5 shot groups "kinda worthless"?

Hmm. No real science involved here. Once you have your 100 yard grouping to where you're satisfied, move it out to 200 and shoot. One shot or a group. Then give 300 yards a whirl.
Right about here is where "most" rifle shooters start to see a difference. Not talking about the Camp Perry crowd, just the average shooter mind you.
 
Cityevader said:
Sorry if already posted, but i just saw a video. Mathmatically speaking, 5 shot groups are "random".

My argument "against the math" is if say, one brand of ammo is consistantly tight-grouped after 5, and another ammo is consistantly all over the place after 5 then duh, obvious...but if different ammos are sorta kinda similar, then 1000's of hits need to be averaged to determine grouping.

Click to expand...


Instead of using this software to assume the number and level of variables, I think a better test would be to do 1,000 5-shot groups and see how different they are.

Experience shows that a 5 round group is able to predict repeatable performance from the round, rifle, and shooter - within a margin of error influenced by things like humidity, arthritis, or something.
 
jmr40 said:
Anyone can get lucky and put together ONE good group of even 10 shots, or just have a bad day and shoot poorly. I'm more interested in how consistent my 3 shot groups are over multiple range trips.
Click to expand...

Absolutely agree with this. But, my main goal is hunting. Never had a kill that took more than two shots unless it was just a mercy shot. I'm not shooting bench rest or F-class, so 10 shot groups mean nothing to me. Normal dispersion and bell curves mean very little, repeatable 3 shot groups d. I'm most concerned with the first cold bore shot. If its distance from the aim point is within the group size every time, I've got what I need.
 
"My argument "against the math" is if say, one brand of ammo is consistantly tight-grouped after 5, and another ammo is consistantly all over the place after 5 then duh, obvious"

Not really an argument against the statement. "Consistenty tight grouped" is many more than 1 5 shot group. Also "consistently all over the place" is a lot more than 1 group.

I think what the article says is that one 5 shot group by itself may be misleading.

Personally my favorite rifle heats fast and goes wild, so I shoot rapid 3 shot groups. But..I have done that over many different range sessions. And what I am really interested is the first of those 3 shots from a cold barrel.

I am not really interested in telling small differenced in stuff that it takes good statistics to determine. I am in the "it shoots pretty good or it shoots like crap" zone when I go to the range.
 
See I take 5 shot groups for each particular load I'm evaluating and i usually shoot some factory ammo if I have it to confirm zero before so I have some heat in the barrel already. So for instance take these 6.5 PRC groups. These were shot at 25 yards out of my Mossberg Patriot Predator. Sporter profile barrel with a muzzle brake.
Fired basically consecutively.

20230125_185113.jpg

20230125_185118.jpg

20230125_185131.jpg

20230125_185126.jpg

20230125_185141.jpg

So multiple 5 shot groups with different loads shot basically the same. If a load doesn't shoot well you'll know pretty quick, if you take 20 rounds of one load and shoot all 20 rounds in generally the same spot, call it good enough for government work and move on to trying a new load. Like as you can see my 140gr Partition and 140gr Sierra MatchKing loads are basically the same. Same powder charge and brass, just different bullets. I actually tested those by request from guys over in the what have you done in the reloading room today thread cause we were debating/wondering what difference a flat base bullet vs a boat tail bullet has at short range. I need to test them at a bit further range tho.
 
I like 5 shot groups as it test myself and the load. More than 5 shots unless you have a heavy barrel heats up to much and will throw shots. On a hunting rifle once I establish a load it's one cold shot per range trip since a cold shot can be different. I have on a hunting rifle loaded a long oal that is consistent for the first shot and then load the following rounds with a shorter oal to fit the mag.
 
ooohh posting groups!

index.php

My best group ever, those are 1-inch squares and that is a 200 yard group.
 
I finally broke down and watched the video. Some of what he says is correct, and I think some of it is flat wrong. Comments, not in order of importance:

1. His software is using the Mann-Whitney U test to see if groups are statistically different. This is NOT an appropriate test. Mann-Whitney is for interval or ratio data, not for measures of dispersion. And to boot, it's a relatively weak test that will not detect small differences. Big boo-boo. None of his statistical inferences are valid. If you notice, he also did not apply any of the conventional tests to evaluate normality, such as the Anderson-Darling test.

2. His assertion that the distribution of points of impact is bimodal is a new idea to me. I have not tested that idea, but am strongly skeptical. His targets don't look bimodal to me. But, as I said, I haven't tested that. I've also never come across it in the literature. Maybe he is right, but I'll hold onto my doubt for now. Edit to add: DrDreFab posted an article that busts the bimodal assertion. The video is wrong.

3. His point that sources of variation do not add linearly is absolutely correct. It's also true that if one of the sources of variation is much larger than the rest, the lesser sources almost don't matter. For fine rifles, shooter skill will almost always be the largest source of variation. The type of test he is attempting requires a really good bench rest. And, incidentally, it also requires very still air. So his results probably reflect shooter skill and air turbulence (larger sources of variation) more than rifle and ammunition performance.

