What is a "good" standard deviation?

aiming fluid · August 20, 2010, 02:39 PM

I'm new to chronographs, but not so new to reloading. I've had occasion to chronograph some 45 ACP loads, and had SD's in the range of 15 to 20, with extreme spreads about 30-75. I'm guessing that these are pretty good numbers, and I'm guessing that they mean that my reloading procedures are fairly consistent from round to round, but my lack of exposure to these devices is apparent.
If any of you that chrony alot can give further insight into SD and ES, I would greatly appreciate it!

Ike666 · August 20, 2010, 04:44 PM

There is no absolute answer to your question. However, as a general rule, "smaller is better." The standard deviation measures the dispersion of a group around the mean such that approximately 68% of your sample should be within +/- 1 SD of the mean. As a practical consideration it tells you how closely your shots cluster about the average MV. The tighter the clustering the more consistent the rounds are. The SD will also be affected by the total number of shots in your string (it is the average of the squared differences from the mean). The more shots you have, the lower your SD will be (typically).

For a mean MV of 875 and an SD of 15, you'd expect 68% of your shots to be between 860 and 890 fps.

The extreme spread is also a crude measure of dispersion, but it really tells you more about the effect of outliers on the mean. In simplest terms it is the difference between the High MV and the Low MV. Like the SD, the smaller the ES the better. An extremely high or low MV will "pull" the mean in that direction. Generally, any shot that is 1.5 SDs above or below the mean can be considered an outlier (not typical or expected). So, from the example above, a shot with a MV of 852 or less is suspect (short poweder load???).

There is no absolute "test" of how much (or how little) SD is right. For a string of 10 shots an SD of 15 is pretty respectable.

aiming fluid · August 20, 2010, 07:28 PM

Thank you Ike for the information. I guess what I'm trying to figure out is how these numbers can help me with the quality of my ammo, and specifically, how does it match up against factory stuff. Since I don't yet own a chronograph, I haven't been able to chrony factory ammo to see how consistent it is. Here are the numbers from one of my loads:

45ACP 230 Grain Berry's RN
5.3 grains HP38
Low 694.5
High 733.9
Average 713.5
ES 39.37
SD 13.26
8 Shot string

This group was one of three I shot with different powder combinations, and had the lowest SD. The other two were 16.8 and 23.7.

I am a very meticulous reloader, and do try very hard to make the highest quality loads that I can. I used the same dies and techniques on all the loads: the only variable being the amount and type of powder used. The lowest and the highest SD's were with the HP powder, and the 16.8 was with bullseye.
Have you experienced large swings in SD's for the same bullet with different powder charges (same powder, primer, case)? Any info is really appreciated as the chronograph seems to allow me to look at my ammo in a different light.

Ike666 · August 20, 2010, 08:20 PM

The way that I use SD & ES is as a consistency "score." In a perfect reloading situation, every round would go down range at the same MV - perfect reliability/consistency. Can't happen - there are too many variables that enter the equation. So, the SD & ES gives us a means to evaluate how close we are getting to the unobtainable ideal (0 SD, 0 ES).

I think that the single biggest variable is not the weapon, bullet, or case but is the powder & primer. Just a little time lurking on this list and reading the discussions about favorite powders will quickly give you some insight into the wide number of variables that affect how powder effects your loads.

However, of all of those, I suspect that powder metering is the biggest within a powder type. For example, I was a long time user of Unique for pistol loads. But in my press (Dillon 550) I get a natural variance in thrown loads that swings up and down several tenths of a grain. But with Power Pistol in the same press, I get much more consistent loads. This difference shows up in my chronograph data, specifically the SD & ES.

Because SD & ES are dependent on the specific distribution from which they are drawn they really are not terribly useful comparing two powders to one another. About the only way you could approximate that would be to load for the same MV with two different powders (select a load for example that is intended to produce a consistent MV of 850 fps).

Another way, and this is overkill, would be to collect a sample of SDs (shoot 10 strings with the same load) for each of two powders. Then you could convert the SDs to standard scores and compare them with something like a t-test. Like I said this is probably way over the top.

