Statistics Megathread

[ilc]

There have been numerous threads over the years (most recently Do barrel harmonics matter) that have evolved into debates on the merits of using statistics for load development and other aspects of the shooting sports. These topics have revealed some very talented individuals with an extensive knowledge of statistics who could make better use of their time helping others that have an interest in applying these techniques to their own shooting, rather than debating with those who have a vehement opposition to them.

In light of this I have created this Statistics Megathread to provide a place where interested people can discuss and learn about statistics, and how they might be used in shooting.

Who should post here;

• Those with a knowledge of, or an interest in, statistics
• Those who want to learn or ask advice about statistics
• Those who want to apply statistical techniques to their shooting
• Those who want to report on how they have used statistics with their shooting

Who should not post here;

• Those who have no interest in, or no interest in learning about, statistics
• Those who want to argue or debate about the usefulness of statistics
• Those who want to derail discussions off the topic of statistics
• Those who want to personally attack or belittle others, or question their political, religious or other beliefs.

This thread is for the discussion and teaching of statistics, not debate on their fundamental utility.

 

[ilc]

Resources

Hornady Podcast Ep. 050 - Your Groups Are Too Small
Hornady Podcast Ep. 052 - Your Groups Are Still Too Small
Outdoor Life - Rifle Nodes: How You've Been Wasting Your Time and Money on Load Development

Resources will be progressively added

 

[ilc]

AI summaries (GPT-5) of the Hornady Podcasts (watch them in full if you don't trust AI). These are a good introduction, especially if you are unsure or overwhelmed by maths and statistics.



Here's a clear summary of the Hornady podcast episode 50 "Your Groups Are Too Small | Sample Size":

---

Core Message

Most shooters rely on 3–5 shot groups to judge accuracy or load development, but statistically those groups are too small to be meaningful. Rifles naturally produce random scatter, and small samples can give a misleading picture of performance.

---

Key Points

• Sample size matters:
  • Small groups can eliminate a bad load (if it's clearly poor), but they cannot prove a good one.
  • To be statistically confident in small differences (like 0.1 MOA), you'd need dozens of shots — Olympic shooters often use 30–60 round groups for testing.
• Velocity data is critical:
  • Extreme spread (ES) and standard deviation (SD) of muzzle velocity are more reliable indicators of long‑range performance than tiny group size at 100 yards.
• Confirmation bias:
  • Shooters often "throw out flyers" or cherry‑pick groups, which creates a false sense of precision.
  • True accuracy is about consistent performance across many shots, not a single lucky cluster.
• Practical advice:
  • Use larger sample sizes when zeroing (20 shots recommended for a true zero).
  • Focus on meaningful changes (powder type, bullet choice, charge weight in larger increments) rather than chasing tiny tweaks with tiny groups.
  • Remember the shooter is the biggest variable — skill and consistency outweigh micro‑adjustments in load development.

---

Takeaway

The podcast drives home that statistics don't lie: 3–5 shot groups are fine for quick checks, but they don't tell the truth about a rifle's accuracy. If you want reliable data, you need larger sample sizes and velocity analysis, otherwise you're just chasing noise.

---

Episode 52 ("Your Groups Are Still Too Small") is the follow‑up to Hornady's earlier discussion on sample size. It doesn't just repeat the message — it adds more depth, real test data, and some practical conclusions that go beyond the first podcast.

---

What's new in the follow‑up

• Real‑world test data: They share results from extended shooting strings (20–50 rounds) to show how group size and velocity statistics stabilize only with larger samples.
• Quantifying sample size:
  • ~50 rounds are needed to get a ~97% valid measure of group size and velocity SD/ES.
  • ~20 rounds will get you "in the ballpark" (within ~25% of the true values).
• Dispersion drivers:
  • Powder charge tweaks (0.1 grain steps) had almost no measurable effect on dispersion until near max loads — and even then, only barely visible after 50 shots.
  • Powder choice and bullet design were far more influential than micro‑adjustments.
  • Seating depth showed little effect in modern match rifles (though it can matter in older surplus rifles with looser chambers).
• Other variables tested:
  • Barrel heating (in their tests) didn't significantly affect dispersion, though they note thin barrels may behave differently.
  • Primers had no measurable effect on group size.
• Better metrics than "group size": They recommend using mean radius (distance of each shot from the aim point) rather than extreme spread, since group size is just the distance between the two worst shots and has little predictive value.
• Practical workflow: Instead of burning time on 5‑shot ladders with tiny charge steps, they suggest:
  1. Pick a sensible powder and bullet for your rifle.
  2. Load ~20 rounds at a safe, non‑max charge.
  3. Shoot them as a string, record velocity and dispersion.
  4. If it looks promising, scale up to 30–50 rounds to confirm.

