stagpanther
New member
"Statistics don't prove anything, they suggest correlation for decision-making" the immortal words from my professor who taught advanced statistics.
Chronograph numbers
- Thread starter Aguila Blanca
- Start date
I have found that chrono stats can vary from group to group with the same load within any given session depending on my hold. While the smallest groups almost invariably have the lowest ES/SD the consistency of my technique is a lot more important than the ammo even at mid and long range. Always remember that people were shooting tiny groups long before the first shooting chrono was available. It's what on paper that counts, don't obsess over numbers.
In a nutshell, statistically significant means it actually matters. This hi ges on a couple of things. First that the amount of change is actually important. I knew I guy that ripped the headliner out of his car to save weight so it would go faster. 5 lbs in a 3500 car is not significant. The other part is that there is enough data (data points) that you can be sure your numbers are accurate. 5 doesn't do it, 7 neither from a statistics standpoint. When I've done component testing, the statisticians want to see sizes of 15, 29, 50, and up. They want enough to generate a good bell curve and prove the data is normal. That said, 10 usually gives pretty decent set. You might get by with less (like 5) if they really stack on top of each other.
BTW- said friend, he actually ruined what was a mint condition 1980 Cameron turning it into a "race" car. And it's not even all that fast.
BTW- said friend, he actually ruined what was a mint condition 1980 Cameron turning it into a "race" car. And it's not even all that fast.
Short answer is SD is meaningless for the purpose of accuracy. What its good for not a clue (I was lucky to manage Algebra). Average is important FPS wise as is the ES (which throws average into the dumpster if its way off, ie, you have a quality control issue).
Yep
Ok, I am shooting up some 270 factory ammo that does not shoot worth diddly in a hunting gun (I have a 270 target barrel as I have been gifted with gobs of 270 bullets and its fun)
Now I am curious on what the variance in accuracy is out of the Target gun (the Sako 270 hunting guns hates factory)
Well the factory in the 270 target pretty well sucks as well. Ok, however, some Winchester Coated plastic tip nickle I gets a nice 3/4 inch group out of (which is the best I can do with the Sako 270 and hand loads though that beats the 2.5 inch factory groups all to hell).
So, 5 shot average is 3140 ES: 46 SD: 19.7.
The previous group was 150 gr Sierra Bullets in a factory load, 2 inch group
Avg: 2927 ES: 21 SD: 8.8
So clearly the 150 gr rounds were hugely better (via SD) even though it was by far the worst group.
Me thinks SD is irrelevant, as I had one shot in another group that was really wild, but it also was 200 FPS lower than the lowest of the other 4. Mmmm me thinks, kind of sucky quality control and I bet it was not the SD!
From what I can see, if your ES is in the 50 range, you done good quality controls wise and see where the holes in the target are.
Now, If I had an ES of 100 and I had a 1/4 group I would be in hog heaven as well. Seems to be for sure under 60-70 for ES and the hell with SD.
Yep
Ok, I am shooting up some 270 factory ammo that does not shoot worth diddly in a hunting gun (I have a 270 target barrel as I have been gifted with gobs of 270 bullets and its fun)
Now I am curious on what the variance in accuracy is out of the Target gun (the Sako 270 hunting guns hates factory)
Well the factory in the 270 target pretty well sucks as well. Ok, however, some Winchester Coated plastic tip nickle I gets a nice 3/4 inch group out of (which is the best I can do with the Sako 270 and hand loads though that beats the 2.5 inch factory groups all to hell).
So, 5 shot average is 3140 ES: 46 SD: 19.7.
The previous group was 150 gr Sierra Bullets in a factory load, 2 inch group
Avg: 2927 ES: 21 SD: 8.8
So clearly the 150 gr rounds were hugely better (via SD) even though it was by far the worst group.
Me thinks SD is irrelevant, as I had one shot in another group that was really wild, but it also was 200 FPS lower than the lowest of the other 4. Mmmm me thinks, kind of sucky quality control and I bet it was not the SD!
From what I can see, if your ES is in the 50 range, you done good quality controls wise and see where the holes in the target are.
Now, If I had an ES of 100 and I had a 1/4 group I would be in hog heaven as well. Seems to be for sure under 60-70 for ES and the hell with SD.
