5rd groups aren't statistically significant! Wanna bet?!!

[Ledzep]

1. This isn't all about you. Keep in mind it's also about people parroting you in their own interpretations. Who lack the nuance to understand there's a special condition to necessitate this large data sample on an unknown gun that was unspoken.

"I control what I say, not what they hear", Eric Cortina.

But ...even now, in this thread, I honestly feel like I hear the goal posts being moved in what you're saying. Here's why.

There's never been any caveat given about DOPE. Data on prior engagements. That's never been in the conversation until now. And like the other guy, ....in what world are we gathering meaningful data on the first 30 rounds in a gun?

No. Actually. We've specifically said on the podcast that what we do is to shoot 100-150 rounds to make sure everything on the gun is solid (no wonky bedding, loose rings, let the barrel speed up or do its thing whatever), let the barrel brake in, then conduct whatever load development we're going to do. At the same time, doing 20-30 shot strings for load development, guess what? When I pick the best one I already have the data! I plug it in and go. The only other time that shooting a large sample is necessary is in truing a ballistic file at long range or if something changes or goes wrong.

Of course we have previous data and history with the gun. It's our gun! Lol. And we get a certain number of rounds down the barrel before we start taking the results real seriously. So our understanding of the rifle, the load, and it's capabilities is always a constant in these discussions. So when you say broadly, without caveat, "A 30rd sample is the minimum amount to truly understand your gun", everyone assumes that's along with and on top of what they're already doing with their rifles. (Yeah, you didn't say that in your last post, but you've said it before. And so has everyone that parrots you). Here's another reason why. Despite what I just typed, you are also saying this by 30rd by giving the basic statistical truth that 30rds will give a better statistical truth than 5. I know, I agree, in a vacuum. But just that one sentence alone gets exported to people believing they need to shoot 30rd groups every time they go to the range. The basic, undeniable truth that a large sample size gives greater confidence....skips right over the consideration of what a shooter can practically use from that data set for a lot of people when they hear it.

Again, I can control what I say, not what people read/hear... Dunno what to tell you. It's a podcast. I don't have the time and nobody (well, not many) wants to listen to 7 hours of preamble on statistics 101 before I give a dissertation on 5,000 rounds worth of recorded data. It's not a great platform for disseminating hard data. We've had that conversation inside and outside of the company before. We do our best to condense it down but at the end of the day it's a free-flow conversation with some limited aides.

Look at it this way. What if on your podcast you had said, "You really need at least 30rds to understand what your gun and load are capable of, but it doesn't need to be shot in one sitting or even on the same day".

I remember myself and Jayden talking about shooting multiple sets of small groups as long as you correlate POI/POA it's the same thing. Might not have been the original "your groups are too small" podcast but one of the following ones. He shoots 7x 3 shot group for his hunting rifles because the thin barrels and magnum cartridges perform differently due to heat on a 3x vs. even a 5x or especially a 10x. Totally valid. No issue.

Mixing it up on different days only serves to make the data set more messy. If the wind changes direction or magnitude it changes POI. If the temperature changes it can affect average MV (a good test to do anyway, but better when it's more controlled if you can imagine). It's doable but less than ideal.

Then it would be a pretty unnoteworthy statement and everyone would have shrugged their shoulders and walked away. And it wouldn't have justified the click bait title of the video, "Your groups are too small". And honestly, I don't think that's even what you meant. I very much think you straight up meant to tell people that they need to lay down and shoot a 30rd group every time they want to see what their MV, SD, and group size looks like because anything smaller is a lie.

The marketing team at Hornady is tired of hearing me bitch about "marketing" and "clickbait". But guess what, they're marketing nerds and the more clicks they get the better (or so they say.. Idk.). Such is life. Engineers make poor salesmen.

And to just play the same game, I agree! A larger sample size is going to provide better data. But I still maintain that "better data" isn't always usable and the cons of shooting 30rd groups everytime you go to the range is F'ing retarded.

I feel like I've said this before (in this thread....), but I shoot 30x rounds once *Unless I change a meaningful variable (muzzle device, load, optic, barrel, etc.)*. After that I shoot steel and animals. The data from the first 30x shot string after the barrel is broken in is the same throughout the useful life of the barrel. The only thing that should change is maybe MV creep with temperature or the barrel wearing out. I build a 4DoF profile and rock and roll.

The only time you need 30x shots is to get that initial data, or to compare different loads or to zero a new scope, or if I believe something is awry etc. I don't shoot 20x every range trip. My 4DoF file is set I lay down and smack steel and will only touch 100yd if I think something is wrong. Truthfully I prefer 300yd for "close range verification". Better resolution, less parallax issues, etc.


At the end of the day, do whatever makes you happy. We get a ton of hate thrown our way for what is essentially talking about common knowledge in other fields and the entire intent is to shoot less on paper at 100yd and more at steel. You can dick around with a 100yd zero check every range trip and burn up components in a near-useless 5-shot or ladder test or OCW test or Satterlee test, or you can put the shit together, break in the barrel, find an acceptable load in short order, get solid data on it and run with it. If you interpret that as "You must shoot 30 shots every time you lay down", I can't help you. The point is to knock out the BS early, set it up and rock and roll, always has been.