---

The extra takeaway

Episode 50 made the case that 3–5 shot groups are statistically meaningless. Episode 52 goes further: it shows why with real data, and it gives shooters a more efficient way to approach load development — focusing on the big levers (powder, bullet, barrel quality, shooter skill) instead of chasing noise with micro‑tweaks.

---

 

[VenatusDominus]

Here is a well done study on powder charge "nodes", independently verifying the findings from Hornady.

Rifle Nodes: How You’ve Been Wasting Your Time and Money on Load Development

Everything you know about rifle nodes and load development might be wrong. Click here to see the results for yourself.

www.outdoorlife.com

AI (ChatGPT) summary for the TL;DR crowd:

Key Points & Takeaways

Background: What Are "Rifle Nodes"?

• In reloading and precision shooting, "nodes" refer to theoretical charge weights at which barrel vibration is minimized, yielding consistent velocity and groupings.
• Common load‑development methods — velocity ladder tests, OCW (Optimal Charge Weight) tests, and seating depth tweaks — are used by shooters to try to find those "sweet spots."

Challenging the Traditional Approach

• Freel describes how a Hornady podcast (featuring ballistician Jayden Quinlan and engineer Miles Neville) questioned many of these traditional practices, especially when based on small sample sizes.
• The core critique: small sample sizes can create illusions of repeatability or "nodes" which vanish under larger‑scale testing.

Freel's Experiment / Testing

• He tested three rifles of different calibers ( .223 Rem., 6.5 Creedmoor, and .30/06) using the usual methods (ladder and OCW tests) to identify "velocity nodes," "accuracy nodes," and "antinodes."
• Then he loaded 30‑shot samples for each of those identified charge weights, and fired them under controlled conditions to see how they held up when sample size increases.

Results & Observations

• Across all three rifles, the "nodes" identified via small samples did not consistently produce noticeably better accuracy or velocity consistency when using 30-shot batches.
• In many cases, the lowest tested charge weight performed as well or better (in terms of dispersion and consistency) than the so‑called node loads.
• Differences in group size, mean radius, and velocity standard deviation among the sample loads were generally small and within expected variability.

Conclusions & Advice

• The author suggests that many reloaders are investing substantial time and powder chasing "ideal" nodes that may not offer a meaningful advantage.
• Instead of running many tiny sample groups, he recommends going to larger sample sizes earlier in testing, or even comparing a "random or minimum safe" load against what you believe is ideal, using 30‑shot groups to see if differences are real.
• He notes that changes in variables (e.g. temperature) can shift behavior, undermining the notion of fixed optimal nodes.
• He also did not test seating depth changes in this study, but mentions that earlier work from Quinlan & Neville suggested seating depth changes likewise don't yield meaningful improvements in larger sample testing.

 

[sep]

I'm with you and had previously read these. For my hunting rifles, I have settled on shooting ten, three shot groups to verify my loads as a result of seeing all this info. I've tested Hornady's seating depth experiences but only with two 30-06s both shooting 168 TTSXs and H4350. I got results similar to theirs.

Seating depth did not make a huge difference. .050 difference in average group size in one rifle and .057 difference in average group size with another rifle. Sample size in rifle one was 45 three shot groups spanning .089 vs 12 three shot groups in the .006 wide sweet spot. In rifle two, I fired 10 three shot groups at one seating depth then fired 10 more three shot groups with bullets seated .075 longer.

Miles stated in episode 121, seating depth produced a difference in group size of about .150 at 200 yards. If we extrapolate that to be .075 at 100 yards, my results aren't too far off from what they saw. Will this hold true for all bullet designs and calibers? I have no idea.

Does .050 or .057 matter at 100 yards? Depends on what you are doing. I think it could for competitive shooting but for hunting from field positions, I can't shoot that difference. I can shoot that difference from the bench but not in the field hunting.

