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Realistic SD expectation debate!!

Cz455guru

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Minuteman
Oct 13, 2017
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I am working up a load for my prs comp gun and being is I can't find varget I'm trying reloader 16 in my dasher. In my research I have found some people that I assume are trustworthy by there sponsorship status amongst others that I have no idea who they are, posting stuff about 1-2fps standard deviation. Is this realistic even? surely they aren't posting false info or deleting their shots that don't fit within there velocity range from there Labrador or whatever they are using to record velocity.
I have been reloading for around 10 years, dabbled in benchrest and won some benchrest matches, spent a lot of time and money trying to figure out how to get low sds and I just haven't achieve that level, 6-8 fps SD seems to be more normal if I'm honest with myself and have a big enough sample size.
Or is this a lot like them people that post a picture of a group in the ones and they say their gun can shoot 1/4 in groups all day long. I'm a skeptic by nature so forgive my rant if it offends anybody. I just want somebody to prove it to me before I go down the rabbit hole of trying to figure the secret out.
 
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Single digits are fine, SD shows up at distance more so than in close,

so in a PRS match how far, how often are you shooting those extended distances where you will see the SD show up in a negative way?

If I was getting 6-8fps I would be fine if it was me. Once you drop below 10fps you are on a pretty good footing.
 
The number gets larger, the bigger the sample size. Lots of people don't run enough numbers to truly discover what the actual SD is. So what is statistically significant? 10 shots? 20? 100?

However, SD in the 2-3 range isn't unheard of once you have the brass formed, necks burned, and primer pockets/flash holes manicured. However, you need all the right tools on your reloading bench to make this happen. ... and the right skillset to run them too.

Primer seating depth uniformity and a rifle with silky smooth properly timed ignition is a must. During development/testing of our competition primer seater, I discovered a couple of my own rifles with ignition timing problems. Having the rifle setup flawlessly is a big deal. The relationship between the trigger/sear and cocking piece determines a lot... as does any firing pin/cocking piece/cocking piece shroud drag.

So, low SD's are indeed achievable. It's just more work and money than a lot of guys want to put in.
 
The further you shoot the more it matters.
My favorite AR loads have tragic SD but shoot great at their expected distances.

My two bolt guns can get 10 or better easily.
Usually I’m in the 4-7 range with ten shots.
That’s proven good enough for me at the moment.
I’m a pretty lazy reloader.
No sorting brass or bullets and I’m using a cheaper electronic powder measure.

I do prep primer pockets on my cheap Winchester brass and lightly neck turn.
 
Isn't this what drove AB to develop the Enabler cartridges? They couldn't keep their SD numbers tight enough for long strings of firings for ELR IIRC. Obviously its only as important as it necessary to accomplish your goals for the shooting you are doing. If you were shooting KO2M you would be taking it to the Nth degree on every component in each reload and condition of your barrel. Everybody loves tiny groups but I'm not aware of anybody that loves doing all the reloading steps if the return on investment isn't seen in the results.

To answer your original question R16 seems to be a good alternative to other powders but can have temperature sensitivity issues. I've not experienced it myself but I don't compete much nor do I shoot in weather in the 90s
 
Isn't this what drove AB to develop the Enabler cartridges? They couldn't keep their SD numbers tight enough for long strings of firings for ELR IIRC.

To answer your original question R16 seems to be a good alternative to other powders but can have temperature sensitivity issues. I've not experienced it myself but I don't compete much nor do I shoot in weather in the 90s
Competition is a different animal than recreational LR plinking.
Those guys have their name, equipment and possibly sponsors on the line.
It becomes a job.
They better have their shit together.

I’m just a shmuck out in the woods banging steel.
While I certainly am not going to be running a load with a 25 SD
I’m also certainly not gonna get all OCD for that extreme low SD’s.
I’ll take them but it will be luck not super science reloading.

This is a past time for me, not a job.



My findings have shown that R16 is pretty amazing in the temp sensitivity department.
My 260 load with it is showing a speed difference from 20 to 85 degrees that you can basically just ignore it.

You thinking of R17 possibly?
 
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Competition is a different animal than recreational LR plinking.
Those guys have their name, equipment and possibly sponsors on the line.
It becomes a job.
They better have their shit together.

I’m just a shmuck out in the woods banging steel.
While I certainly am not going to be running a load with a 25 SD
I’m also certainly not gonna get all OCD for that extreme low SD’s.
I’ll take them but it will be luck not super science reloading.