In the final analysis, and assuming you are a reasonably proficient marksman, the real test is group size. Group size is dependent on a multitude of variables, all of which need to coalesce into a consistent and repeatable pattern. The load data is but one of those variables.

If you are reloading to send more bullets down range, don't get too obsessive about load data. If your are shooting to maximize accuracy (e.g. benchrest) then all this becomes much more relevant.

FWIW, your SDs seem about right to me. For fun shooting the TLAR principle works best (that looks about right). Tight groups.

Brian Pfleuger · August 21, 2010, 12:17 AM

A good standard deviation is the one that your most accurate load has. Most accurate will not always be lowest SD. Truth is, SD is not of much importance in most situations.

zippy13 · August 21, 2010, 12:57 AM

Greetings aiming fluid and welcome aboard,

As I recall my statistics, the power of knowing your SD and ES comes not from having a uniform method to analyze a sample's performance but as tool to predict the performance of future samples. To that end, I gotta go with peetzakilla on this one, data based on target impact is a better indicator than velocity, YMMV.

FlyFish · August 21, 2010, 07:07 AM

In theory, the standard deviation is an inherent property of the population from which it is drawn and therefore should be independent of the sample size, i.e., should neither increase nor decrease with increasing sample size (more shots in the string). A shot that is +/- 1.5 sd from the mean would not be close to being considered an outlier by statisticians (about 14% of the distribution lies outside +/- 1.5 sd, so the probability that the shot is not from a different population is approximately 1/14*100 = ~7%. The usual rule of thumb is +/- 4 sd, which would be a probability of about 0.1%, and some of the statisticians I work with would argue that even that isn't low enough.

More importantly, distributions of velocities are inherently heteroscedastic, which means that the sd is correlated with the mean, so that you can't simply compare two sds and say which is "lower," nor is it possible to give a value for a "good" sd without knowing what velocities are involved. For example, you would expect the sd of a population of low-power pistol bullet velocities to be lower than the sd for a population of, say, .22-250 measurements. A better way to compare is to express the sd as a percentage of the mean, a statistic known as the coefficient of variation: sd/u*100 = CV (where u is the mean).

That said, I too tend to agree with peetzakilla. It's too easy to get wrapped around the axle with this stuff and if you're not a statistician you honestly don't really know what the numbers are telling you in any case.

aiming fluid · August 21, 2010, 09:47 AM

Thank you gentlemen for the outstanding information. You have given me much to ponder......

It still seems to me that there could be usable info gleaned from the SD and ES. As Ike explains it, these numbers ultimately gauge the consistency of your rounds, and it would seem to me that consistent ammo is important in any hopes of accuracy. Would it be safe to say that if your ES was 5% or less of your average velocity, the consistency of your ammo would be considered adequate?

Thank you FLyFish for expanding my vocabulary. For the "unwashed Masses" here's a definition of heteroscedasticity http://en.wikipedia.org/wiki/Heteroscedasticity. It is a very cool word.

Yup, I had to look it up.

Also has anyone chronied factory ammo?

Slamfire · August 21, 2010, 10:28 AM

Back in the 60's, 70's, and 90's, shill gunwriters would recommend powders without having chronographed the loads. Some of those loads were with Blue Dot. Today they still won't publish standard deviations and extreme spreads.

SD and ES will provide you a way of evaluating whether a powder is appropriate for a certain application.

Case in point, Hercules/Alliant provides data for Blue Dot in low pressure cartridges, yet when I test the stuff, I get these horrible ES’s. Examine the SD and ES for Bullseye and compare to Blue Dot. I have come to the conclusion that when I get ES’s in terms of hundreds of feet that powder is inappropriate for the application.

I believe the varying levels of muzzle blast were due to irregular burning of powder. That is bad as you do not want the propellant producing irregular pressure waves in the case.

You will find that good loads in pistols always (like 95% always) have greater SD’s and ES’s than good loads fired in rifles.