I should add ..... SD is an indication of how likely your data is going to deviate from the average (mean). It's based on typical data fitting a bell curve. Think of how many data points you need to start to shape a bell. It's a lot more than 10. Even 15 is weak. That doesn't mean you need 15 points for good data though. If you have 5 to 10 points and they are all very close, you can be pretty sure the average of those points will give you good results. The SD on that few of points will be pretty meaningless though.
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In my experience a good SD or es is important. However from an accuracy standpoint there are other things at play, depending on how deep down the rabbit hole you want to go. For me I dial in a good es/SD, then tune the seating depth. The ES/SD ensures consistency, and the seating depth tunes the group size.
I have always learned towards ES rather than SD personally as I understand the function itself better.
Wow, this has gone NASA. In my EXPERIENCE of 40 years with a Oehler 33 and now a 35p, every 10 shot string I've ever shot that had a low extreme spread had a low standard deviation together with <MOA accuracy. Listed below are the calibers that I reload. An old Finance professor told me that "statistics are like bikinis, what they reveal is interesting, but what they conceal is vital"!
Put a barrel good tuner on a rifle and take a decent load and play with the tuner. Shoot 5 round groups , say 20 groups while adjusting the tuner. Group sizes will change dramatically yet the load is the same. Why?
Then take a load that shot sub 10 SD and sub 20 ES on a 5 round test group, wait a week shoot again. Is it still a sub 10 SD and sub 20 ES ?
Earlier in this thread I posted a pic of three 10 shot groups shot at 300 yards. First group had a ES of 168 and a vertical spread of 2.12 inches, another had a ES of 47 and a vertical of 1.452 inches , the third had a ES of 97 and a vertical of 3.56 inches. All 30 rounds were loaded in the same session and to the same BTO and powder charge weighed to within plus or minus .02 gns. So where is the correlation between ES and vertical spread here? How can a group with a 47 ES shoot a sub .5 MOA group at 300 ? Why did three groups loaded and shot at the same time have radically different FPS spreads?
Then take a load that shot sub 10 SD and sub 20 ES on a 5 round test group, wait a week shoot again. Is it still a sub 10 SD and sub 20 ES ?
Earlier in this thread I posted a pic of three 10 shot groups shot at 300 yards. First group had a ES of 168 and a vertical spread of 2.12 inches, another had a ES of 47 and a vertical of 1.452 inches , the third had a ES of 97 and a vertical of 3.56 inches. All 30 rounds were loaded in the same session and to the same BTO and powder charge weighed to within plus or minus .02 gns. So where is the correlation between ES and vertical spread here? How can a group with a 47 ES shoot a sub .5 MOA group at 300 ? Why did three groups loaded and shot at the same time have radically different FPS spreads?
I normally consider in my component costs OR Components on hand when working up loads. The last year this has been an even bigger factor.
If I am working up what I consider to be reasonably accurate numbers I will Fire SIX Rounds that are all loaded alike, and throw out the one shot in that group that is Highest or Lowest and Average the remaining Five Shots.
2560
2563
2559
2571 I would throw this number out of the average
2560
2562
This is Statistically accurate enough for me.
Bob R
If I am working up what I consider to be reasonably accurate numbers I will Fire SIX Rounds that are all loaded alike, and throw out the one shot in that group that is Highest or Lowest and Average the remaining Five Shots.
2560
2563
2559
2571 I would throw this number out of the average
2560
2562
This is Statistically accurate enough for me.
Bob R
Sorry Aguila... I said all that and never answered your question. When I was crunching numbers, I used ten shot strings; mostly because that is what I'd seen done in firearms publications for decades.
Not quite; standard deviation is a descriptor of spread regardless of the actual distribution shape. With some distributions, Gaussian (or Normal, the "typical" bell curve) it provides a great deal of information (with the mean and standard deviation you can tell what proportion of results will occur within any given range of values). If the actual data is a different shape, such as Uniform distribution (i.e. every outcome occurs with the same probability such a "fair" 6-sided die or flipping an honest coin) not much help.
You typically need a sample "large enough" to tell if a particular example set of data may come from a given distribution. How large depends on the distribution and how certain you need the answer.