This is a past time for me, not a job.



My findings have shown that R16 is pretty amazing in the temp sensitivity department.
My 260 load with it is showing a speed difference from 20 to 85 degrees that you can basically just ignore it.

You thinking of R17 possibly?

No, R16 has taken a bad rap compared to the Hodgon powders here in the 6.5 threads. As I stated above, I've not experienced the issue myself but have read it repeatedly. I'm completely with you on the diminishing returns of chasing the numbers, its a rabbit hole that just keep you from more trigger time.
 
The number gets larger, the bigger the sample size. Lots of people don't run enough numbers to truly discover what the actual SD is. So what is statistically significant? 10 shots? 20? 100?

ES will definitively get larger with larger sample size, but SD will not necessarily do so. SD will level out at its actual value the larger the sample size. Small sample sizes could just as easily yield much higher as much lower SDs than a larger sample size.
 
If you anneal every round and weight every charge to a .01 weight, you should be around 5-8 realistically Dont anneal 8-15 round to the .1 and dont anneal 15-40
 
Under 15fps for 20 shots. 20 shots is the number that, while it doesn't tell you everything, is typically a large enough sample size to show you a fairly clear picture of what you've got. Group size, ES, SD, mean point of impact, etc...

FWIW, Prebanpaul, in two 6.5 Creedmoor barrels I've tested recently for 50 shots per sample size, I saw maybe 1-2fps difference in SD between weighed to +/- .02gr (to the kernel) and thrown charges +/- 0.4gr. 10 and 13 weighed vs. 12 and 14 thrown respectively. Virgin cases, RL-16, 140 ELDM, Fed210M.
 
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20 shots is the number that, while it doesn't tell you everything, is typically a large enough sample size to show you a fairly clear picture of what you've got. Group size, ES, SD, mean point of impact, etc...

Standard error is a function of the square root of the sample size. So, taking the SD of 4 shots is roughly 2.25 times more the standard error than the SD of 20 shots. To get that same gain from 20, you'd need to go up to about 100. So, you get diminishing returns going for higher accuracy of SD.

As Ledzep says, 20 tells you enough. 20 is a reasonable number to shoot to validate the SD of a load. 100 is overboard.
 
In all of the 30-50 shot samples I've tested, all it's shown me is that for CERTAIN you can't trust single strings of 5, 10, or even 15 shots. If you plot the average, SD, mean point of impact, etc... as a function of how many shots fired, you get very erratic results within the first several shots. Sometimes they're exactly on the large sample size average and maintain it throughout, but most don't.
 
Standard error is a function of the square root of the sample size. So, taking the SD of 4 shots is roughly 2.25 times more the standard error than the SD of 20 shots. To get that same gain from 20, you'd need to go up to about 100. So, you get diminishing returns going for higher accuracy of SD.

As Ledzep says, 20 tells you enough. 20 is a reasonable number to shoot to validate the SD of a load. 100 is overboard.
I also use 20, but what I said stands. You shoot more, and you'll get more outliers that will widen the spread. The more data you have, the more accurate the answer. Its simple statistical probability.
 
I also use 20, but what I said stands. You shoot more, and you'll get more outliers that will widen the spread. The more data you have, the more accurate the answer. Its simple statistical probability.

Yes, more data is better, but standard deviation definitively does not automatically go up with sample size, it goes toward the mean. Extreme spread will go up.
 
Most people failed statistics and probability. ES is pretty much meaningless. No matter how many shots you fire, you are using two data points. ES can be used to reject a load, but that's all. SD is a better prediction of consistency, but it requires enough data. A 20 shot string that produces an SD of 10 has a 90% confidence level of being between 7,5 and 13.3 true deviation. A 5 shot string would predict between 5 and 20 for the same SD of 10.

Also bear in mind there is some degree of chronograph error, which is mostly unknown.

Bottom line, anyone who says they have an SD of < 5 probably has no idea what they are talking about. If my Labradar can show an SD of 10 for a 20 shot string I'm pretty happy with the results, not much reason to tweak anything any further as far as velocity goes.
 
Most people failed statistics and probability.

Most people have never taken a class,

Bottom line, anyone who says they have an SD of < 5 probably has no idea what they are talking about.

you should probably say “most people who say...”

I get mid-4s to 5 on my 6 BRA. I usually keep the LabRadar running during most of my shots on any given day, and this holds up over many 30+ shot series.