4. I don't think he understands P value. Most tests produce a P value. That is the probability of getting a result at least this strong just by random chance. If your P value is less than .05, there is evidence that the difference you are seeing is real. If it is greater, then we usually choose to believe that the difference we see is just random variation. The so called "scientific basis" for choosing .05 was that someone asked Ronald Fischer what he thought, and he said, about 1 in 20. And it stuck. For industrial applications, .05 is often a good choice. But there are times when .25 is good enough, and times that .01 isn't good enough. It depends.

5. If you want to do statistical tests on measures of dispersion, you do indeed need large samples, but not quite so many as he claims. As a rough rule of thumb, if the ratio of two standard deviations is 1:2. then 25 samples from each group are sufficient. If the ratio is 2:3, then each sample needs to be at least 35. Two samples of 50 will usually detect a ratio of 3:4. That's a rough, quick, and dirty approximation.

You've heard me say it many times: A single 5-shot group will give you your long term average 5-shot group size within about plus or minus 50%. The average of three 5-shot groups will give you an answer within about plus or minus 25%. Getting better precision than that takes a whole lot more shooting. Quadrupling the number of groups fired only cuts the error by half.

And so concludes your grim and theoretical lesson for today..... :)

He shops a Gunnies, and his outdoor video looks like the west side of Utah Lake. So maybe he is my neighbor. We might enjoy doing some shooting together.
 
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DrDeFab said:
Here's some related reading, for those who don't want to be saved from the mathematicians.:neener:

https://www.sciencedirect.com/science/article/pii/S2214914717300776
Click to expand...
RATS!!! DRAT!!!!! DANG!!!!!!!

Here you had me salivating over the article, and it turns out that at the outset, the authors fell into one of the same traps that got the video author: General Full Factorial ist nicht für measures of dispersion. Like Mann-Whitney, it is for interval or ratio data. Sigh.

There is one very nice thing that they did, which is applying the correct tests for normality to the shot dispersion. Their result, and Figure 6 very solidly debunk the video claim about the data being bimodal. As far as we can tell, the data are normally distributed.
 
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jmorris said:
I believe in just cold bore shot placement, 3 shot, 5 shot, and up and up. “Kinda useless” depends on what you are wanting to know.
Click to expand...

Yep.

Most times I'll do a five shot group when shooting plinking/for fun ammunition. On occasion, I would shoot 30 round "groups" with my Three Gun rifles to see how the point of impact changes as the barrel heated up.
 
Cityevader said:
Myself feels better now.
i spent countless hours of comparing 20-some brands of .22 in a marathon weekend, for each of three different guns (10 shot groups and i walked miles setting up new targets for each 75yd test.)

Two or three brands were "best" and duplicate-ably better by a modest margin...and two or three brands sucked. But the VAST majority were simply average and tough to distinguish.
Click to expand...
For 22lr there's no excuse not to shoot an entire box of 50 on paper to test out that ammo to see if it's good. Doesn't matter if you do all 50 on one paper, 5 targets 10 shots each 10 targets 5 shots or whatever.
I have been saying individual 3 and 5 shots groups are useless for 20 years.
People brag about a 5 shot group being about 1 inch at 200 yards, show me multiple 10 shot groups shot different days then we will see if you really have something.
The biggest lie ever, the 1 inch mini14 three shot groups at 100yd.
 
If i can put 20 rounds into 1-1/2 inch at 100 yards I have a good shooting gun.;);)
If i can put 20 rounds into 1 inch at 100 yards I have a great shooting gun.:):)
If i can put 20 rounds into 1/2 inch at 100 yards I'm going buy a bunch of lottery tickets!:D:D
 
denton said:
RATS!!! DRAT!!!!! DANG!!!!!!!

Here you had me salivating over the article, and it turns out that at the outset, the authors fell into one of the same traps that got the video author: General Full Factorial ist nicht für measures of dispersion. Like Mann-Whitney, it is for interval or ratio data. Sigh.

There is one very nice thing that they did, which is applying the correct tests for normality to the shot dispersion. Their result, and Figure 6 very solidly debunk the video claim about the data being bimodal. As far as we can tell, the data are normally distributed.
Click to expand...

You seem to know a thing or two about math. I feel like the question and answer here are reversed - we should be asking what number of shots is necessary to identify the primary failing variable.

My hypothesis, based on experience: 3 shot groups are the minimum to have enough data to infer something - if the shooter is experienced and excludes their ability and the weather from possible problems, then the ammo or rifle are more likely the problem. If the shooter is the problem, a 10,000 group won't provide much more helpful or actionable information than a 5 shot group.

The goal of grouping isn't really to prove the limits of the machine (rifle and ammo), it is to develop a track record that will either identify areas for improvement or predict later performance.
 