 

[Ledzep]

Not technically correct that the average of the SDs will always be lower than a combined SD.

I ran a simulation study where the sample SD from 6 groups of sample size 5 were calculate, then averaged and the grand SD of all 30. There’s about 21.7% likelihood that the average of the 6 SDs would be greater than the grand SD with a 99% CI [21.3%, 22.0%].

I ran it with sample sizes as 50 and the likelihood jumped to 25.6% with a 99% CI [25.2%, 25.9%]. The main take away is that the SD distribution is highly variable compared to other distributions like the sample mean.

But, I think your general point is fair since what you claimed happens on average 74.47-78.3% of the time.

I'll look into that. I could be wrong but I do not ever remember seeing that happen with real data, nor my simulated distributions.

I did 'the maths in skool' boss, I understand sample size populations, and will never argue against the statistical importance of a larger population.

My point *outside the part you quoted* was to the relevance of the sample size of an aggregate vs large sample - as it pertains to the vast, vast majority of shooters.

Let's use your SD point... Is a ~4 FPS SD increase (30 shot result of OPs samples vs his lowest 5 shot sample) relevant to elevation adjustment at say 800 yards? We know the answer, it is about a half inch, or a little less than one-fifth of .1 mil.

Either way man, we're going around in circles partially agreeing, and partially not. There's enough animosity already here that I don't need to add to it.

No animosity on my end. It's just math and physics. It's better for me, it's better for everyone to know more. Whether or not it's worth the effort is up to the individual. If you're going to smoke a whitetail at 54yd in the same stand your family has used since 1974, this is all a waste of time.

If you're hunting mulies out west and you want to know if you have a true SD of 8fps or 12fps, well that means a possible ES of ~50fps or ~75fps and that drives the cone of fire both vertically (velocity variation) and horizontally (wind deflection variation due to MV variation). And if you're so inclined you can run simulations and find out exactly what effect that has on a kill-zone target and how that, and many other things affect your potential shots. Mental masturbation, sure. Unnecssary? Maybe??? Depends on who you are and what you're doing.

All it is, is a better understanding of what you're doing.

 

[Beefmanne]

 

[Aftermath]

There are guys here that will take 2 bites out of a shit sandwich.

 

[Holliday]

I've been around long enough to see trends come and go. Just a few years back, you were labeled as mentally handicapped if you didn't shoot a 10-shot ladder and 'look for flat spots'. Prior to that it was OCW.

Exactly.

It is amazing how the level righteousness from the latest “have you heard the good news” crowd, never diminishes.

 

[JR1200W3]

Mixing it up on different days only serves to make the data set more messy. If the wind changes direction or magnitude it changes POI. If the temperature changes it can affect average MV (a good test to do anyway, but better when it's more controlled if you can imagine). It's doable but less than ideal.

Personally, I like shooting my zero in different conditions and positions. And collecting incidental data here and there just to reaffirm confidence. Obviously, I don't put a lot of stock in shooting a shit ton of ammo at 100yd test targets to build SD, Mean, and ES libraries. But I will shoot 100yd paper from challenging positions on the clock to check, not my guns zero, but my ability to shoot a consistent POI and practice seeing my impacts on target.

IMO being able to maintain the same zero across all ranges, positions, and environments is the big dick move. I think a lot of people assume they do but they don't. They confuse shooter-zero issues with ballistic computer, profile, CDM, F'n David Tubbs DTAC BC's, mirage influence, the lighting changed, data issues. The anchor of your ballistic solution is your zero and most people only test their zero in a contrived prone, flat range, slow fire type of environment. When I can shoot my zero in varied and challenging environments on the clock, and my gun maintains a similar enough MV and the load keeps single digit SDs, the only remaining challenges are the mental game and wind. Personally, I don't sweat my data at distance. I have enough confidence and faith in Berger bullets, AB, and CDMs that I don't need to spend a lot of time checking true at distance. And you build that intuition after you shoot a match and you had no elevational misses.

When I'm actually zeroing my gun, I zero my 300yd data at 300. Your bullet will be within 0.1" inch for 10-20 yds prior to 100 and 10-20yds after 100. So when you're zero'ing at 100, you have a much smaller chance of perfectly nailing it than you do at 300. And we don't shoot 100yd targets in competitions. Perhaps this is the only thing we can both get on board with.

As far as shooting more on steel than paper, sure. I think most of us do but I also think there's a lot of unresolved misunderstandings that get made on steel. The issue with steel is people only want to shoot it once. And man, they take that high center shot as the gospel. That one round represents the exact center of their shot group. Sure. Somehow forgetting they're employing a certain cone of fire and that one hit was just in the extreme edge of their group size at that distance. And you can see it in play when they miss off the left, correct right and miss off right. Shake their head swear the wind just fucked them.

If you interpret that as "You must shoot 30 shots every time you lay down", I can't help you.

No, I don't interpret that as you must shoot 30rds groups everytime you lay down but I do interpret "Your groups are too small" as you need to shoot larger(30rd) groups. Who said that?

 

[DasherDialedIn]

wait...so how small are your groups in that 30 shot string? Show us your 1/4moa 5 shot group...that's all we care about

 

[Ledzep]

So we get a the "You Hornady guys only talk about mediocre performance, not real precision" blah blah... Here's my match rifle from last year testing a few different muzzle breaks. The Oehler only holds 20 shots in a test so they're all 20 shot tests. Check out the repeatability on avg MV, MV SD, and mean radius, though.