My 300 is more like 6-7. Just tried it with new ADG brass and got high 6s over like 20 shots with a load that wasn’t quite tuned.
 
Standard deviation is the square root of: the sum of the squares of the differences of each data point from the mean, divided by n-1. It is NOT the standard error.

As an example, say we run 20 shots and each shot is for the sake of argument 5 fps away from the mean on either side. So your mean is 3050 and half the shots are 3045 and the other half of the shots are 3055. Because of how I've set up the example, the difference from the data point and the mean is 5 and -5 in each case. Those both square to 25. Since there are 20 of those squares, the sum of them is 20x25 or 500. Divide that by n-1 or 19=26.32. Take the square root of that, and get 5.12 is the standard deviation.

supposing we instead ran 100 shots. We now have 100 of those squares (25), so the sum of squares is 2500. Divided by n-1 (99) is 25.25 and the square root of that is 5.02

Result: your standard deviation shrinks by diddly squat as you increase your sample size from 20 to 100.

But let's see the 5 shot string. Sum of squares will now be 5x25=125. divided by n-1 (4) 125/4=31.25. Sqrt of 31.25 is 5.59. Also VERY close to the 5.12 you got with a 20 shot string.

So, if the sample size matters so little, for the calculation of standard deviation, what's going on?

Selective sampling is what's going on. Guys are posting pics of of very small SDs that they get every now and a blue moon. When they get an SD of 1 or 2 with a 5 shot string, it is a statistical outlier, which is not uncommon with small sample sizes.

If you forced them to report the SD on all of their shots, it would be much larger, probably something like 5-10 if experience is any guide.

There is nothing wrong with the stats or the SD - nothing magical going on here with the maths. The issue is selective data recording and reporting. This is the analog of publication bias in the biomedical literature. Lots of stuff with P=0.04 published, but little with P=0.06 - the latter go in the file drawer or the circular file.

Your 20 shot string is just less likely to involve selective sampling, that's all.

So, here is my challenge: Somebody use your Labradar or your Magnetospeed, DO NOT DELETE ANY SHOTS, and show us the SD you get with a 20 shot string. Very few are going to have less than SD 5 is my wager. And I'm willing to wager money, up front if anybody wants to take me up on it.
 
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If you forced them to report the SD on all of their shots, it would be much larger, probably something like 5-10 if experience is any guide.

So, here is my challenge: Somebody use your Labradar or your Magnetospeed, DO NOT DELETE ANY SHOTS, and show us the SD you get with a 20 shot string. Very few are going to have less than SD 5 is my wager. And I'm willing to wager money, up front if anybody wants to take me up on it.

i started challenging some buddies to this months ago...not for actual money, just for data...in general

all top of the line reloading gear/components/etc...SDs usually in the 5-8 range over multiple trips and strings

step the reloading gear down, and drop the brass quality...it goes to 8-12...step it down again, etc

when i wasnt there to witness it, everything was usually magical....but when ive been there, everything seems to change a bit? lol
 
^^^This phenomenon pervades all of shooting in terms of error control. The name of the game is obviously to reduce variability and eliminate unknowns. group size, velocity, SD, bullets, the gamut.

The problem of selective reporting affects all of these things, and, when you start out, you can think that you suck pretty bad, haven't found the "magic". It affects even your own memory - you say you have a 1/4MOA gun from that one group you convinced yourself represented the final "dialing in" of the system. Next couple times it's barely 1/2 MOA. What happened? Selective memory.

It's important for the new guys to know this, so they can have realistic expectations for themselves.

I recall one of the AB guys bragging on here a few years back after they connected the long target and won. Man, he was convinced he'd found the perfect system. Gonna just bang that 2 miler every time from now on. The next year nobody (him included) even qualified for the 2 miler.
 
The sad reality for those with the questions; if you want the answer, heavy firing schedule of high round count (purposeful rounds) is the only way you'll get an answer. Trustworthy sources on the net are extremely hard to come by. Too much emphasis on being trendy and seeming "cool" to let the data be shown for what it is.

Real experience takes a long time to get, and most simply don't have the patience to wade through it. They want to skip the time and effort so they can be "in." Any data that doesn't allow that perception to prevail, is obviously "a flyer" and is deleted. So then the guys that truly do put in the effort to achieve excellent results, may as well not post, because no one will believe them anyway. The guys with the $300 "reloading-kit-in-a-box" are in the majority, while most of the guys with $15,000 in equipment and measuring tooling simply aren't heard from. If they attempt to speak, they get drowned to death in "you don't need that" comments.