I have also found their experiences with powder charge weight might be accurate too. I bought a new 30-06 about a month ago. Again shooting 168 TTSXs and H4350, I fired ten, 3 shot groups and got an average group size of .73. I then loaded up 30 more rounds bumping the charge weight up 1/2 a grain. The average group size for nine three shot groups was .83. (I had to discount one group because of an anomly in velocity of one round by almost 300 fps)

Miles has said the Hodgdon extreme powders will either stay flat or only slighly increase in group size as the charge weight goes up. My preliminary results seem to confirm that statement. So, that's where I am so far.

 

[FEENIX]

Oh boy!

 

[Mrvmax]

Here is my question, if 3-5 shot groups are meaningless, then obviously more rounds need to be fired. The more you fire, the more you change conditions. Gun temp changes, ammo temp changes due to gun temp, fouling in the barrel is not consistent, ambient temp changes things like mirage which can affect aiming, wind continually changes,

You have continuously changing conditions so is it really seating depth, OAL or is it he changing conditions causing differences? The larger the groups the less you can tell what is causing changes.

Do the OAL and seating depth theories contradict this: Houston Warehouse

I can see how statistically the small groups are meaningless, but unless conditions are kept the same, larger groups are ballistically meaningless.

 

[FireFlyFishing]

I shoot one shot groups. I end up having one hole sized groups and an SD and ES of 0. Beat that!

 

[sep]

Here is my question, if 3-5 shot groups are meaningless, then obviously more rounds need to be fired. The more you fire, the more you change conditions. Gun temp changes, ammo temp changes due to gun temp, fouling in the barrel is not consistent, ambient temp changes things like mirage which can affect aiming, wind continually changes,

You have continuously changing conditions so is it really seating depth, OAL or is it he changing conditions causing differences? The larger the groups the less you can tell what is causing changes.

Do the OAL and seating depth theories contradict this: Houston Warehouse

I can see how statistically the small groups are meaningless, but unless conditions are kept the same, larger groups are ballistically meaningless.

Everything you stated about changing conditions is true and always has been. Your rifle has a dispersion profile and you won't know what the boundaries of that dispersion profile are until you shoot enough rounds to see it.

An example Jayden gave is if you have a rifle which averages MOA at 100 yards, it will shoot groups as small as .3 inches and as big as 1.7 inches. That is its statistical dispersion profile. So, if you only fired two, three shot groups with this same rifle and they printed 1.2 and 1.4 inches you might think that rifle is not capable of averaging MOA and you'd be wrong. That's well within the dispersion profile.

I shoot my ten 3 shot groups over two days and only early in the morning before the wind picks up crazily when shooting conditions are most favorable at my range. I'm interested in determining how good the load is going to shoot at this point. A crosswind of 5 mph can push my bullet .4 inches at 100 yards. So, I try to be careful of wind conditions when evaluating ammunition.

The changing atmospheric conditions we can't control is why you should shoot a large sample size in changing conditions. This gives you a better idea of how the load is actually going to perform in the field. Barrel conditions we can control to some extent by regular cleaning and firing fouling shots to get you back to some semblance of a baseline but it can't be identical each time though for obvious reasons.

The Houston Warehouse demonstrated the only time a rifle shot in the zeros was when the bullet was seated touching or into the lands (IIRC). Not practical for a hunting rifle.

In my test results, so far, I haven't seen seating depth make a big difference. If I were a benchrest shooter, my results would necessitate me doing seating depth testing and powder charge testing because matches are won or lost by such small amounts you can't afford to leave anything on the table.

 

[VenatusDominus]

Here is my question, if 3-5 shot groups are meaningless, then obviously more rounds need to be fired. The more you fire, the more you change conditions. Gun temp changes, ammo temp changes due to gun temp, fouling in the barrel is not consistent, ambient temp changes things like mirage which can affect aiming, wind continually changes,

You have continuously changing conditions so is it really seating depth, OAL or is it he changing conditions causing differences? The larger the groups the less you can tell what is causing changes.

Do the OAL and seating depth theories contradict this: Houston Warehouse

I can see how statistically the small groups are meaningless, but unless conditions are kept the same, larger groups are ballistically meaningless.