EDIT: These are all at 200yd, not 100yd

Had I done this testing with a series of 5 shot groups it would be pretty inconclusive. As 20 shotters I can see that maaaybe there's a slight preference in dispersion to running a .30 cal brake vs. 6.5mm.

Here's rounds 21-40 on my newest match barrel:

Here's last year's match barrel:

I'll dig around with these and others today if I get a break and check the avg. 5-shot SD thing vs. 20 shot SD.

 

[Maurygold]

So we get a the "You Hornady guys only talk about mediocre performance, not real precision" blah blah... Here's my match rifle from last year testing a few different muzzle breaks. The Oehler only holds 20 shots in a test so they're all 20 shot tests. Check out the repeatability on avg MV, MV SD, and mean radius, though.

EDIT: These are all at 200yd, not 100yd

View attachment 8745381

View attachment 8745382

View attachment 8745383

Had I done this testing with a series of 5 shot groups it would be pretty inconclusive. As 20 shotters I can see that maaaybe there's a slight preference in dispersion to running a .30 cal brake vs. 6.5mm.

Here's rounds 21-40 on my newest match barrel:
View attachment 8745384

Here's last year's match barrel:
View attachment 8745385


I'll dig around with these and others today if I get a break and check the avg. 5-shot SD thing vs. 20 shot SD.

Let’s see that factory loaded ammo test

 

[Rocketmandb]

I’d prefer they have a private range like me though.

Show off

 

[Hickswr]

The entire time I was reading your dissertation, I assumed you shot and measured six different 5-shot groups.

Unfortunately you didn’t. I think the premise of the 5-shot group argument is group size on paper (not velocity variance).

For example the first 5-shot group goes into a single bullet hole…..”I’ve discovered the NODE”

2nd 5-shot groups is 0.8”….”this is a terrible load, must adjust seating depth and add or subtract powder, maybe change primer, etc.

In short, your time would have been spent much more wisely if you shot separate 5-shot groups at a grid target and perform the statistical analysis on the individual groups vs the aggregate.

 

[JB.IC]

So we get a the "You Hornady guys only talk about mediocre performance, not real precision" blah blah... Here's my match rifle from last year testing a few different muzzle breaks. The Oehler only holds 20 shots in a test so they're all 20 shot tests. Check out the repeatability on avg MV, MV SD, and mean radius, though.

EDIT: These are all at 200yd, not 100yd

View attachment 8745381

View attachment 8745382

View attachment 8745383

Had I done this testing with a series of 5 shot groups it would be pretty inconclusive. As 20 shotters I can see that maaaybe there's a slight preference in dispersion to running a .30 cal brake vs. 6.5mm.

Here's rounds 21-40 on my newest match barrel:
View attachment 8745384

Here's last year's match barrel:
View attachment 8745385


I'll dig around with these and others today if I get a break and check the avg. 5-shot SD thing vs. 20 shot SD.

I partitioned each series into 4 groups of 5 shots. Calculated a grand SD for all 20 shots and averaged the 4 group SDs. Only the first series had an average SD greater than the grand SD. Which is right in the neighborhood of what the simulation estimated.

 

[flogxal]

Here's a question for the crowd. Are my six 5rd strings unrepresentative and noticably different than what you get? Are you regularly jumping between 5 and 15fps SDs? ES's in the 30's and 60's? My data isn't that crazy is it?

The weird shit does happen. A few days back I had a 20 shot set of data on my Xero, for IMI RazorCore 77gr. The ES was something absurd like I'd never seen before from this ammo. The temperature was only 80 F... not 110 F or 20 F.

Also, alamo5000 at post #92 does a great job of explaining what I was assuming is Hornady's POV -- just because of their business, as compared to a home reloader. And Ledzep has done a yeoman's job of giving us his additional POV to help on that score.

Nerdy as F or not, this has been a good discussion.

 

[TriggerJerk!]

Here’s what we have learned so far….

 

[Ledzep]

I partitioned each series into 4 groups of 5 shots. Calculated a grand SD for all 20 shots and averaged the 4 group SDs. Only the first series had an average SD greater than the grand SD. Which is right in the neighborhood of what the simulation estimated.

View attachment 8745453

Interesting. Is this a case of smaller sets of data being noisy (like specific to 4x5's and 6x5's vs 20 or 30 shots)? All of the simulations I did in MatLab where I ran it to 10,000+ samples showed similar trends that the smaller group SD's were smaller than the global population. *edit* I think! I'm second guessing my memory now...

I took a 100 shot group with factory 108's and made 95x 5-shot groups out of it (1-5, 2-6, 3-7, etc..). Then averaged the SD's of those 5 shot groups and got 10.10fps. The global SD was 12.18.

If there was a metric where it would be this way, I'd believe it to be SD on MV. It tends to be more evenly distributed (above and below) the global average. I am very certain that this (sample smaller than global) trend is true with group size and mean radius because myself and Jayden picked apart my math very carefully for those and over the long run, average group size (or mean radius) of 5 shoters is significantly smaller than population.