Code:

4" S&W M10-5						
						
						
125 Valiant BBRNFP 4.0 grs Bullseye Mixed cases WSP 						
9-Apr-06	T = 59 °F	 Elevation at least 4" low		Windage centered		accurate
						
Ave Vel =	863.4	 				
Std Dev =	30				 	
ES	70.78				 	
High	907.5			 	 	
Low	836.7			 	 	
N =	6				 	
						
						
						
						
125 Valiant BBRNFP 4.5 grs Bullseye Mixed cases WSP 						
9-Apr-06	T = 64 °F	 Elevation at least 4" low		Windage centered		accurate
						
Ave Vel =	945.6	 				
Std Dev =	27.28				 	
ES	75.21				 	
High	995.2			 	 	
Low	920			 	 	
N =	6				 	
						
						
125 Valiant BBRNFP 6.5 grs Blue Dot Mixed cases WSP 						
9-Apr-06	T = 64 °F	 Elevation Point of aim		Windage centered		accurate
						
Ave Vel =	734	 				
Std Dev =	63.53				 	
ES	260				 	
High	829.6			 	 	
Low	569.5			 	 	
N =	18				 	
						
125 Valiant BBRNFP 7.0  grs Blue Dot Mixed cases WSP 						
9-Apr-06	T = 64 °F	 Elevation Point of aim		Windage centered		accurate
						
Ave Vel =	788.2	 				
Std Dev =	63.3				 	
ES	241.3				 	
High	926.7			 	 	
Low	685.3			 	 	
N =	12				 	
						
						
125 Valiant BBRNFP 7.5 grs Blue Dot Mixed cases WSP 						
22-Apr-06	T = 68 °F	 Elevation low 			poor accuracy	

Ave Vel =	867.3	 				
Std Dev =	53.06				 	
ES	235.6				 	
High	959.7			 	 	
Low	724.1			 	 	
N =	25				 	
						
						
125 Valiant BBRNFP 8.0 grs Blue Dot Mixed cases WSP 						
22-Apr-06	T = 68 °F	 Elevation all over the place 		very poor accuracy		loud at times

Ave Vel =	990.2	 				
Std Dev =	56.55			 	 	
ES	236.1				 	
High	1093				 	
Low	857.5				 	
N =	25

Brian Pfleuger · August 21, 2010, 12:08 PM

Quote:

Also has anyone chronied factory ammo?

Yep.

12ga slugs, 7mm-08 rifle and 357sig handgun.... Standard deviations are horrid and extreme spread is worse. I've done what would be considered limited testing and I've seen factory rifle ammo with an extreme spread of almost 300fps on 2900fps 7mm-08 loads and over 100 fps on 1300 fps 357sig loads, from the same box in both cases.

As a case in point though, the 7mm ammo shoots 1moa or less at 100 yards. So, what does the extreme spread and SD mean? Little of nothing.

farmerboy · August 21, 2010, 12:27 PM

peetzakilla is right on, on both replies!

FlyFish · August 21, 2010, 03:32 PM

Quote:

Would it be safe to say that if your ES was 5% or less of your average velocity, the consistency of your ammo would be considered adequate?

Probably, but ES is really a very poor measure of population variability because it only uses information from two data points, essentially ignoring everything else no matter how many other shots you made. That's why standard deviation, or average deviation (which would be affected less by the shots more distant from the group center) is preferable as a measure of uniformity. And really, the only thing that counts in the last analysis is how accurate (precise, to be correct) the rifle/cartridge/load combination is. (For the same reason, maximum spread is a very poor way to measure group size even though that's what everyone - well, almost everyone because the US military has a different and better procedure - uses because it's easy to calculate.)

Ike666 · August 21, 2010, 09:02 PM

ditto on the Pizza Killuh - I also recently chronied some factory 357SIG loads. The only thing it did for me was tell me that my handloads were, um, "better." This was actually a little depressing b/c I thought I could use factory loads as some kind of standard.