Meanwhile anyone new to the scene gets fooled into thinking he can get there with low end gear and no brass work, and is frustrated when that turns out to be untrue.
 
I’ve seen a number of people on these forums say that SD goes up with sample size. There is a fair amount of confusion around exactly what SD is and is not.
No, we say those small sample 1-3 SDs go up.

Aka, we are a skeptical bunch who dont easily believe the BSing on the internet lol
 
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I just want somebody to prove it to me before I go down the rabbit hole of trying to figure the secret out.

I shoot a lot of PRS/NRL and the secret is that it doesn't matter. I only bother to test 5 shot strings every now and then to confirm, if it's below 6-7 SD then I don't worry about it.

I'll proof my load at distance to check if it holds vertical dispersion. If so, rock on and go shoot. I can't say I've seen many targets at 1000 yards+ that were less than 0.2-0.3 mils tall.
 
The trick to one-hole groups is to fire lots of shots. Eventually you get one big hole.
It works... Here's 100rnds fired, 20 shots in each group. I was demonstrating clean barrel to dirty barrel accuracy and POI shift. Started out with 218rnds on the barrel. One hole. ... and even some bonus one holes.

5T2TycRh.jpg
 
This thread is making my head hurt and bringing back memories of my undergrad and grad school days where I was tortured with 24 credit hours of statistics. Now I will have to go sleep with images of matrix algebra and non-linear regression analysis floating around in my head.
 
Same phenomenon with group size. If we just consider 3 or even 5 shot groups at 100 yards, then there are lots of 1/2 moa guns out there.

Shoot those same guns at 200 for 20 shots, and things are a bit different.
 
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It works... Here's 100rnds fired, 20 shots in each group. I was demonstrating clean barrel to dirty barrel accuracy and POI shift. Started out with 218rnds on the barrel. One hole. ... and even some bonus one holes.

5T2TycRh.jpg
Am I correct in deducing from your picture that your zero shifted up as it got dirty?

Interesting test, thanks for posting this. It definitely caused me to raise an eyebrow, as I never really considered a lateral shift as a barrel got dirty. Always thought it would be more dispersion rather than an actual shift...
 
Am I correct in deducing from your picture that your zero shifted up as it got dirty?

Interesting test, thanks for posting this. It definitely caused me to raise an eyebrow, as I never really considered a lateral shift as a barrel got dirty. Always thought it would be more dispersion rather than an actual shift...
Yup, Groups opened up and POI shifted upward.

That barrel won't do that inside of 200rnds after cleaning... but it does it from 200 on like clockwork, and groups just keep getting bigger. Its a solid 1/4moa rifle for those first 200rnds. At least 1/2. ;)
 
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But to the OP and Frank's point;

For PRS/NRL type matches where typically ~ 80-85% of the shots are 800-ish yds and in--SD below 10 is certainly adequate and even low teens is probably just fine?

Concur/non-concur?

ZY
 
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This thread is making my head hurt and bringing back memories of my undergrad and grad school days where I was tortured with 24 credit hours of statistics. Now I will have to go sleep with images of matrix algebra and non-linear regression analysis floating around in my head.
I have the same problem when I watch twerk videos.
 
I have never enjoyed discussions that involve the "good enough for (insert specific here)." My enjoyment of the sport comes from the ever expanding knowledge and continued pushing of the boundary.

I'll not argue the merits of the thought process, as it pertains to many people. In that a great many people would no doubt benefit to setting boundaries for themselves that include reasons to not continue advancing.

However, I do believe that most of the "good enough" thought process can stem from the comfort gained by alleviating the pressure to buy new equipment and do more. Complacency can bring a great deal of comfort to some. If everyone had unlimited budgets, this "good enough" mentality would be dead as disco. Yet with budget being a primary concern, they ignore the reality that better gear can bring better results, and they spend huge effort to ensure others share that mindset. There is comfort in numbers.

There are others which do not fall into that category, and simply have a specific goal and want to spend the minimum to achieve it. Nothing wrong with that. So long as they aren't fooled into thinking there are no other plateau's to climb.

So how do you sequence the 20 shot groups? 5 shot groups with barrel cool time in-between for a few minutes?
That would depend entirely on what you're looking to test. If you're trying to learn if the rifle can properly place shots for long strings of fire, as in a timed unlimited round count stage... then you'd be looking to shoot back to back until the rounds start deviating.