 

[Ledzep]

20 of the 95 5-shot groups are larger SD than the 100-shot SD, ~21%

edit: Sorry for your mouse wheels, suckers!

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[JR1200W3]

The weird shit does happen. A few days back I had a 20 shot set of data on my Xero, for IMI RazorCore 77gr. The ES was something absurd like I'd never seen before from this ammo. The temperature was only 80 F... not 110 F or 20 F.

Also, alamo5000 at post #92 does a great job of explaining what I was assuming is Hornady's POV -- just because of their business, as compared to a home reloader. And Ledzep has done a yeoman's job of giving us his additional POV to help on that score.

Nerdy as F or not, this has been a good discussion.

Sure. All bets are off with factory ammo. I shot 15rds of factory Berger 73gr out of my Ridgeline LPR-15 this morning. Chrono'd 10. I was demonstrating tripod technique and shot 5rds prone, 5rds tripod clipped in, and 5rds tripod bag. The SDs and ES were horr-i-ble`.

 

[Ledzep]

I think this is what's going on. Is this the case?

Some interesting information that may sway this. In my experience, MV distribution is not perfectly normal. It tends to skew a higher occurrence of less-than-average MV shots with a lower occurrence of higher-than-average shots that are of greater magnitude. I don't know if that plays a part off the top of my head.

edit: 100 shot global data on the left, 5-shot sampling histogram on the right.

 

[flogxal]

JR1200W3 -- Worth the extra time to clip in on the tripod eh?

 

[ballisticdaddy]

The ongoing, neverending argument over how many rounds a shooter needs to generate a reasonable estimate of the quality of his ammo, rifle precision, and average MV for his ballistic profile.

Hornady says minimum of 30rds and quite a few people agree.

Some people say a handful of 5rd groups from this or that shooting session.

Who's right?

"You're sample size isn't statistically significant! REEEE!!!!"

All I want to know is what load does it take to be able to hit steel from the bed of a tiny Nissan truck? Too soon? I think another barrel is in order so we can get an adequate sample size of data!

 

[JR1200W3]

All I want to know is what load does it take to be able to hit steel from the bed of a tiny Nissan truck? Too soon? I think another barrel is in order so we can get an adequate sample size of data!

That stage still pisses me off. Fritz is spinning up 3 more for me as we speak!

 

[JR1200W3]

JR1200W3 -- Worth the extra time to clip in on the tripod eh?

I usually prefer to shoot off a bag on the tripod but the LPR is pretty light compared to a PRS gun. Another consideration is if you're using the rifle and tripod professionally you need the gun set up and ready for hours on end potentially. You don't want to have to have a hand on the rifle all the time to keep it from falling off the bag when you're not shooting.

 

[Aftermath]

I think this is what's going on. Is this the case?

View attachment 8745483


Some interesting information that may sway this. In my experience, MV distribution is not perfectly normal. It tends to skew a higher occurrence of less-than-average MV shots with a lower occurrence of higher-than-average shots that are of greater magnitude. I don't know if that plays a part off the top of my head.

 

[JB.IC]

Interesting. Is this a case of smaller sets of data being noisy (like specific to 4x5's and 6x5's vs 20 or 30 shots)? All of the simulations I did in MatLab where I ran it to 10,000+ samples showed similar trends that the smaller group SD's were smaller than the global population. *edit* I think! I'm second guessing my memory now...

So the results are sensitive to the number of groups (m) you have and the sample size n. For instance, n=5 and m=6 vs n=5 and m=20. The reason for this sensitivity is because when you go to calculate the grand SD from the n by m data, the second case above is going to have more data to estimate with (30 vs 100).

If you run a simulation where n=2 and m=20, you’ll find that the probability percent of the average of the SDs is larger than the grand SD is around 1.935%. This makes sense because we know the small sample SDs are more likely to be lower than the true SD and the grand SD is much closer to the true SD than the average of the SDs.

Here’s some results where m=6 as the OP had his set up and m=20. Both at varying sample sizes up to some ridiculously large sizes just to see what happened. I relabeled m to be Group since most people don’t think in matrix algebra.

 

[flogxal]

For sure I don't think in matrix algebra or algebra generally. Hell I struggle with Gun Number.

Stats guys, CI = confidence interval?

 

[JB.IC]

For sure I don't think in matrix algebra or algebra generally. Hell I struggle with Gun Number.

Stats guys, CI = confidence interval?

Yes. And LL and UL are lower limit and upper limit.

 

[Doom]

I think this is what's going on. Is this the case?

View attachment 8745483


Some interesting information that may sway this. In my experience, MV distribution is not perfectly normal. It tends to skew a higher occurrence of less-than-average MV shots with a lower occurrence of higher-than-average shots that are of greater magnitude. I don't know if that plays a part off the top of my head.

Just to be clear the sample is never expected to be perfectly normal. Only the population will be normally distributed for a very large sample size.

The graph you show is the way that the standard deviation responds to the sample count. SD is not only not normally distributed but fits more closely to the Chi-Squared distribution. Hence the preference for the low SD for low sample counts. The reason is based on probabilities. 68% of the population is expected to lie within one SD of the true Population mean. Only 32% lie outside of one SD. Hence there is a higher probability of picking a velocity within one SD on any particular sample. But the more you sample the greater the probability that you get a value outside of one SD.