I use a LabRadar Chrono so the following data is accurate. But keep in mind, as long as your Chrono is consistent even if off true, it does not matter if its spot on. If 2750 FPS on the Chrono get you your accurate load, it does not matter if its acualy moving at 2650.
At the base that is true but that does not mean a Chrono does not tell you some relevant information. SD is not it, but a velocity range is.
For instance, I am loading for a hunting 270 (it hates factory ammo). I had the load data, a few rounds left and went to duplicate it.
The 270 did not like my new loads though they were duplicate. Hmmm. Ok, Chrono the old loads and those were 2650 average and the new ones 2600.
I need to up the powder a bit to get back into that velocity range the 270 likes. I may well be at the bottom with the good loads and will explore the upper as well.
At the base that is true but that does not mean a Chrono does not tell you some relevant information. SD is not it, but a velocity range is.
For instance, I am loading for a hunting 270 (it hates factory ammo). I had the load data, a few rounds left and went to duplicate it.
The 270 did not like my new loads though they were duplicate. Hmmm. Ok, Chrono the old loads and those were 2650 average and the new ones 2600.
I need to up the powder a bit to get back into that velocity range the 270 likes. I may well be at the bottom with the good loads and will explore the upper as well.
You have the issue of SD relevancy. Its a data piece that goes with FPS, but that does not mean its relevant.
As noted, you can have spot on velocity of 40 FPS spread and you will get a nice low SD.
Yippeee, but the gun does not like the velocity. uhhhhhhh.
The Bikini (SD) by itself is not relevant, its only when it goes with the girl that it is (ES).
Ergo, low SDs reflect low ES. Now SD may have some real world application in statistic someplace, but its nothing more than a reflective number in shooting.
As the sample size gets bigger, the ratio of ES to SD grows, as my diagram below shows for a constant SD of one. It grows because all the members of a small sample are more likely to be in the higher probability part of the curve, where a large sample offers more opportunities for data points to appear in the lower probability extremes. You can see it tossing runs with a coin. The majority of tosses tend to alternate heads and tails pretty often. Still, after a while, you accumulate a smaller number that are two heads or two tails in a row, then you get still fewer with three heads or tails in a row, and still fewer with four in a row, and still fewer with five in a row, etc. The longer the run of same-side tosses, the lower the probability of them occurring, but with enough tosses, eventually, they do. It’s the same with shot velocities or shot locations in a group. The values furthest from the mean value are the least probable, but with enough shots, they start to accumulate. Once in a while, one shows up with just a few shots, as may have happened with Viper225’s data.
One thing that is nifty about the root-mean-square basis for calculating standard deviation is the growth with sample size shown in that plot doesn’t change the result of the calculation based on its total data. It remains equal to one. So you don’t usually have to drop out-of-place-looking points from your data. In Viper 225’s data, the difference made to SD by including the higher velocity point he dropped is significant. But unless I knew I had let that round cook too long in the chamber or had got the powder back more solidly over the flash hole before firing or had some other known reason for it to be faster, I’d refire several more sample groups to confirm it was likely an outlier. Dropping data has to be judged carefully because you don’t want to inadvertently bias your result, as often happens when high and low values are tossed out without careful consideration.
Where the standard deviation comes from is it is one of the coefficients in Carl Friedrich Gauss’s equation that plots the bell curve that so neatly describes how nature distributes most things randomly around a mean. The basic equation has three coefficients: one that determines the height of the curve, one that determines the width of the curve, and one that determines the center location of the peak. He knew that for the area under the curve to represent a whole population (100% of it), the area under the curve needed to be equal to one. He then figured out he could replace the height coefficient with a function of the width coefficient such that as the curve got wider, it also got shorter and vice versa in the right proportion to keep the area under the angle always equal to one. That width coefficient is called sigma and is also called the population standard deviation. That’s how you end up with a standard deviation that bounds 68% of the population around the mean. Any sensible person intentionally choosing a bounding point would choose 50% or some other easy-to-use number, but the number that does that is only 0.6745 times as large as the standard deviation, so it doesn’t fit the equation to keep the area under the curve equal to one. Thus, the exact value of standard deviation is really an artifact of the math that is describing nature.