From the https://precisionrifleblog.com/2013...-warehouse-lessons-in-extreme-rifle-accuracy/

Reloading & Components:

• One thing he stressed is that bullets must be precisely seated against the lands. He NEVER fired a single official screamer group when he was "jumping" bullets. All his best groups were always seated into the lands, or at the very least touching the lands. His practice was to seat the bullets so the engraving was half as long as the width of the lands.
• You can change the powder charge slightly, and it won't really make any difference, but if you change the bullet seating depth or the grip on the bullet, you're going to see bad things happen fast.

Myths Busted:

• Powder charges, as long as they were fairly consistent and bracketed within a couple of grains, were not important. He threw all of his charges with a Belding & Mull powder measure, and for one experiment he shot groups using three different powder measure settings (51, 52 & 53) … all three groups were identical.
• Lot variation in powder didn't seem to have any effect on accuracy, even on when using IMR 4198, which has a reputation for varying considerably from lot to lot. He would just buy powder as he needed instead of laying in a big supply, because he found no evidence to support that powder lot variance affected accuracy in the least.
• He never saw an inaccurate primer, and was unable to detect any accuracy variances resulting from seating pressure.
• Rumors have persisted for years that some rifles shoot proportionally better at 200 yards than 100 yards, or vice versa. Virgil files that one under "occultism." His experience in the warehouse was, if a rifle was shooting a consistent .100″ at 100 yards, it shot a consistent .200″ at 200 yards.
• He did NOT uniform primer pockets or turn the case bases. He also did NOT size his case necks.

 

[Mrvmax]

Everything you stated about changing conditions is true and always has been. Your rifle has a dispersion profile and you won't know what the boundaries of that dispersion profile are until you shoot enough rounds to see it.

An example Jayden gave is if you have a rifle which averages MOA at 100 yards, it will shoot groups as small as .3 inches and as big as 1.7 inches. That is its statistical dispersion profile. So, if you only fired two, three shot groups with this same rifle and they printed 1.2 and 1.4 inches you might think that rifle is not capable of averaging MOA and you'd be wrong. That's well within the dispersion profile.

I shoot my ten 3 shot groups over two days and only early in the morning before the wind picks up crazily when shooting conditions are most favorable at my range. I'm interested in determining how good the load is going to shoot at this point. A crosswind of 5 mph can push my bullet .4 inches at 100 yards. So, I try to be careful of wind conditions when evaluating ammunition.

The changing atmospheric conditions we can't control is why you should shoot a large sample size in changing conditions. This gives you a better idea of how the load is actually going to perform in the field. Barrel conditions we can control to some extent by regular cleaning and firing fouling shots to get you back to some semblance of a baseline but it can't be identical each time though for obvious reasons.

The Houston Warehouse demonstrated the only time a rifle shot in the zeros was when the bullet was seated touching or into the lands (IIRC). Not practical for a hunting rifle.

In my test results, so far, I haven't seen seating depth make a big difference. If I were a benchrest shooter, my results would necessitate me doing seating depth testing and powder charge testing because matches are won or lost by such small amounts you can't afford to leave anything on the table.

I posted a link to it, consistency was the key and they cleaned the barrel every 6 shots. My main point is that conditions can never be duplicated but the Houston Warehouse mitigated many of them. Here are some of the myths busted:

Myths Busted:

• Powder charges, as long as they were fairly consistent and bracketed within a couple of grains, were not important. He threw all of his charges with a Belding & Mull powder measure, and for one experiment he shot groups using three different powder measure settings (51, 52 & 53) … all three groups were identical.
• Lot variation in powder didn't seem to have any effect on accuracy, even on when using IMR 4198, which has a reputation for varying considerably from lot to lot. He would just buy powder as he needed instead of laying in a big supply, because he found no evidence to support that powder lot variance affected accuracy in the least.
• He never saw an inaccurate primer, and was unable to detect any accuracy variances resulting from seating pressure.
• Rumors have persisted for years that some rifles shoot proportionally better at 200 yards than 100 yards, or vice versa. Virgil files that one under "occultism." His experience in the warehouse was, if a rifle was shooting a consistent .100″ at 100 yards, it shot a consistent .200″ at 200 yards.
• He did NOT uniform primer pockets or turn the case bases. He also did NOT size his case necks.

Sorry, someone posted similar right before I did.

 

[jseandsje]

I am an ex-chemical engineer. I understand a little about statistics, but am no statistician.

I absolutely agree that to prove something, the more tests the greater confidence in the results.