 

[carbonbased]

The SDs and ES were horr-i-ble`.

Horrible? Ha!

Here’s my data one fine October night in 2024 for factory Hornady 204 40gr Superperformance ammo…

48° / 65% / 29 inHg

I think I had mixed some older and newer lots together, but still. “Older” = since 2019, but not sure the exact date.

Not a lot of choices in 204 factory ammo, and the 40gr is used because theoretically it does better in the wind.

In Hornady’s defense, I often hit what I’m aiming at (pdogs), and I usually shoot only out to 400-450yds.

Edit: 26” factory Remington varmint barrel. Seems slow compared to my 22” Bugholes Muller 204 on my Tikka, which is nearly as fast.

 

[TriggerJerk!]

 

[Rocketmandb]

Here’s my data one fine October night in 2024 for factory Hornady 204 40gr Superperformance ammo…

What's your barrel life on that thing?

 

[Ledzep]

No, I don't interpret that as you must shoot 30rds groups everytime you lay down but I do interpret "Your groups are too small" as you need to shoot larger(30rd) groups.

As near as I can tell this is an argument of semantics.

If you have prior experience with the rifle, your sample set is larger than 5 rounds. Larger sample sets are more repeatable and more accurate to the population. I don't care if you shoot 10 3-shot groups, 4 7-shot groups, 6 5-shot groups, or any other combination.... Having 100 rounds worth of hitting steel plates at various ranges is still data but it's muddy. It would be better if it was all hard-recorded.

However, when it comes to comparing performance of different rifles or loads or bullets, or obtaining MPOI data for setting zero, or collecting realistic MV data for use in hit probability or getting inputs for a ballistic calculator, you need 20-30 shots worth of data. Period. Less data than that WILL cause errors that WILL result in misses down range that can be easily avoided by doing the homework up front.

The whole thing started as an evaluation of "load development" methods that involved shooting 1x, 3x, or 5x of each variable change. They're all hogwash. If you want to tell me that 5 shots of two different loads is enough data to pick which one will shoot better in the long run (Yes, in a vacuum, Yes, as the first time you've shot these two loads in this particular rifle), then you're full of shit. I am very confident in saying that.

Now it led into some other discoveries about the nature of dispersion in rifles. Again, all of that setting a zero, plugging in a MV into a calculator, collecting down-range information to "true" drag models, etc... It all requires larger sample sizes to ensure MPOI is reality and to ensure the input for average MV is reality.


You say "So what? I'm 7fps one way or the other?" Run the numbers. It's worth a few inches at 1000yd. So you think to yourself, ahh 0.1 mils at 1k, no big deal.

You are moving the entire shot distribution cloud by that amount, not an imaginary perfectly centered shot. You start with a basically linear dispersion of 0.8 MOA (from your first post) at 100yd. It will stay basically linear to ~400-500yd assuming good conditions. However, by 600-800yd, you will see that cone of fire nearly double, and by 800yd the vertical displacement of individual shots based on drag variability and MV variability will start to skew results in the vertical direction. If there is any wind at all, it will have variability to it (gusts) and that will cause windage variability to your impacts. In "good" conditions, you will be lucky to have 1.3-1.5 MOA at 1000yd for 30 shots with the same rifle/load posted above (Please do the test and post the results).

So you are not moving an individual, perfectly centered shot a few inches high or low, you're moving a 1.5 MOA cloud up and down (in good conditions). Now overlay that cloud on a 1.5-2 MOA steel plate. You start losing hit probability. Now add in wind, MV variation (wouldn't it be nice to know the true population ES you can expect??) so you have a 1.75 MOA tall and 2.25 MOA wide group and you start really losing hit probability. Now add in the fact that you zeroed on a 5 shot group and your zero is 0.06 mils off and you lose another slice of hit probability.

All of the little details matter and they all add up to misses. AGAIN.. it's entirely up to the end user what is "worth it" for what they do or what isn't. Regardless, the better data lies in the larger sample sizes. You will be better prepared and have a better understanding of system capability. Period.

 

[Ronws]

In the end, I still come down on the side of Hornady. And it is mostly the statements of Jayden Quinlan, the chief ballistics and stats guy there. It makes it simple enough that I can understand it and I don't have to learn all the terms. He has done all the heavy lifting.

He is also speaks out on the problem of making too much out of a small group result. For example, take a rifle and shoot 3 rounds as if you were a hunter. Let's say that the dispersion was .375 inches. You say, "I have a 3/8" rifle."

Then you expand out to 30 rounds or more and the dispersion has increased to 1.2 inches. So, the rifle was only sub-MOA in the context of 3 shots with the first one being cold bore.

I also agree that by the time one gets to just a 5 round group, you have already had history for that rifle and the lifetime sample is larger than 5 rounds.

I also do not see the value in using just a 5 round group to predict. 30 to 40 rounds brings the most bang for the buck, pun maliciously intended.

And, if after break-in, we get a solid 30 round group, even if the rifle is 1.2", use that as valuable information depending on the job.

 

[Beefmanne]

 

[supercorndogs]

Me headed to the range, not giving two fucks about statistics.

 

[Emerson0311]

As near as I can tell this is an argument of semantics.

