enough statistics to fake it through engineering school. :rofl:
 
Sure but you’ve missed my point which was simply that mean is different than median and your previous post seemed to be describing medium
 
Sure but you’ve missed my point which was simply that mean is different than median and your previous post seemed to be describing medium

Ahhh yes typically mean and median are not the same but I believe in this one case mean and median happen to be the same. This has to do with the assumed probability functions being used in the calculations here. I am on shaky ground without doing some more reading.
 
Median by definition means half the points are on one side and half on the other. That is not the case with mean as my example pointed out with 4 holes inside the average and 1 outside.
 
Median by definition means half the points are on one side and half on the other. That is not the case with mean as my example pointed out with 4 holes inside the average and 1 outside.
That I realize but the mean radius is the by definition the 50% Circular Error Probability.

In reality a group as you described probably does not fit the distribution functions being assumed by Circular Error Probability math. The idea of 4 in one hole (zero error) and then a 1-inch flier usually point to an something outside of the norm. A damaged projectile, bad powder charge, shooter error, not the normal distribution due to small variation in the parameters we are trying to measure. Like I said we are on the ragged edge of my knowledge.
 
As D.Pris said here, the purpose of articles is to give the reader "a taste". One of the techniques is using low shot counts, such as three shot groups, or, the current in print gold standard, five shot groups, as measures of accuracy. Readers assume in print writers are experts, honestly evaluating the article under test, and nothing could be further from the truth. The in print writer is given about $400 (per D.Pris) per article and he has an economic incentive not to spend too much ammunition or time evaluating the latest boom stick. Plus, you are not going to read about the weapon being a blunderbuss. It won't go in print, or the test will be altered to make the weapon look good. No article goes into print without three or more levels of management reviews. In terms of making turkeys look like eagles, there have been hundreds, if not thousands of articles on 45 LC Colt SAA's which have 0458" chamber mouths. Apparently all 45 LC Colts have 0.458" chamber mouths since the second generation issue, but when did you ever read an article about the things shooting 5 to 6 inch groups at 25 yards with anything but hollow base bullets? If there were "accuracy" tests, it was with the only ammunition that would shoot acceptably. It is as Noam Chomsky said "Advertising is designed to create ill informed consumers who make irrational decisions".

Do you have links to where D.Pris made those claims? Thanks.
 
So, I shared this thread with a friend who is a non gun guy. He works as an actuary. An actuary as I understand it, is someone who evaluates statistical data to determine probability of outcomes. He does statistical analysis for United Healthcare to help them asses risk and profitability.

I gave him a quick overview of normal load development practices and asked him how he would evaluate the data provided by shooting groups at a target. I asked him to assume that all other factors besides powder charge were equal. Here was his take:

• The most relevant information is distance from point of aim (assumes gun is sighted in to center of target or 0,0 on an x,y axis). In other words, do you hit what you aim at?
• The object of the evaluation is to determine the level of confidence one can have in their point of impact falling within a certain distance from their point of aim.
• Small sample sizes give less confidence. Larger sample sizes give more. More data is better.
• It is impossible to devise a test that gives 100% confidence. (Unless you are God, then you already know so you don’t need a test.)
• It is impossible to eliminate all but one variable (i.e. powder charge, seating depth, ect.) in our testing. Human error and wind are just two of the possible factors that degrade the integrity of our data and lessens our confidence level in our results.
• Our load testing falls under the category of experimental statistics. There are allowances in this discipline for factors beyond our control.

Here was his suggestion for evaluating a load:
• Measure each point of impact’s distance from POA.
• Add all measurements and divide by number of shots to find the mean distance from point of aim.
• Subtract the mean from the distance for each shot and square each result.
• Add all squares together and divide by ONE LESS than the number of shots. (This statistically makes allowance for another variable beyond our control).
• Take the square root of your result above. The result is your Standard Variance from POA. The confidence level varies with sample size. My friend believes 25 data points is sufficient for this method to give about 95% confidence level.

I never took statistics in school. This guy makes his living with statistics. His method sounds practical and objective. It also sounds more complicated than measuring CTC of a five round group. When I mentioned this, I got a 15 minute lesson on why that measurement and/or the “eye test” isn’t very statistically valid. His perspective is at least interesting coming from someone who isn’t involved with firearms. It’s just math without passion or prejudice. I think that kind of objectivity is what we are looking for.
 
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Headed to the range with a virgin barrel to put this discussion into practice. Kinda excited. This is my first non-stock barrel (26” Shilen 223 Wylde 8 twist). Gonna begin break in, sight in, and chronograph 3 ladders of 69 SMK with N135, N140, and Varget. Gonna emphasize low SD and vertical over 5 shot group size. Winner gets a seating depth ladder. That winner gets a 25 shot evaluation. Report to follow.
 