In the end, my handloads were faster overall, and they grouped better, had less felt recoil (very subjective), were quieter (also subjective), and generated less muzzle flash at EENT.

I do think that running the factory loads through the 'graph was a worthwhile exercise. It gave me more confidence in my loading technique - even with the dreaded Unique powder.

I was able to generate "factory" replica MVs best with a near-max load of Power Pistol. The SDs and ESs were also better but were not the deciding factor.

BTW, FlyFish is on-target with his info. I still use to x1.5 SD to consider dropping a shot from the calculations - but that's my idiosyncrasy. Another technique is to drop the top and bottom quartiles if you've got a large enough sample - but I rarely shoot a string large enough for that.

Win_94 · August 22, 2010, 03:41 AM

Quote:

If any of you that chrony alot can give further insight into SD and ES, I would greatly appreciate it!

Unless you are shooting the pistol at extended ranges, the "SD and ES" doesn't tell you as much as your groups will.

I shoot at extended ranges with my 8" barrel hunting 357. When I work up loads for it, I take more notice of the velocity deviations.
When I work up a load for a 2" barrel concealed carry 357, I am more interested in the groups.

Groups are what I look to first, whether it be load development with a rifle or pistol; if I have numerous areas in my ladder test that group as well, I will try the node with less velocity deviation.

mongoose33 · August 22, 2010, 06:24 AM

Quote:

In theory, the standard deviation is an inherent property of the population from which it is drawn and therefore should be independent of the sample size, i.e., should neither increase nor decrease with increasing sample size (more shots in the string)

This is not the case.

It will take a certain number of shots for the standard deviation to settle down. By implication, the above suggests that the SD for 3 shots will be the same as for 30 shots, and that's decidedly not the case.

SD is a sample statistic, i.e., an estimate of the population parameter. The more cases you have in the sample, the more accurate that estimate will tend to be.

To answer the OP's question, IMO if your SDs are 1 percent of the mean for rifle date, you're doing very well.

I've done a lot of chrono testing for pistol, using mixed headstamp brass, and for pistol about the best consistency I can achieve for SD is 2 percent of the mean.

Finally, ES is mostly useless. If you have a very narrow ES that will tell you something about your level of consistency. But since a single extreme case widens the ES, you can't know whether you have one very bad outlier or if the entire range is populated by cases which are more or less spread out.

And I agree w/ those who have noted that accuracy is a better indicator than SD. I use SD as a measure of how consistently well I'm reloading, as a way to establish, in a crude way, how consistent my pressures are.

TXGunNut · August 22, 2010, 07:52 AM

If you want to compile mounds of data a chrono will do that for you. If you're having issues with a load or a rifle a chrono may help you sort it out. A long distance shooter may need one to get actual instead of theoretical MV for a baseline to determine bullet drop at the longer distances. As has been pointed out numbers aren't everything for a target shooter but they can be very helpful.

FlyFish · August 22, 2010, 12:00 PM

Quote:

This is not the case.

It will take a certain number of shots for the standard deviation to settle down. By implication, the above suggests that the SD for 3 shots will be the same as for 30 shots, and that's decidedly not the case.

We agree. You misunderstood what I was saying, or (more likely) I didn't make myself sufficiently clear. My comment was in response to an earlier post where it was claimed that the sd would decrease (i.e., monotonically) as the number of shots in a string increased. As we both know that's not the case - as the number of measurements increases the sd will decreasingly vary either plus or minus from the true population sd, eventually converging on it as the sample size approaches the population size. The true sd of the population that's being sampled from is indeed fixed, however - what's changing is the estimate of it that we make from the data in the sample. An sd calculated from a sample size of 3 will differ from one based on a sample of 30 from the same population, and the sd based on 30 data points will be closer to the population sd, but the difference can go in either direction.

Quote:

SD is a sample statistic, i.e., an estimate of the population parameter.