For sample size, you have to choose the certainty you need to determine what constitutes significance. Some examples of choices made by others are:
10. SAAMI’s system of determining pressure and velocity is based on test sample sizes of 10. This is to avoid members having to spend exorbitant amounts of time and money on testing during the manufacturing process. To get away with such a small sample, they make generous allowances for standard deviation and extreme spread. They don’t let an individual round reach the proof load range, but it is allowed to get closer than you might think. This is why you occasionally still get ammunition recalls.
15. Denton Bramwell, who ran a manufacturing process statistics company and who wrote several articles for Varminter Magazine that include the use of statistics, said he is satisfied that he learns enough about a load from a sample size of 15. His article, The Perverse Nature of Standard Deviation, is worth a read.
30. Board member Statshooter, who teaches statistics at the college level, is not satisfied with fewer than 30 rounds in a sample. Thirty is a number that was pretty much the minimum used before Gosset (aka, Student) and Fisher came along, and it is still frequently used today. 30 will let you arrange the data into a histogram that starts to reveal the outline of the bell curve clearly with a normal distribution. It is also the number at which using the sample standard deviation calculation, with its n-1 variance denominator to compensate for small sample size no longer represents much practical improvement in accuracy as compared to using the simpler population standard deviation calculation with n as the mean variance denominator.
100-300. Commercial and military ammunition accuracy testing often involves numbers in this range. One measure of accuracy is to find the smallest circle that still covers 50% of the holes in a 200-round sample. This is called the 50% Circular Error Probable (or circular probable error). You can convert between the two with that factor. Another is to measure and average the vertical and horizontal locations of every hole to find the mean position (the group center), and then take the distance of every hole from that location and find their standard deviation to get the radial standard deviation. If you the radial SD it by 0.6745, it gives you the CEP 50% number.
One thing that is nifty about the root-mean-square basis for calculating standard deviation is the growth with sample size shown in that plot doesn’t change the result of the calculation based on its total data. It remains equal to one. So you don’t usually have to drop out-of-place-looking points from your data. In Viper 225’s data, the difference made to SD by including the higher velocity point he dropped is significant. But unless I knew I had let that round cook too long in the chamber or had got the powder back more solidly over the flash hole before firing or had some other known reason for it to be faster, I’d refire several more sample groups to confirm it was likely an outlier. Dropping data has to be judged carefully because you don’t want to inadvertently bias your result, as often happens when high and low values are tossed out without careful consideration.
Where the standard deviation comes from is it is one of the coefficients in Carl Friedrich Gauss’s equation that plots the bell curve that so neatly describes how nature distributes most things randomly around a mean. The basic equation has three coefficients: one that determines the height of the curve, one that determines the width of the curve, and one that determines the center location of the peak. He knew that for the area under the curve to represent a whole population (100% of it), the area under the curve needed to be equal to one. He then figured out he could replace the height coefficient with a function of the width coefficient such that as the curve got wider, it also got shorter and vice versa in the right proportion to keep the area under the angle always equal to one. That width coefficient is called sigma and is also called the population standard deviation. That’s how you end up with a standard deviation that bounds 68% of the population around the mean. Any sensible person intentionally choosing a bounding point would choose 50% or some other easy-to-use number, but the number that does that is only 0.6745 times as large as the standard deviation, so it doesn’t fit the equation to keep the area under the curve equal to one. Thus, the exact value of standard deviation is really an artifact of the math that is describing nature.
For sample size, you have to choose the certainty you need to determine what constitutes significance. Some examples of choices made by others are:
10. SAAMI’s system of determining pressure and velocity is based on test sample sizes of 10. This is to avoid members having to spend exorbitant amounts of time and money on testing during the manufacturing process. To get away with such a small sample, they make generous allowances for standard deviation and extreme spread. They don’t let an individual round reach the proof load range, but it is allowed to get closer than you might think. This is why you occasionally still get ammunition recalls.
15. Denton Bramwell, who ran a manufacturing process statistics company and who wrote several articles for Varminter Magazine that include the use of statistics, said he is satisfied that he learns enough about a load from a sample size of 15. His article, The Perverse Nature of Standard Deviation, is worth a read.
