Accuracy: Spending Time on Things That Matter

[bullseye308]

It's hard to argue with a false pretense. Nobody spends the extra $3,000 fighting for that kind of accuracy they do it for other reasons

Think Gucci, Aston Martin, Rolex, names like that. I can easily get by for my needs with Haynes, Ford, and Timex, but some just gots to have the name, and the prestige that goes with it. Same with my guns, Savage, Ruger, and Glock do everything I need, but some could never allow themselves to sink that low. I have been able to hold my own against those guys with the nicer brands most often, and they do look nice weeping when it’s over and they have to pay up for paying for the name while I’m paying to use my “crappy” equipment to its fullest potential.

Like mentioned above, put forth the time, money, and effort where you will most benefit from it and don’t worry about the minor details until they become relevant and all you have to work with.

 

[Varminterror]

Square root (25^2 + 10^2) = 26.9 FPS. That is a small change, very hard to detect.

27fps is an extra 8” of drop at 1000 yards for a 308win. An extra 6” of drop in a 6 Dasher. Pretty easy to notice when round groups at 100-300 pick up an extra 1/2-3/4moa of unresolvable vertical dispersion at longer range.

 

[Bill M.]

I guess I disagree with, or at least do not understand, the OP's initial argument anyway.

It certainly seems to me that if I am shooting a 2 MOA rifle consistently at 8" groups and I switch to a 1/4 MOA rifle my groups will get smaller. Probably by 1 3/4 inches. I would like to see a statistical calculation that shows why that is not true.

None of the discussion about .1 grain charge differences seems to address the original supposition about relative accuracy between shooting a 2 MOA rifle versus a .25 MOA rifle as far as I can tell.

 

[lordpaxman]

The ONLY way to make big improvements in variation is to find and control the major sources.

That may be but first you need to identify them. If it was deterministic there’d be a thread pinned to the top of this forum.

I can easily get by for my needs with Haynes, Ford, and Timex, but some just gots to have the name, and the prestige that goes with it.

We all have different criteria for assessing the value proposition. I appreciate living in a free country and being able to choose.

 

[Bfh_auto]

This post might be a little bit theoretical, but it leads to a very important conclusion.

Variation does not simply add. If you are shooting 8" groups offhand at 100 yards with a 2 MOA rifle, switching to a 1/4 MOA rifle will NOT shrink your groups by 1 3/4". In fact, the improvement will be barely detectable.

Here is a simple example, using powder charge weights:

You have been making 223 reloads that have a 25 FPS standard deviation in MV. Part of your process is a special scale that allows charge accuracy down to the microgram. It works, but it is a very tedious process. You are thinking of switching to a powder measure. The powder measure you are considering dumps loads with a standard deviation of .1 grain. For your particular load, a grain of powder chamges MV about 100 FPS, so .1 grain is 10 FPS. How much will this change affect the MV of your reloads?

Standard deviations add by the square root of the sum of the squares, so the standard deviation of the new loads will be:

Square root (25^2 + 10^2) = 26.9 FPS. That is a small change, very hard to detect.

Because of the peculiar way that variation adds, you will NEVER make a big improvement in variation by fiddling with the less important variables. The ONLY way to make big improvements in variation is to find and control the major sources.

In theory your ideas hold up.
In reality powder charges don't always increase velocity in a linear fashion.
Also small changes can break your accuracy node.
I do agree you have to fix the big issue before the small ones.
But the human in me makes it easy to blame my missed shot on 3 moa ammo where 1/2 to 3/4 moa ammo tells me I need to fix my inconsistencies.

 

[Walkalong]

It certainly seems to me that if I am shooting a 2 MOA rifle consistently at 8" groups and I switch to a 1/4 MOA rifle my groups will get smaller.

Enough to matter? I think that is the jist of it.

 

[Bill M.]

"Enough to matter"? The initial proposition was that the groups would not shrink by 1 3/4 inches. I still think they will.

 

[GeoDudeFlorida]

Enough to matter? I think that is the jist of it.

Yup. And that's the gist of it. Who, how, what, where and why always matter.

If I'm shooting whitetails over clear cut, my only shot might be around 300 yards (in N. Florida). Being me, I wouldn't take the shot if my best accuracy with the rifle/load combo I brung is an 8" circle at 100 yards distance. In fact, I would not bring that rifle or ammo to hunt over clear cut knowing my nearest shot might be close to 300 yards. I think I might sell that rifle unless it's a really, really good close-range hog stopper, like a Marlin 1895 .444Marlin with big-ring peep sights and a slicked-up action, ior just give up hunting over clear cut slash-pine fields. That Marlin's a good 100 yard rifle but not so good for past 150 yards and I'm not sure my best 350gr. WFN cast load will do for a whitetail at that 300 yard range. I never tried it and don't intend to. I have better rifle/load combos for them situations.