Yes and no. You can calculate the sd of the sample that you've taken, or you can calculate the sd of the population from which it is drawn, the difference lies in whether you choose n or n-1, respectively, in the formula. In most cases, you're correct in that we're usually interested in the population sd, not the sample sd, but that's not always the case. Excel provides a formula for each option, and it's important to know which is which (STDEV for the population, STDEVP if you're only interested in your sample).

Quote:

The more cases you have in the sample, the more accurate that estimate will tend to be.

Yes, although the amount of "improvement" in the estimate with each increasing data point is not linear, it decreases exponentially. So, for example, if you've got a 3-shot string, making it a 5-shot string will improve your estimate of the sd considerably, but if you've already got, say, a 10-shot string there's no practical benefit in going to 12, etc.

GeauxTide · August 22, 2010, 07:53 PM

For rifles, if I can get the ES in the 30fps range, then the typical SD is below 10. When I get these numbers, accuracy is MOA or better. In the manual powder measure days, every rifle charge was weighed. Now that I've got Lyman 1200, all is measured. I haven't chrony'd any pistol rounds lately, but my 45LC loads group much better.

FrankenMauser · August 22, 2010, 11:12 PM

When recording velocities for actual use, remember not to count anything coming out of a clean barrel, either.

I compared clean-bore shots to fouled-bore shots with two of my rifles, a couple weeks ago. The clean-bore shots were more than 100 fps slower than the later shots -- and in my .270, it took 4 shots before the velocity stopped climbing, and stabilized.

Also keep in mind: Some powders are temperature sensitive. If you have your ammo sitting in the sun, while running these velocity strings... you're adding an additional variable, that won't be clear in your data.

For example: In testing some Remington Factory 130gr Core-Lokts in my .270 for velocity and consistency, I had to take a 30-45 minute break, so my father could finish doing what the chronograph was actually there for. When I got back in the hot seat, the ammunition and rifle temperature had gone up almost 15 degrees (from 80 F, to 94 F). I was absolutely blown away, to see an average increase of more than 100 fps.

The whole point of using a chronograph, for most shooters, is to identify and isolate variables - to create a better end product. But... if we forget about the variables encountered during actual testing, it's a futile effort.

noylj · August 23, 2010, 02:30 AM

S.D. just hasn't proven to be of much value in terms of predicting an accurate load. A truly accurate load (not a load that occasionally will produce a small group) will be accurate over a range of powder charge values. In other words, despite a variation in velocity, the harmonics of the barrel/gun are such that the bore direction is nearly the same over a range of velocities. This will be your most accurate load and a relatively large S.D. will not affect the accuracy much. This is where benchrest shooters work to find. Once this load is found, you can just throw powder by volume and not worry about each charge being ±0.3 gn or more.
Now, Let's discuss S.D.: The S.D. doesn't mean anything without the mean value. You take the S.D. and divide it by the mean, multiply by 100, and get the Coefficient of Variance as a percent of the mean. In general, you want a CoV of 3% or less to consider a batch to be consistent, and even that depends on what parameter you are tesing. Of course, you really need to have a sample set of at least 20 values.
The standard deviation is used to determine if, based on a sub-set sampling of units, do the units meet the specification requirement. The other use is when you make a change to one variable and you want to determine if the samples from the changed production lot are the same as the production lot without the change (the null hypothesis) or does it represent a statistically significant change in the tested parameter by running a t-test.
The two main uses for a chronograph and the S.D. for velocity is to ensure that you are not significantly exceeding expected velocity (and you know you had better carefully inspect for high pressure) or if you will meet the target Power Factor for whatever game you are participating in. Your aim may be to ensure that your velocity is 2 standard deviation units higher then the required velocity to meet the power factor. You don't want too much velocity, but you also do want to fail and drop down to minor from major or out of the competition entirely.
One other use I found was that some cartridges (those that run at 30-35k psi or higher) show an effect where, at max pressure, an additional increase in charge weight will not produce the expected increase in velocity. There is also the effect I found for the .38 special shooting a 148gn L-HBWC where a slight increase in powder would produce a large jump in velocity (generally with sudden pressure signs on the case, also). As soon as you see either condition, you know that you have reached the effective maximum for that gun and reload combination, and it is time to back off.