30. Board member Statshooter, who teaches statistics at the college level, is not satisfied with fewer than 30 rounds in a sample. Thirty is a number that was pretty much the minimum used before Gosset (aka, Student) and Fisher came along, and it is still frequently used today. 30 will let you arrange the data into a histogram that starts to reveal the outline of the bell curve clearly with a normal distribution. It is also the number at which using the sample standard deviation calculation, with its n-1 variance denominator to compensate for small sample size no longer represents much practical improvement in accuracy as compared to using the simpler population standard deviation calculation with n as the mean variance denominator.
100-300. Commercial and military ammunition accuracy testing often involves numbers in this range. One measure of accuracy is to find the smallest circle that still covers 50% of the holes in a 200-round sample. This is called the 50% Circular Error Probable (or circular probable error). You can convert between the two with that factor. Another is to measure and average the vertical and horizontal locations of every hole to find the mean position (the group center), and then take the distance of every hole from that location and find their standard deviation to get the radial standard deviation. If you the radial SD it by 0.6745, it gives you the CEP 50% number.
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IF ES and SD really make that much difference in group size does it matter what the actual numbers are? If they are really relevant the you should be able to look at a test target and know that group A had the better ES/SD than group B, C, D and E just because the group size was smaller on group A ?
That is why the only time I do velocity FPS now is at the end of my 100 yard development cycle. Three shots with a Magnetospeed just to get the FPS data for my ballistics calculator. Funny thing is my group sizes at long range continue to improve and I get sub .5 MOA performance at long range. For those who want to overcomplicate things feel free to do so, myself I would rather spend my time and effort shooting. It is like a mentor of mine said, there are those who reload to shoot and those who shoot to reload.
That is why the only time I do velocity FPS now is at the end of my 100 yard development cycle. Three shots with a Magnetospeed just to get the FPS data for my ballistics calculator. Funny thing is my group sizes at long range continue to improve and I get sub .5 MOA performance at long range. For those who want to overcomplicate things feel free to do so, myself I would rather spend my time and effort shooting. It is like a mentor of mine said, there are those who reload to shoot and those who shoot to reload.
At 100 yards, the time of flight is too short for gravity to act much on the bullet, so you don't really see much vertical stringing from velocity variation at that short range. This is why Randolf Constantine recommended 300 yards for shooting an Audette ladder. It's short enough that small wind shifts don't take a big toll on POI, but long enough to start to see vertical POI change with velocity pretty clearly. A ballistic calculator will show you that if you had a perfectly rigid gun, 100 fps difference at typical .308W velocities with a 175-grain SMK would only make 0.19 moa of difference to POI at 100 yards. But at 300, it makes 0.66 moa or 2.1" of difference, so you can see the separation round-to round velocity differences make. By the time you get to 1000 yards (by then subsonic), it's a whopping 4 moa and nearly 4 feet of difference. So the effect of ES on POI is mainly a concern for longer ranges.
Another thing SD can alert you to is ignition problems. If you change your primer or your powder lot or start shooting in significantly different temperatures and see a change in SD, it can mean ignition has gotten better or worse. Worse (wider SD, less consistent) ignition is a factor at all ranges because it tends to vary the 3 ms or so delay between the primer being struck and the pressure building enough to start moving the bullet. This means every vibration, muscle twitch, or other problem with keeping the barrel still is acting for different lengths of time, changing where the muzzle is pointed at the moment of bullet exit. This opens groups up.
The bottom line, I think, is that it is so cheap to store data these days that if you can collect data points like your velocity and its SD and ES automatically off your chronograph, there is always a chance it may be useful for future diagnostics, so why not keep it?
Another thing SD can alert you to is ignition problems. If you change your primer or your powder lot or start shooting in significantly different temperatures and see a change in SD, it can mean ignition has gotten better or worse. Worse (wider SD, less consistent) ignition is a factor at all ranges because it tends to vary the 3 ms or so delay between the primer being struck and the pressure building enough to start moving the bullet. This means every vibration, muscle twitch, or other problem with keeping the barrel still is acting for different lengths of time, changing where the muzzle is pointed at the moment of bullet exit. This opens groups up.
The bottom line, I think, is that it is so cheap to store data these days that if you can collect data points like your velocity and its SD and ES automatically off your chronograph, there is always a chance it may be useful for future diagnostics, so why not keep it?