21H40 said:
My hypothesis, based on experience: 3 shot groups are the minimum to have enough data to infer something
Click to expand...

The problem is that the analytics discussed in the last 2 pages have disproven this hypothesis for almost all manners in which reloaders make inferences from 3 shot groups.
 
Varminterror said:
The problem is that the analytics discussed in the last 2 pages have disproven this hypothesis for almost all manners in which reloaders make inferences from 3 shot groups.
Click to expand...

OK, so I wasn't as clear in my writing as I was in my imagination.
None of these posts have said that a group with fewer than 3-shots is effective, unless you're referencing something I missed.

For real statistics (IANAStatician but I can Google) we need to know what level of confidence and margin of error are acceptable before we can select the appropriate sample size. Then we need to identify the variables we can or want to measure. There could be a lot of variables for reloaders like COAL, ogive, brass thickness, etc.

The other problem for reloaders is whether they consider each shot as a sample or each group. I think the more valuable information for the reloader comes from using each group as a sample.
 
One should understand our “teachers” on firearm accuracy are nothing more than shills for the firearms industry. We all read these articles which are nothing but advertising, and over the decades, the writers have gotten better in the mis use of statistics to hide the inherent accuracy of the item under test, and to prevent comparisons between tests in previous articles. Gunwriters don't want to exhaustively test the weapons they are given, for a number of reasons. The first is time and materials. Gunwriters are given a flat fee for their articles, DPris said it was $400. I think he took that down because I could not find that later. It is obvious, the less the influencer shoots, the more money they get to keep. Shooting takes time, the less time at the range the more time on the recliner, etc. Based on the compensation rate DPris stated, I think it is probable that articles are in fact a loss leader for many writers, and that they are only doing it for promotion of “their brand”. Book sales and celebrity endorsement are probably the big money makers for these guys. It is obvious the in print guys are not interested in shooting enough ammunition to establish the inherent accuracy of the thing, one reason is, because the inherent accuracy of the thing may not meet the communities' expectations. And that would upset an advertiser.

You do know, magazines don’t make their money on subscriptions. This is the business model since the 1880 and the Lady’s Home Journal. The subscription is more or less, earnest money. The subscriber has some skin in the game. The magazine makes its profits from advertisers. A magazine will absolutely do nothing to upset an advertiser.

The accuracy analysis we read in firearms “evaluations” is statistical pseudoscience. Gunwriters post the smallest group size out of three shots, and then claim an “average” group size. Notice they are no longer posting the largest group. Averages are not good measures of consistency. Averaging makes the group size appear smaller. The extreme spread of is the size of the largest group. You hit or miss based on the extreme spread of the group, not some average.

Perhaps the best measure of accuracy and consistency is the mean radius figure used by the Department of Defense. However, I don’t think in terms of mean radius. This year I was looking over the shoulder of a Smallbore National Champ as he showed us the results of 22lr lot testing at Laupa. The composite group sizes, on the best lots, were statistics on 40 shots. The number this guy was pointing at was extreme radius. That is the furthest any bullet was from center. That is a good number. As a point of discussion, I will use the diameter of the A23 target X ring. The A23 is a 50 yard target and the diameter of the X ring is .39 inches. The diameter of the ten ring is .89 inches. Any shot more than 0,445 inches from center is going to be a nine. Obviously that would be bad if the inherent accuracy of your ammunition will not hold the ten ring. If no rounds exceed 0.195, (half the X ring) then it is possible, if you do your part, to shoot a 50-5X on all four 50 yard bulls, resulting in a perfect score of 200-20X. That would be good.

There is an excellent article at the end of the Oct 2014 Shooting Sports USA on group size and accuracy: http://www.nxtbook.com/nxtbooks/nra/ssusa_201410/ This foundational article was written by small bore prone competitors who wanted to shoot perfect scores. In small bore prone a Match is a 40 shot event of two twenty shot targets. The typical 1600 round Smallbore bore prone tournament is 160 rounds fired for record, divided up into four 40 round Matches. Therefore the referenced article assumes that a 40 round group is the baseline.

As anyone can see in table six, at least at 100 yards, a five shot group is 59% of the size of a 40 shot group, a 10 shot 74%, and a twenty shot 88%. A three shot group is below contempt.

This is another good article on the limitations of five shot groups

Accuracy Testing: Shortcomings Of The Five-Shot Group

by Brad Miller, Ph.D. - Wednesday, September 25, 2019
https://www.ssusa.org/articles/2019/9/25/accuracy-testing-shortcomings-of-the-five-shot-group

one that addresses statistics for accuracy.

Shot Group Statistics for Small Arms Applications
https://apps.dtic.mil/sti/pdfs/AD1034885.pdf

you may have to go to the main DTIC web site and then find it, as Government web sites are consistently changing and churning.
 
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