RKG · August 25, 2010, 12:04 PM

As this thread demonstrates, you've asked a question that can generate complex answers and really complex answers. Whether you want to tumble into the subject of descriptive statistics (you can't really dabble in this subject), is up to you.

However, here is a simple answer, so long as you don't ask any follow-ups:

A) Load at least 10 rounds, using bullets and primers from the same box, powder from the same can, and brass with at least the same headstamp.

B) Collect instrument velocities and compute mean and SD

C) Ignore ES.

D) Divide an SD derived from at least 10 samples by the mean derived from the same samples and express as a percentage. Less than 1% is good; between 1% and 2% is not uncommon and not bad; over 3% implies a fair probabilty that something is wrong that requires further investigation.

temmi · August 25, 2010, 12:07 PM

Unless you have a large sample, the SD really is not helpful…. But the smaller the better

aiming fluid · August 25, 2010, 06:45 PM

Thank you members for your replies; outstanding info and great patience exhibited on my query.

I did have the opportunity to go shooting with my chrony friend again today, and we evaluated some military .45 ACP with headstamps from the early 1940's. I will post the details soon as I tear the remaining bullets apart and get some pictures. One string of rounds had an SD of 8! Pretty cool for 67 year old ammo.

August 20, 2010, 02:39 PM	#1
aiming fluid Member Join Date: July 1, 2010 Posts: 44	What is a "good" standard deviation? I'm new to chronographs, but not so new to reloading. I've had occasion to chronograph some 45 ACP loads, and had SD's in the range of 15 to 20, with extreme spreads about 30-75. I'm guessing that these are pretty good numbers, and I'm guessing that they mean that my reloading procedures are fairly consistent from round to round, but my lack of exposure to these devices is apparent. If any of you that chrony alot can give further insight into SD and ES, I would greatly appreciate it!

August 21, 2010, 12:17 AM	#5
Brian Pfleuger Moderator Emeritus Join Date: June 25, 2008 Location: Austin, CO Posts: 19,578	A good standard deviation is the one that your most accurate load has. Most accurate will not always be lowest SD. Truth is, SD is not of much importance in most situations. __________________ Nobody plans to screw up their lives... ...they just don't plan not to. -Andy Stanley

August 22, 2010, 07:52 AM	#16
TXGunNut Senior Member Join Date: January 16, 2010 Location: If you have to ask... Posts: 2,860	If you want to compile mounds of data a chrono will do that for you. If you're having issues with a load or a rifle a chrono may help you sort it out. A long distance shooter may need one to get actual instead of theoretical MV for a baseline to determine bullet drop at the longer distances. As has been pointed out numbers aren't everything for a target shooter but they can be very helpful. __________________ Life Member NRA, TSRA Smokeless powder is a passing fad! -Steve Garbe I hate rude behavior in a man. I won't tolerate it. -Woodrow F. Call Lonesome Dove My favorite recipes start out with a handful of used wheelweights.

August 22, 2010, 07:53 PM	#18
GeauxTide Senior Member Join Date: April 20, 2009 Location: Helena, AL Posts: 4,426	I'm also with Peetzakiller For rifles, if I can get the ES in the 30fps range, then the typical SD is below 10. When I get these numbers, accuracy is MOA or better. In the manual powder measure days, every rifle charge was weighed. Now that I've got Lyman 1200, all is measured. I haven't chrony'd any pistol rounds lately, but my 45LC loads group much better.