Headed to the range with a virgin barrel to put this discussion into practice. Kinda excited. This is my first non-stock barrel (26” Shilen 223 Wylde 8 twist). Gonna begin break in, sight in, and chronograph 3 ladders of 69 SMK with N135, N140, and Varget. Gonna emphasize low SD and vertical over 5 shot group size. Winner gets a seating depth ladder. That winner gets a 25 shot evaluation. Report to follow.
Should be interesting! I’ve been gathering different powders/primers for 223 load development in a factory rifle. My question is initially what is your COAL/CBTO gonna be for the test shots prior to the seating depth ladder? Published data? A certain thousandths off the lands? Etc..

For my testing I plan to start either 10 or 20 thousandths off the lands.
 
I always start at book recommended length set by the mfg of the bullet. In you case 69gr SMK is max magazine length of 2.260". This length has always worked good for me. I could not go any longer due to magazine restriction unless I single bullet feed. Which I do for testing in my AR's with the use of a Bob-Sled. Varget is what I mainly use for but have a load developed with TAC and few other powders.

I have a brand new Kreiger match barrel setting in the closet waiting for me when I shoot out my current barrel. It has a min spec chamber with very short leads. The 69gr SMK will be jammed into the leads if I load book length. I would suggest you determine what you MAX length is and back off like you said. It may take 50+ shots or so for the barrel to settle down. Just keep an eye on it.
 
Should be interesting! I’ve been gathering different powders/primers for 223 load development in a factory rifle. My question is initially what is your COAL/CBTO gonna be for the test shots prior to the seating depth ladder? Published data? A certain thousandths off the lands? Etc..

For my testing I plan to start either 10 or 20 thousandths off the lands.
I used .002 less than the average measurement with the Hornady OAL gauge. I can seat (jam) a 69 SMK with the bolt to 2.355. The Hornady OAL gauge gives me 2.322. I find it hard to believe I can jam a bullet 33 thousandths. Regardless, I went with the “safer” of the two @ 2.320.
 
Preliminary range report:
69 SMK
Lapua brass
FGMM primers
C.O.A.L. 2.320

Winners with each powder:
23.8 grains N135
2840 fps
4.4 SD
.5625 five shot group

24.2 grains N140
2822 fps
9.7 SD
.74 five shot group

25.8 Varget
3094 fps
13.3 SD
.675 five shot group

Honorable mention:
65 grain SGK (used for fouling/sight in)
24.0 N135
Starline brass
FGMM primers
2.80 COL
3124 fps
13.7 SD
.75 five shot group (first 5 round group from new barrel after 3 round sight in.

158 rounds total with many cleanings in between just in case “break-in” is a real thing.

Today I loaded 25 each of the 69 SMK N135 and Varget winners + 25 SGK with 24.0 N135 and 25 SGK with 26.0 Varget for evaluation at a later date using methods discussed previously. Report and pics to follow. I hope to shoot on Tuesday if the range isn’t closed because of the Corona virus.

COL test from .005 - .050 to follow with one of the winners.

When done I’ll have about 320 rounds through the barrel. I’ll alao have a 69 grain SMK load, alternative powder choices, and a 65 grain GK load. In the future, I’ll work up loads for different bullets like 77 SMK and/or 75 ELD. Since I’ll already have an idea about seating depth, powder choice, and approximate charge weight, ladders should be shorter in round count.
 
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@Nature Boy - good info about your solid load development methods. I don’t shoot over 200 very often. I’ll try to add more range to my tests soon.
 
EC2EC93D-77AE-4C2D-AE59-45C93AC2CC54.jpeg image.jpg image.jpg Range report on 100 yard tests of 69 grain SMK:

25.8 Varget/Lapua brass/FGMM/COL 2.320
5x5 shot groups
Avg muzzle velocity - 3121
SD - 18
Average group size - .95
Largest group - 1.375
Smallest group - .5
Average distance from POA - .46

23.8 VV N135
5x5 shot groups
Avg muzzle velocity - 2897
SD - 8
Average group size - .725
Largest group - .9375
Smallest group - .5625
Average distance from POA - didn’t measure

After measuring distance from POA for every shot in the Varget groups and finding they averaged about half the average group size, I’m not doing that any more. I’ll settle for an average of 5 groups.

I only shot two five round groups with each 65 grain Game King Load:

24.7 grains H-4895
Starline brass/FGMM primers/2.28 COL
Avg group - .752
Avg velocity - 3153
SD - 9

24.0 VV N135
Avg group - 1.344
Avg velocity -3010
SD - 13

26.0 Varget
Avg group - 1.094
Avg velocity - 3016
SD - 25
 
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