I can't always bring a handy fence post with me into the areas I hunt so off-hand or a walking/shooting stick are really my only choices. Leaning up against a slash-pine might be worse than off-hand. Not exactly ideal for 1/4MOA shooting. Does switching from a 1950's Remington 721 with an older Redfield 2.5-12x scope which I know from past experience is fully capable of 1 minute, even kneeling or with a stick - to something I never heard of in an off-the-wall caliber with a scope that requires a manual and Bluetooth to operate and costs $3 grand that some magazine writer says is a 1/4MOA rifle - is that really going to get me that whitetail at 300 yards? Only if I practice and find a way to tote a handy fence post with me into the clear cut. Not gonna happen. My old Remington and Redfield loaded with 150gr. SSP and 48gr. of IMR 4064 will get'r done out to close to that 300 yard mark - been doing it for years - but don't ask me to put up a dime-size target at a thousand. Won't even bother.

All the best to everyone and remember, you do you and let me do me. We're all individuals and just because someone doesn't do what you do don't mean they're wrong or you're right.

 

[JFrank]

Must be a slow day to even respond but again, this is internet mis-information pure and simple example of a small thing making a huge difference is quality brass prep that seems insignificant but is DEFINITELY visible on paper.

 

[Varminterror]

It certainly seems to me that if I am shooting a 2 MOA rifle consistently at 8" groups and I switch to a 1/4 MOA rifle my groups will get smaller. Probably by 1 3/4 inches.

I can confirm, imperially, this doesn’t happen as you’re expecting.

However, the original premise is faulty. Stating conclusions based on an imagined 8moa group from a 2moa rifle isn’t apt... what variable has changed to make a 2moa rifle deliver an 8moa group? If a rifle’s maximal raw short range precision potential is 2moa, something significant has changed to cause it to shoot 4x larger than its potential. That variable might be poorly suited ammo change, might be a loose optic mount, might be a shooter standing freehand instead of prone. In many cases, a shooter may not see ANY change to a positional group size by changing ammunition or rifle to improve raw potential. In other cases, the change IS proportionate.

It’s an absolute false premise to promote that a shooter can simply replace a 2moa rifle with a 1/4moa rifle - as the raw potential is far more dependent upon the ammunition than the rifle.

 

[edwardware]

I would like to see a statistical calculation that shows why that is not true.

The OP provided a conceptual explanation, here:

Standard deviations add by the square root of the sum of the squares. . .

and he is exactly correct.

Normal distribution statistics are frequently surprising if you aren't used to using them, but @denton has applied them correctly in this case.

 

[Varminterror]

Must be a slow day to even respond but again, this is internet mis-information pure and simple example of a small thing making a huge difference is quality brass prep that seems insignificant but is DEFINITELY visible on paper.
View attachment 1019125

I don’t believe you’ve inferred the correct implication in that statement.

You and I have spoken rather commonly here about big knobs and little knobs in reloading practices - in terms of proportional influence.

Small changes can have huge influences, those are big knobs. I don’t read any implication in the quoted statement that claims energy input or gross marginal variability is a proportionate measure of net influence. But the statement is confirming something both you and I have often stated ourselves - invest your energy where you’ll see the most results first.

 

[Varminterror]

The OP provided a conceptual explanation, here:

and he is exactly correct.

Normal distribution statistics are frequently surprising if you aren't used to using them, but @denton has applied them correctly in this case.

He’s ONLY correct if and only if the variability exhibits a normal distribution with proportionate influence in net result. Empirically, it has been proven time and time again many of the variables influencing ballistic precision do not follow normal distribution and exhibit variability not proportionate to the net result variability.

 

[JFrank]

@Varminterror
Brother you are much better than I am at putting thoughts on paper.
Well said.
J - out and dark

 

[barnfrog]

But the human in me makes it easy to blame my missed shot on 3 moa ammo where 1/2 to 3/4 moa ammo tells me I need to fix my inconsistencies.

This is my way of thinking exactly.

 

[denton]

OK, lots of questions....

I would like to see a statistical calculation that shows why that is not true.

Good question. Let me answer it this way. It's kind of a backwards example, but maybe it will do: All the random variables that add up to group size add by the square root of the sum of the squares. So assume that you are offhand shooting a perfect rifle, and getting groups where the standard deviation of shots from the center of the group is 2". The variation is 100% from your marksmanship.