Though if you were trying to discover something else, such as fouled condition... then you'd want to run no more than 10 (depending on cartridge) and give adequate cooling time between strings. If the rifle has proven to hang tight for long strings, then the number can vary depending on known qualities of your particular setup.
 
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I have never enjoyed discussions that involve the "good enough for (insert specific here)." My enjoyment of the sport comes from the ever expanding knowledge and continued pushing of the boundary.

I might rephrase the question of "good enough" for PRS into one of where you allocate your effort, rather than of complacency. If I have limited time, then my efforts are best put into the areas where it will produce the best results.

Is my positional shooting good enough? No
Are my fundamentals good enough? No
Is my speed/efficiency getting on the gun and on target good enough? No

Is my SD good enough? Yes... considering that I could better spend my time working on the above. :)
 
My 6bra put an SD of 4.7 over 15 shots with just a random fireform load the other day. No special prep or effort. That number could have been a 7.4 and it would make little or no difference. I cant remember the last time I missed a target from a rooftop or barrel and thought to myself "Damn, it was probably my SD." Maybe if I was shooting BR/Prone/ELR matches I might chase the numbers, but other than that as others have said, under 10 is good enough for the type of shooting I do. Most of the time I hover between 5-7. Seeing a low number still makes me smile, but I dont think it makes me shoot much better.
 
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I'd say 4.7 over 15 shots is pretty darned good. I'll be shocked if many can beat that, unless we had a contest with 100 participants. Then I'd expect a couple or even several to beat it - though not the same ones if we held the contest multiple times. There would be regression to the mean.

What the 4.7 does tell you is that 95% of your velocities will be within +/- 2*4.7 of your mean velocity. That is the so-called 95% confidence interval from that sampling distribution defined by that mean and SD. In this case it is 9.4 fps on either side of the mean.

Note that Extreme Spread (ES) is not a statistical parameter - it is defined empirically by the highest and lowest velocity in your sample. However, multiplying the SD by 4 will given you an approximation of the ES insomuch as it will tell you that, under assumptions normally distributed data, 95% or so of your shots will be expected to fall within that range of 4SD.

From this we can now see that anybody who claims single digit extreme spreads bears the burden of proof. That means that their SD is on the order of 2.4 or less. A very unlikely prospect given the aforementioned discussions about selective data reporting and the inherent and uncontrollable variability in powders and the pressures they generate.

If anybody thinks they can do this, post a 20-shot sample with a ES in the single digits (<10 fps), come to Salt Lake and show me. If you do, I'll pay for your trip. If you don't, you pay for it. We'll have fun either way.

(ETA, we should wait till Wuhan Flu is gone before doing this.)
 
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IMO, single digit ES not necessarily impossible, but really outstanding especially if a consistent result! Sheldon's point about investing where big gains are to be had is spot on, for me. Cardio probably being #1 LOL.
 
My guess is that to get it you have to have numbered cases that are selected based on their repeated demonstrated consistency. And a consistent powder and way to measure it, eg, sartorious or FX whatever, and a consistent bullet that generates the same pressure each time. I'm interested to see how people who achieve reliably and consistently are able to do it.
 
I have tracked cases through several firings and there is no correlation in the testing that I've done that shows a particular case is better than any of the others.
 
I have tracked cases through several firings and there is no correlation in the testing that I've done that shows a particular case is better than any of the others.

same ^^

overall ES/SD numbers were similar, but the individual cases responsible was random over multiple tests, at least within my ability to measure/sort components
 
I'd say 4.7 over 15 shots is pretty darned good. I'll be shocked if many can beat that, unless we had a contest with 100 participants. Then I'd expect a couple or even several to beat it - though not the same ones if we held the contest multiple times. There would be regression to the mean.

What the 4.7 does tell you is that 95% of your velocities will be within +/- 2*4.7 of your mean velocity. That is the so-called 95% confidence interval from that sampling distribution defined by that mean and SD. In this case it is 9.4 fps on either side of the mean.

Note that Extreme Spread (ES) is not a statistical parameter - it is defined empirically by the highest and lowest velocity in your sample. However, multiplying the SD by 4 will given you an approximation of the ES insomuch as it will tell you that, under assumptions normally distributed data, 95% or so of your shots will be expected to fall within that range of 4SD.

From this we can now see that anybody who claims single digit extreme spreads bears the burden of proof. That means that their SD is on the order of 2.4 or less. A very unlikely prospect given the aforementioned discussions about selective data reporting and the inherent and uncontrollable variability in powders and the pressures they generate.