If you have prior experience with the rifle, your sample set is larger than 5 rounds. Larger sample sets are more repeatable and more accurate to the population. I don't care if you shoot 10 3-shot groups, 4 7-shot groups, 6 5-shot groups, or any other combination.... Having 100 rounds worth of hitting steel plates at various ranges is still data but it's muddy. It would be better if it was all hard-recorded.

However, when it comes to comparing performance of different rifles or loads or bullets, or obtaining MPOI data for setting zero, or collecting realistic MV data for use in hit probability or getting inputs for a ballistic calculator, you need 20-30 shots worth of data. Period. Less data than that WILL cause errors that WILL result in misses down range that can be easily avoided by doing the homework up front.

The whole thing started as an evaluation of "load development" methods that involved shooting 1x, 3x, or 5x of each variable change. They're all hogwash. If you want to tell me that 5 shots of two different loads is enough data to pick which one will shoot better in the long run (Yes, in a vacuum, Yes, as the first time you've shot these two loads in this particular rifle), then you're full of shit. I am very confident in saying that.

Now it led into some other discoveries about the nature of dispersion in rifles. Again, all of that setting a zero, plugging in a MV into a calculator, collecting down-range information to "true" drag models, etc... It all requires larger sample sizes to ensure MPOI is reality and to ensure the input for average MV is reality.


You say "So what? I'm 7fps one way or the other?" Run the numbers. It's worth a few inches at 1000yd. So you think to yourself, ahh 0.1 mils at 1k, no big deal.

You are moving the entire shot distribution cloud by that amount, not an imaginary perfectly centered shot. You start with a basically linear dispersion of 0.8 MOA (from your first post) at 100yd. It will stay basically linear to ~400-500yd assuming good conditions. However, by 600-800yd, you will see that cone of fire nearly double, and by 800yd the vertical displacement of individual shots based on drag variability and MV variability will start to skew results in the vertical direction. If there is any wind at all, it will have variability to it (gusts) and that will cause windage variability to your impacts. In "good" conditions, you will be lucky to have 1.3-1.5 MOA at 1000yd for 30 shots with the same rifle/load posted above (Please do the test and post the results).

So you are not moving an individual, perfectly centered shot a few inches high or low, you're moving a 1.5 MOA cloud up and down (in good conditions). Now overlay that cloud on a 1.5-2 MOA steel plate. You start losing hit probability. Now add in wind, MV variation (wouldn't it be nice to know the true population ES you can expect??) so you have a 1.75 MOA tall and 2.25 MOA wide group and you start really losing hit probability. Now add in the fact that you zeroed on a 5 shot group and your zero is 0.06 mils off and you lose another slice of hit probability.

All of the little details matter and they all add up to misses. AGAIN.. it's entirely up to the end user what is "worth it" for what they do or what isn't. Regardless, the better data lies in the larger sample sizes. You will be better prepared and have a better understanding of system capability. Period.

Which is why unless I’m shown match results or detailed precise testing like you folks and Brian Litz does, I remain sceptical of claims from shooters who avoid such accountability.

 

[Emerson0311]

In the end, I still come down on the side of Hornady. And it is mostly the statements of Jayden Quinlan, the chief ballistics and stats guy there. It makes it simple enough that I can understand it and I don't have to learn all the terms. He has done all the heavy lifting.

He is also speaks out on the problem of making too much out of a small group result. For example, take a rifle and shoot 3 rounds as if you were a hunter. Let's say that the dispersion was .375 inches. You say, "I have a 3/8" rifle."

Then you expand out to 30 rounds or more and the dispersion has increased to 1.2 inches. So, the rifle was only sub-MOA in the context of 3 shots with the first one being cold bore.

I also agree that by the time one gets to just a 5 round group, you have already had history for that rifle and the lifetime sample is larger than 5 rounds.

I also do not see the value in using just a 5 round group to predict. 30 to 40 rounds brings the most bang for the buck, pun maliciously intended.

And, if after break-in, we get a solid 30 round group, even if the rifle is 1.2", use that as valuable information depending on the job.

Now consider shooting a careful 5 rnd group and multiplying it by 1.3 or whatever the simulations suggest. Results very close to reality without the resource cost of time and components. Everything we do is done to a cost point. Many times we squander resources to feed our neuroses.
I just spent several hours carefully reloading 39 rounds for my 300PRC. I could go out and blast them all downrange in pursuit of nerd nirvana. I would enjoy it. Cost time and $$$$. Tell me nothing I didn’t already know, ie. generally it will be around 1 MOA or slightly less, in idea conditions. Which is solid deer/moose/elk out to as far as I will shoot them. I read how Francis and Brian’s testing ends up around 1.2 MOA and consider, who the fuck am I to expect better from my random collection of skills and gear?

 

[carbonbased]

That is a pretty funny pic! What show is it from and what’s going on there? Lol

 

[The Knuckle]

That is a pretty funny pic! What show is it from and what’s going on there? Lol

Get smart ? and the "Cone of Silence" if I remember correctly

 

[hlee]

 

[flogxal]

A five round group isn’t an estimator. The statistic estimating a population parameter is an estimator. So, the sample mean is an estimator for the population mean and 5 rounds, assuming the variance is low, can be quite good as an estimator. But the same cannot be said about sample standard deviation for population standard deviation. The variance is quite high at 4 degrees of freedom. This applies to ES as well. Worse, ES is dramatically more biased than SD and has a larger variance.