About 95% of your shots will fall within plus and minus 2 standard deviations, so plus 2 standard deviations is 4", and minus 2 standard deviations is another 4", so that's an 8" circle that will contain 95% of your shots. So, for practical purposes, that's our 8" groups.

Now assume your technique remains constant, and you switch to that rifle that shoots 2" groups off a bench. The random error due to the rifle has a standard deviation of 1/2". That is, plus 2 standard deviations is 1", and minus 2 standard deviations is another 1", for a total of 2" where 95% of shots will land.

How much does that degrade our 8" groups from a perfect rifle?

square root (2^2 + .5^2) = 2.059". 2.059" x 4 = 8.23"

Using our plus and minus 2 standard deviation rule, that says that our groups will grow from 8" to 8.23" by switching to the inferior rifle.

Most people have a hard time getting their heads around the concept, but it works that way because the probability of all the contributing variables happening in the same direction at the same time is small. Sometimes the errors are in opposite directions, and partially cancel, and sometimes they are in the same direction and partially add.

As other posters have pointed out, in this made up case, by far the largest source of variation is the shooter. Working on charge weight, neck tension, etc. isn't going to improve the results. It's practice, practice, practice. I deliberately chose that example because it illustrates the futility of working on the smaller sources of variation. An example for a bench rest situation would be a different situation, because that would eliminate the single largest source of variation.

He’s ONLY correct if and only if the variability exhibits a normal distribution

The square root of the sum of the squares works for all real world distributions, not just the normal distribution.

In reality powder charges don't always increase velocity in a linear fashion.

Actually, over the range of normal loads, MV is very linear with respect to charge weight. I find this puzzling, because intuitively I would expect kinetic energy to be linear with load. But my intuition is wrong on that one. I had a lovely data set from Ken Oehler, and when I ran the math, my mouth dropped open. The linear correlation was tighter than any relationship I had found in the reloading world.

27fps is an extra 8” of drop at 1000 yards for a 308win.

Not relevant. What was presented was a change from a 25 FPS standard deviation to a 26.9 FPS standard deviation, not a 26.9 FPS shift in the mean. That's a different proposition entirely. If you follow through the example I worked out for Bill M, you can find out just how egg shaped your groups become for a given rifle, for given MV standard deviation. It's not much, even for very fine rifles.

 

[Bfh_auto]

OK, lots of questions....



Good question. Let me answer it this way. It's kind of a backwards example, but maybe it will do: All the random variables that add up to group size add by the square root of the sum of the squares. So assume that you are offhand shooting a perfect rifle, and getting groups where the standard deviation of shots from the center of the group is 2". The variation is 100% from your marksmanship.

About 95% of your shots will fall within plus and minus 2 standard deviations, so plus 2 standard deviations is 4", and minus 2 standard deviations is another 4", so that's an 8" circle that will contain 95% of your shots. So, for practical purposes, that's our 8" groups.

Now assume your technique remains constant, and you switch to that rifle that shoots 2" groups off a bench. The random error due to the rifle has a standard deviation of 1/2". That is, plus 2 standard deviations is 1", and minus 2 standard deviations is another 1", for a total of 2" where 95% of shots will land.

How much does that degrade our 8" groups from a perfect rifle?

square root (2^2 + .5^2) = 2.059". 2.059" x 4 = 8.23"

Using our plus and minus 2 standard deviation rule, that says that our groups will grow from 8" to 8.23" by switching to the inferior rifle.

Most people have a hard time getting their heads around the concept, but it works that way because the probability of all the contributing variables happening in the same direction at the same time is small. Sometimes the errors are in opposite directions, and partially cancel, and sometimes they are in the same direction and partially add.

As other posters have pointed out, in this made up case, by far the largest source of variation is the shooter. Working on charge weight, neck tension, etc. isn't going to improve the results. It's practice, practice, practice. I deliberately chose that example because it illustrates the futility of working on the smaller sources of variation. An example for a bench rest situation would be a different situation, because that would eliminate the single largest source of variation.



The square root of the sum of the squares works for all real world distributions, not just the normal distribution.



Actually, over the range of normal loads, MV is very linear with respect to charge weight. I find this puzzling, because intuitively I would expect kinetic energy to be linear with load. But my intuition is wrong on that one. I had a lovely data set from Ken Oehler, and when I ran the math, my mouth dropped open. The linear correlation was tighter than any relationship I had found in the reloading world.



Not relevant. What was presented was a change from a 25 FPS standard deviation to a 26.9 FPS standard deviation, not a 26.9 FPS shift in the mean. That's a different proposition entirely. If you follow through the example I worked out for Bill M, you can find out just how egg shaped your groups become for a given rifle, for given MV standard deviation. It's not much, even for very fine rifles.