I also know that theory and lab results often need adjustment when put into real world practice. And you can use up a lot of resources that you could use for real world testing.

That's why I spend little time on the bench. With my system It rarely takes more than 15 shots from the bench to pick a load for real world testing.

Then My system - rifle properly bedded - no gimmick bedding system, stiffened forearm, scope with level, and canting bipod, test load, and me - are tested in the prone position, the only position that I use for long range shots.

I have a hill with tip of ridge that drops sharply to a creek back up to a hill ridge. 200 yard tests.

I have 5 test positions, one on top of ridge relatively flat, one 1/3 way to bottom, one 2/3, on both sides of ridge. So I can test canting rifle, and me, left and right from varying degrees.
At each location I have a relatively flat piece of stone. I test from soft ground and rock.

i do my testing on days with temperatures in the middle of my hunting extremes.

I shoot one shot from each position, soft/hard rest, for 5 positions. Total of 10 shots. All at the same target.

I come back an another day and repeat. At the same target as first day

I come back another day and repeat. At the same target as 1st day.

Out of 30 shots, I throw out 3 shots, 10%

If I'm under 1.5 moa, I'm satisfied that I can take a shot out to 600 yards from any shooting position.

If I'm more or less than 1.5, I adjust the distance Limit accordingly.

What you'll find is that it's amazing how many 1/2 moa bench groups will grow to 1.5 moa when you test this way.

And sometimes I disqualify a 1/2 moa bench rifle from long range hunting becaues I can't shoot 2 moa from those field test positions.

That is how I test for real world so I have 90% confidence that I won't wound an animal.

So, and I'm not being a smart butt, I'd like your input, as a statistician, on my test method. As a hunter I just wast confidence if I'm going to squeeze the trigger on a target bast 500 yards.

Thanks in advance.

 

[coop2564]

I think all this 20 and more shots is not workable for hunting. My hunting is cold bore on fouled barrel. I see you tube videos one after another that guy shoots cold bore and its 1"" or more from main group when he shoots 10 shots or more. The cold bore gets factored out and he sights in. So there sight in is on hot barrel. Then they go hunt and shoot at animal at 500 yds and miss or make poor shot because his sight in was not proper for his old bore hunt. As a hunter I shoot 2 shots wait 25 mins to get all the way back to cold bore 2 more and same for 2 more. I sight in on that 6 shot group and it has never failed me for hunting. If I was target shooter your mentioned methods are great, but not for hunting. Trying to get 20 or more cold bore shots would take all day to let barrel truly cool to cold bore state. Most of my guns are sporter contour where this is very important. If you hunt with a very heavy contour probably wouldn't be as far off. But many of us refuse to carry 12+ lb rifles hunting. As a hunter i don't care where shot 5,6,7 hit. Only 1,2 maybe 3. All others from a hot barrel are actually hurting my accuracy for my cold bore hunting.

 

[Mrvmax]

I think all this 20 and more shots is not workable for hunting. My hunting is cold bore on fouled barrel. I see you tube videos one after another that guy shoots cold bore and its 1"" or more from main group when he shoots 10 shots or more. The cold bore gets factored out and he sights in. So there sight in is on hot barrel. Then they go hunt and shoot at animal at 500 yds and miss or make poor shot because his sight in was not proper for his old bore hunt. As a hunter I shoot 2 shots wait 25 mins to get all the way back to cold bore 2 more and same for 2 more. I sight in on that 6 shot group and it has never failed me for hunting. If I was target shooter your mentioned methods are great, but not for hunting. Trying to get 20 or more cold bore shots would take all day to let barrel truly cool to cold bore state. Most of my guns are sporter contour where this is very important. If you hunt with a very heavy contour probably wouldn't be as far off. But many of us refuse to carry 12+ lb rifles hunting. As a hunter i don't care where shot 5,6,7 hit. Only 1,2 maybe 3. All others from a hot barrel are actually hurting my accuracy for my cold bore hunting.

I agree, people foul the barrel on purpose after cleaning. For hunting, use the old story of how Carlos Hathcock (sp?) suggested sighting it. Basically one cold bore shot under as many possible difference scenarios as achievable (cold, hot, windy, rainy etc.), log that info and use it when hunting for that first shot.

If anyone has stats with one cold bore shot please chime in, I would like to see that.