If I used 5rd groups to sort powder charges -- and then used 30rd groups to confirm that what I thought was good at 5rds -- am I being over-optimistic, reasonable, stupid?

I'm still rookie at reloading and thus far have not minded "wasted" resources, I consider it all learning and not waste.

But I may not "see" correctly what is happening in my 5rds test groups. Too optimistic maybe. Statistically speaking.

And, considering I am loading for me and one barrel, not doing things at Hornady's level of volume or rifle universality.

 

[JB.IC]

If I used 5rd groups to sort powder charges -- and then used 30rd groups to confirm that what I thought was good at 5rds -- am I being over-optimistic, reasonable, stupid?

I'm still rookie at reloading and thus far have not minded "wasted" resources, I consider it all learning and not waste.

But I may not "see" correctly what is happening in my 5rds test groups. Too optimistic maybe. Statistically speaking.

And, considering I am loading for me and one barrel, not doing things at Hornady's level of volume or rifle universality.

So I think I’ve been pretty consistent in these types of threads where I spent my time talking about theory, simulations, or correcting some of the information, but I don’t make any rules that someone must follow or criticize them if the do something different. I generally do not believe anyone should get into the weeds with this stuff (unless you have a million dollar sponsorship which is not likely). If you want to shoot 2, 3, 10, or 100 rounds then that’s cool.

That being said, if we talk about estimating a parameter, then all estimators are not created equal. Most of what is said below is based of estimation theory.

MV average can be estimated well with 5-10 rounds.
MV SD can be estimated well with 20-30 rounds.
MV ES is so biased and variable that no reasonable amount of rounds will correct it.

I have to be careful with group sizes because I’ve ran some simulation studies that produced some weird results, but:

Group Center Location on target can be estimated well with 10-20 rounds.
Group SD (along a single axis) on target can be estimated well with 20-30 rounds. This isn’t common measurement.
Group ES is so biased and variable that it’s not worth using as a metric.
Group Mean Radius can be estimated well with 5-10 rounds.

Knowing the group center and mean radius are probably all one needs here.

There are probably a ton of caveats that could be said, but if you have a really precise and accurate rifle, those round counts could be reduced. For instance, if by some miracle someone can reloaded to have a MV SD of 2, then a sample SD of 1 doesn’t matter. They don’t need to shoot 30 rounds. I believe this is why Bench rest and F-class shooters do so well with tiny samples. They have low variability to begin with.

 

[carbonbased]

So I think I’ve been pretty consistent in these types of threads where I spent my time talking about theory, simulations, or correcting some of the information, but I don’t make any rules that someone must follow or criticize them if the do something different. I generally do not believe anyone should get into the weeds with this stuff (unless you have a million dollar sponsorship which is not likely). If you want to shoot 2, 3, 10, or 100 rounds then that’s cool.

That being said, if we talk about estimating a parameter, then all estimators are not created equal. Most of what is said below is based of estimation theory.

MV average can be estimated well with 5-10 rounds.
MV SD can be estimated well with 20-30 rounds.
MV ES is so biased and variable that no reasonable amount of rounds will correct it.

I have to be careful with group sizes because I’ve ran some simulation studies that produced some weird results, but:

Group Center Location on target can be estimated well with 10-20 rounds.
Group SD (along a single axis) on target can be estimated well with 20-30 rounds. This isn’t common measurement.
Group ES is so biased and variable that it’s not worth using as a metric.
Group Mean Radius can be estimated well with 5-10 rounds.

Knowing the group center and mean radius are probably all one needs here.

There are probably a ton of caveats that could be said, but if you have a really precise and accurate rifle, those round counts could be reduced. For instance, if by some miracle someone can reloaded to have a MV SD of 2, then a sample SD of 1 doesn’t matter. They don’t need to shoot 30 rounds. I believe this is why Bench rest and F-class shooters do so well with tiny samples. They have low variability to begin with.

This is helpful practical guidance and as a non-maths person, it might be the only thing I halfway understand in this thread haha!

 

[Ronws]

Now consider shooting a careful 5 rnd group and multiplying it by 1.3 or whatever the simulations suggest. Results very close to reality without the resource cost of time and components. Everything we do is done to a cost point. Many times we squander resources to feed our neuroses.
I just spent several hours carefully reloading 39 rounds for my 300PRC. I could go out and blast them all downrange in pursuit of nerd nirvana. I would enjoy it. Cost time and $$$$. Tell me nothing I didn’t already know, ie. generally it will be around 1 MOA or slightly less, in idea conditions. Which is solid deer/moose/elk out to as far as I will shoot them. I read how Francis and Brian’s testing ends up around 1.2 MOA and consider, who the fuck am I to expect better from my random collection of skills and gear?

I have a rifle that shoots .54 inches for the first three shots, great for hunting. I still consider the entire system, which includes me, a 1 MOA system. So that and impact velocity help define usable range but on deer, I am not likely to shoot past 300 yards. And the deep woods I hunt, you are straining to see past 70 yards.

 

[TriggerJerk!]