I haven't found that to be the case with over bore cartridges. There seems to be a general progression with slight plateaus where I find my accuracy near.
I haven't played with chronographs and smaller cartridges very much so it could be that way.

 

[Varminterror]

Not relevant. What was presented was a change from a 25 FPS standard deviation to a 26.9 FPS standard deviation, not a 26.9 FPS shift in the mean.

A group does not need a mean shift to exhibit vertical dispersion. This is an erroneous statement a non-shooter statistician would make, and I think more of you than that.

When I shoot a load with high SD, my groups are taller than they are with a smaller SD. Some of the sample set are faster than the others, and they spread around the mean velocity up or down relatively at range.

I share this example frequently here of two loads fired at 875 yards - velocity stability matters.

The target at our left shows 3 shots low, then I added .2mils to correct the waterline, then 15 shots for group. You can see my wind estimation error in the horizontal spread - I held one wind speed and sent a fast group, 15 in under a minute, but it’s relatively round at 875 yards. 24fps ES.

The target at right is ammunition with 78fps ES (corresponding relatively closely to your proposed 27fps SD). A hair more wind, but significantly more vertical dispersion. Why? Because some rounds were traveling considerably faster than the mean, some considerably slower, such they hit higher or lower. The group is still a group, and my mean velocity still made impacts, but given a round/square target, many of these would have missed, whereas the other load on the other target would not have.



So as I stated above: 27fps SD WILL present a larger group at 1000 than a single digit SD. The calculated shifts I shared above are a RANGE of the data - ES - whereas your claim was for SD... so my prediction did you the favor of knocking off ~3/4 of the potential. 27fps SD would correspond to a potential Range/ES of ~104-162fps... so a 308win group could experience individual POI influences varying by more than 3 feet at 1000yrds.


I can tell you, directly, that is not a “small change, very hard to detect.”

 

[edwardware]

He’s ONLY correct if and only if the variability exhibits a normal distribution with proportionate influence. . .

While there are a few cases of bi-modal or random distributions, they are rare. I'd be interested in what influences you wouldn't consider normally distributed.

 

[denton]

A group does not need a mean shift to exhibit vertical dispersion. This is an erroneous statement a non-shooter statistician would make, and I think more of you than that.

When I shoot a load with high SD, my groups are taller than they are with a smaller SD. Some of the sample set are faster than the others, and they spread around the mean velocity up or down relatively at range.

I share this example frequently here of two loads fired at 875 yards - velocity stability matters.

The target at our left shows 3 shots low, then I added .2mils to correct the waterline, then 15 shots for group. You can see my wind estimation error in the horizontal spread - I held one wind speed and sent a fast group, 15 in under a minute, but it’s relatively round at 875 yards. 24fps ES.

The target at right is ammunition with 78fps ES (corresponding relatively closely to your proposed 27fps SD). A hair more wind, but significantly more vertical dispersion. Why? Because some rounds were traveling considerably faster than the mean, some considerably slower, such they hit higher or lower. The group is still a group, and my mean velocity still made impacts, but given a round/square target, many of these would have missed, whereas the other load on the other target would not have.

View attachment 1019163

So as I stated above: 27fps SD WILL present a larger group at 1000 than a single digit SD. The calculated shifts I shared above are a RANGE of the data - ES - whereas your claim was for SD... so my prediction did you the favor of knocking off ~3/4 of the potential. 27fps SD would correspond to a potential Range/ES of ~104-162fps... so a 308win group could experience individual POI influences varying by more than 3 feet at 1000yrds.


I can tell you, directly, that is not a “small change, very hard to detect.”

I wish you had been able to come to my Six Sigma Black Belt class. I think we would have had a lot of fun.

Your counter example still misses the point. The question is whether adding a 10 FPS standard deviation to an existing 25 FPS standard deviation process matters much. It does not.

A 26.9 FPS standard deviation in MV generally matters if you are shooting a 1/2 MOA or better rifle at 500 yards or more. The difference between a 25 FPS SD and a 26.9 FPS SD on the other hand is awfully hard to detect. And it is the difference, not the magnitude, that is important here.

 

[Varminterror]

The square root of the sum of the squares works for all real world distributions

One “real world distribution” I commonly experience demonstrably does not follow a normal distribution, and such doesn’t follow common statistical rules.

When I throw one bad trigger pull in a group, that group does not feel a square of the squares prediction.