If anybody thinks they can do this, post a 20-shot sample with a ES in the single digits (<10 fps), come to Salt Lake and show me. If you do, I'll pay for your trip. If you don't, you pay for it. We'll have fun either way.

(ETA, we should wait till Wuhan Flu is gone before doing this.)

I don't see too many people going around claiming single digit ES. SD on the other hand, well it's not super hard to string 20 shots together that are going to run single digit SD if you work with enough forgiving cartridges and rifles. It's going to be a lot harder to come by on something like a 243win than it is a 6BRA.

So it would be a good idea to remember that single digit SD and the chance you're going to see it is not distributed across all cartridges equally. Some cases are going to simply be more stable than others. This is just based on my experience. Some combinations of components, in certain shapes, tend to produce significantly more predictable results.

Go look what cartridges are popular among the rail gun crowd. It certainly isn't ultra-mags. ;)
 
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So, here is my challenge: Somebody use your Labradar or your Magnetospeed, DO NOT DELETE ANY SHOTS, and show us the SD you get with a 20 shot string. Very few are going to have less than SD 5 is my wager. And I'm willing to wager money, up front if anybody wants to take me up on it.
At one point long ago with my 6.5 creedmoor I had stopped tinkering with reloading to shoot 90 rounds of the same charge weight. 1 round was not picked up on the labradar and the last 10 shot group I only took down the stats and not the individual numbers so I ended up with:
Total Sample (79 count)
Avg: 2812.9747
SD: 4.12
ES: 19

I also just ran some 5 shot groups with new Alpha Dasher brass over the magneetospeed and got SD's of 6.1 (I deleted the first shot which was 40 off the rest), 2.6, 4.6, 2.2, 2.8 and 2.8. There was nothing that special about my reloading technique here, dipped the necks in some imperial dry neck lube, ran them through 650 to get primed and put through a expander mandrel for 1 thou tension, deburred and chamfered. I did use a FX120i auto trickler but I have gotten SD's in the teens with an entris 641s with RL15 in my 308, and got single digit SD's with vitavori powder from a chargemaster. I feel like sometimes you get lucky and your rifle likes a particular combo of components and sometimes you get unlucky and need to change things. That 6.5 creedmoor was RL16 and had single digit SD's through load dev but with H4350 it only dipped down to single digit SD's between 42 and 43 grains.

Do note, I shoot 600 yards so I don't rly care about SD's. They just seemed to have worked out well with the 6.5 creedmoor and 6 Dasher with the first powder I used.

The 600 yard ladder seemed to indicate 4.6, 2.2, 2.8 was a good spot though it was 65 degrees in GA so I thought 2.2 or maybe between 4.6 and 2.2 to give room for warmer weather. I will load up 100 rounds of that and take a velocity reading with the magneeto for 20 shots and see if I make it below that 5 SD mark.
 
OK... with SD: 4.12 and ES: 19, apply the "secondofangle2 rule", (4.12 * 4) = 16.48, so your ES indicates >=1 shots performed outside the +/- 2nd sd, which covers 95% of the Normal distribution. But (4.12 * 6) = 24.72, so ES is well inside the +/- 3rd sd, which covers 99.7%. Not bad!
 
OK... with SD: 4.12 and ES: 19, apply the "secondofangle2 rule", (4.12 * 4) = 16.48, so your ES indicates >=1 shots performed outside the +/- 2nd sd, which covers 95% of the Normal distribution. But (4.12 * 6) = 24.72, so ES is well inside the +/- 3rd sd, which covers 99.7%. Not bad!
This is the data
2805, 2805, 2805, 2805, 2806, 2806, 2807, 2807, 2807, 2807, 2808, 2808, 2808, 2808, 2809, 2809, 2809, 2809, 2810, 2810, 2810, 2811, 2811, 2811, 2812, 2812, 2812, 2812, 2812, 2812, 2813, 2813, 2813, 2813, 2813, 2813, 2813, 2813, 2813, 2813, 2814, 2814, 2814, 2814, 2814, 2814, 2814, 2814, 2814, 2815, 2815, 2815, 2815, 2815, 2815, 2815, 2815, 2815, 2815, 2815, 2816, 2816, 2816, 2816, 2816, 2816, 2816, 2816, 2817, 2817, 2818, 2818, 2818, 2819, 2819, 2819, 2822, 2822, 2824