The sample size required to detect a difference between means (e.g., average fps A vs. average fps B) can be estimated. Detecting big differences between means (e.g., 3% change in average fps) would require a relatively small sample size, while a small difference (e.g 1% change in average fps) would require larger sample sizes.

Further, the amount of certainty that you want to have in your answer also effects sample sizes (higher certainty will increase the number of samples required).

If you have a ballpark guess of your mean (e.g., previous load had an average of 2500 fps) and your standard deviation (e.g., 25fps), you can estimate the sample size required to detect a xxfps difference with 90% certainty. This is called “power analysis”.

The above is a simple example, and if you want to do this yourself (e.g., muzzle velocity, mean radius, etc.) I would suggest you get a copy of G*Power (free; available for Windows or Mac) and give it a try (download and read the manual). If you have a background in statistics/power analysis then you can use R, JMP, SPSS, Minitab, or SAS (or other software). G*Power just happens to be free and easy to use. YMMV. If you don’t have stat experience, or you do not understand the relationship between SD, alpha, beta, and effect size, then seek help.

Last thought… please remember that trying to detect small differences with high certainty will require relatively larger sample sizes. Central Limit Theory is just a suggestion!

I hope this helps.

 

[CK1.0]

Has anyone mentioned that all this “statistical data” is skewed by that monkey pulling the trigger every shot who can’t be relied upon to pull it the exact same way every time? Because it is.

I can pretty much bet none of us is mounting our guns into a rigid, immobilized rest and using some type of device to break the trigger exactly the same for every single shot… so one’s got to remember to be honest about the fact that our performance and imperfectness is added into the equation whether we like it or not.

All the wonkiness/variability we add to the mix due to being imperfect meat puppets should be enough for most to see why we need to shoot more than a handful of rounds in order to be confident in what we’ve really got.

Anyone can shoot a couple of good groups in a row with almost anything if they’re even a little lucky… that’s why it takes more than a few rounds to rule out whether what we’ve got is legit or not.

Shoot too few and it’s a Rorschach test, period (and guys will see what they wanna see).

 

[carbonbased]

What's your barrel life on that thing?

I missed your question, whoops!

I bought the Rem700 used. I estimated I shot 500rds on it before I really started counting on a spreadsheet. So, I have 2103 rds on it…1603 I counted and +500 that I estimated, plus whatever the prev owner shot.

It still shoots pretty well. I find that at my stage in this game, and as a dude shooting factory ammo, I sometimes don’t know if I’m testing my bench/tripod technique more (incl. x-sandbag vs bipod A vs bipod B) or my factory ammo more or my wind reading skills more. I’m probably a hack.

In that spirit, behold my dirty (and clean) laundry!

See @Ledzep even if your employer makes some wack 204 40gr ammo, it can shoot ok. I mean, I’m a pdog shooter and not some sniper, so it frees up time for me to enjoy my kids and the stakes are low.

I subscribe to the idea that on one’s deathbed, no one whispers, “I wish I had spent more time adjusting seating depth…urrgh “

Well, since I’m in the reloading forum, some of you dudes might disagree lol

But I’ve learned a bunch just reading this thread, even though it’s (very) slowly sinking in.

 

[diggler1833]

There are probably a ton of caveats that could be said, but if you have a really precise and accurate rifle, those round counts could be reduced. For instance, if by some miracle someone can reloaded to have a MV SD of 2, then a sample SD of 1 doesn’t matter. They don’t need to shoot 30 rounds. I believe this is why Bench rest and F-class shooters do so well with tiny samples. They have low variability to begin with.

This is a much more concise statement than I was able to generate, and probably because the gentleman is better at statistics than I am/was.

Good rifles, good components, consistent shooters, and consistent techniques on the reloading bench produce much more consistent results on the range... and therefore usually produce less variation from one sample to the next.

Those pesky old, fat benchrest guys and their small sample sizes.

 

[TriggerJerk!]

Has anyone mentioned that all this “statistical data” is skewed by that monkey pulling the trigger every shot who can’t be relied upon to pull it the exact same way every time? Because it is.

I can pretty much bet none of us is mounting our guns into a rigid, immobilized rest and using some type of device to break the trigger exactly the same for every single shot… so one’s got to remember to be honest about the fact that our performance and imperfectness is added into the equation whether we like it or not.

All the wonkiness/variability we add to the mix due to being imperfect meat puppets should be enough for most to see why we need to shoot more than a handful of rounds in order to be confident in what we’ve really got.

Anyone can shoot a couple of good groups in a row with almost anything if they’re even a little lucky… that’s why it takes more than a few rounds to rule out whether what we’ve got is legit or not.

Shoot too few and it’s a Rorschach test, period (and guys will see what they wanna see).

The monkey behind the “trigger” is the largest source of variance in most things. I assumed everyone knew that.

 

[Aftermath]

I just baked 12 dozen shit chip cookies.

How many do you eat to determine that there is a deviation from the norm?

 

[CK1.0]

The monkey behind the “trigger” is the largest source of variance in most things. I assumed everyone knew that.

Sometimes when I see guys arguing about a tenth of a grain of powder, or a couple of thou of seating depth, etc, being the difference between a good or a bad load, acting like their performance can’t possibly be the difference… I start to think I might be the only one who remembers