When an optic mount is loose, we don’t see normal variability. We don’t benefit by square of square analyses. When we push a flinch in recoil anticipation, it’s commonly unidirectional. When our rest isn’t stable, often it’s unidirectional...

It is fair to state that “compounding errors” due to individual contributors aren’t compounding, and aren’t even additive, but the square of squares rule really only fits when we’re talking about variables which largely follow normal distributions within the context of ballistic precision.

 

[Varminterror]

A 26.9 FPS standard deviation in MV generally matters if you are shooting a 1/2 MOA or better rifle at 500 yards or more.

Read the data I shared - this statement is absolutely false. A 26.9fps deviation would absolutely prevent anyone from shooting 1/2moa at long range, and would be absolutely apparent to any shooter, not just those who can otherwise hold 1/2moa.

Directly - 26.9fps SD would mean much, much more than 1/2moa at 500yrds or more. Given a normal distribution expecting ~95% of shots to exhibit +/-2SD, a 10 shot group could expect ~100fps Range, meaning 33” of induced vertical influence... over 3moa of influence... whether my short range groups are 1/2moa or not really won’t matter much when my shots string out from a foot below to a foot above my 1 MOA target at 1000...

When one variable sensitivity is an order of magnitude greater influence, it’s pretty clear which needs attention.

 

[sugarmaker]

The idea that random errors (Gaussian distribution) and systematic errors (like a constant velocity difference between loads or a steady state shift in wind speed) are added differently can be non-intuitive. A Gaussian root sum of squares rule of thumb is anything below 1/3 of the dominant error can be ignored with little effect on overall dispersion. Less true with a systematic error which shifts the mean position. Sometimes inconsistency in holding a weapon can look systematic for a single session but it’s really gaussian when viewed over a larger number of sessions. I shoot high power a little and other field positions, some bullseye, so most of the error is me for things I do. Shooting F or Bench etc. the game is different and more focus on little stuff is warranted at high levels.

 

[denton]

The idea that random errors (Gaussian distribution) and systematic errors (like a constant velocity difference between loads or a steady state shift in wind speed) are added differently can be non-intuitive. A Gaussian root sum of squares rule of thumb is anything below 1/3 of the dominant error can be ignored with little effect on overall dispersion. Less true with a systematic error which shifts the mean position. Sometimes inconsistency in holding a weapon can look systematic for a single session but it’s really gaussian when viewed over a larger number of sessions. I shoot high power a little and other field positions, some bullseye, so most of the error is me for things I do. Shooting F or Bench etc. the game is different and more focus on little stuff is warranted at high levels.

anything below 1/3 of the dominant error can be ignored with little effect on overall dispersion
Holy crap! Someone who understands process variation! Thank you.

VT: I think I was reasonably careful in specifying random error, rather than systemic variation, but maybe I wasn't always perfectly clear. You are correct that systemic errors like shooter flinch or a barrel rub do not follow the rules of random error. The point sugarmaker made so much more eloquently than I did is exactly on target.

Again, the point is NOT the effect of a 26.9 FPS SD on long range shooting. The point is that if one source of variation is much larger than the others in the mix, just about all you will see is the effect of that one large source of variation. Showing an example of adding 10 FPS SD to a process already at 25 FPS SD is an illustration of that principle, and nothing more.

 

[Varminterror]

I'd be interested in what influences you wouldn't consider normally distributed.

Powder charge dispensing is typically normally distributed for most dispensers - but often is NOT so for powder measures. Measures can throw less, but virtually never more.

HOWEVER, the influence of powder charge isn’t always proportionate to the error. A higher weight erroneous charge nearer to the top of a node than the same magnitude error below target is near the bottom of a node, or a node with a more aggressive departure above than below will have a disproportionate influence. So a powder charge +1SD high might yield a considerably higher strike than a low error of the same magnitude.

Shooter influences are almost always unidirectional. We push the stock wrong or pull the trigger wrong in the same direction of influence. Especially irregular within the context of positional shooting. Many guys can still shoot sub-moa groups in odd positions, but their POI can shift notably as they contort due to the new positional influence they’re imparting to the rifle.

Incorrect wind readings tend to be consistently over or under estimated by shooters. Typically, I expect over estimation by most new shooters with an anemometer, as they’ll measure magnitude but not scale well for direction, which reduces the net influence. So their groups will favor upwind moreso than downwind...

Parallax error is typically unidirectional as well - guys misalign their head commonly to the same side, so they’re adding a distributed magnitude to one direction which can be additive to one side of other errors while subtractive to the opposite.

There’s a hell of a lot which goes into the assumed “2moa rifle” which has for some unidentified reason fired an 8moa group.