August 22, 2010, 11:12 PM	#19
FrankenMauser Senior Member Join Date: August 25, 2008 Location: In the valley above the plain Posts: 13,427	When recording velocities for actual use, remember not to count anything coming out of a clean barrel, either. I compared clean-bore shots to fouled-bore shots with two of my rifles, a couple weeks ago. The clean-bore shots were more than 100 fps slower than the later shots -- and in my .270, it took 4 shots before the velocity stopped climbing, and stabilized. Also keep in mind: Some powders are temperature sensitive. If you have your ammo sitting in the sun, while running these velocity strings... you're adding an additional variable, that won't be clear in your data. For example: In testing some Remington Factory 130gr Core-Lokts in my .270 for velocity and consistency, I had to take a 30-45 minute break, so my father could finish doing what the chronograph was actually there for. When I got back in the hot seat, the ammunition and rifle temperature had gone up almost 15 degrees (from 80 F, to 94 F). I was absolutely blown away, to see an average increase of more than 100 fps. The whole point of using a chronograph, for most shooters, is to identify and isolate variables - to create a better end product. But... if we forget about the variables encountered during actual testing, it's a futile effort. __________________ Don't even try it. It's even worse than the internet would lead you to believe.

August 20, 2010, 04:44 PM	#2
Ike666 Senior Member Join Date: October 10, 2009 Location: SW VA Posts: 491	There is no absolute answer to your question. However, as a general rule, "smaller is better." The standard deviation measures the dispersion of a group around the mean such that approximately 68% of your sample should be within +/- 1 SD of the mean. As a practical consideration it tells you how closely your shots cluster about the average MV. The tighter the clustering the more consistent the rounds are. The SD will also be affected by the total number of shots in your string (it is the average of the squared differences from the mean). The more shots you have, the lower your SD will be (typically). For a mean MV of 875 and an SD of 15, you'd expect 68% of your shots to be between 860 and 890 fps. The extreme spread is also a crude measure of dispersion, but it really tells you more about the effect of outliers on the mean. In simplest terms it is the difference between the High MV and the Low MV. Like the SD, the smaller the ES the better. An extremely high or low MV will "pull" the mean in that direction. Generally, any shot that is 1.5 SDs above or below the mean can be considered an outlier (not typical or expected). So, from the example above, a shot with a MV of 852 or less is suspect (short poweder load???). There is no absolute "test" of how much (or how little) SD is right. For a string of 10 shots an SD of 15 is pretty respectable.

August 20, 2010, 07:28 PM	#3
aiming fluid Member Join Date: July 1, 2010 Posts: 44	Thank you Ike for the information. I guess what I'm trying to figure out is how these numbers can help me with the quality of my ammo, and specifically, how does it match up against factory stuff. Since I don't yet own a chronograph, I haven't been able to chrony factory ammo to see how consistent it is. Here are the numbers from one of my loads: 45ACP 230 Grain Berry's RN 5.3 grains HP38 Low 694.5 High 733.9 Average 713.5 ES 39.37 SD 13.26 8 Shot string This group was one of three I shot with different powder combinations, and had the lowest SD. The other two were 16.8 and 23.7. I am a very meticulous reloader, and do try very hard to make the highest quality loads that I can. I used the same dies and techniques on all the loads: the only variable being the amount and type of powder used. The lowest and the highest SD's were with the HP powder, and the 16.8 was with bullseye. Have you experienced large swings in SD's for the same bullet with different powder charges (same powder, primer, case)? Any info is really appreciated as the chronograph seems to allow me to look at my ammo in a different light.

August 20, 2010, 08:20 PM	#4
Ike666 Senior Member Join Date: October 10, 2009 Location: SW VA Posts: 491	The way that I use SD & ES is as a consistency "score." In a perfect reloading situation, every round would go down range at the same MV - perfect reliability/consistency. Can't happen - there are too many variables that enter the equation. So, the SD & ES gives us a means to evaluate how close we are getting to the unobtainable ideal (0 SD, 0 ES). I think that the single biggest variable is not the weapon, bullet, or case but is the powder & primer. Just a little time lurking on this list and reading the discussions about favorite powders will quickly give you some insight into the wide number of variables that affect how powder effects your loads. However, of all of those, I suspect that powder metering is the biggest within a powder type. For example, I was a long time user of Unique for pistol loads. But in my press (Dillon 550) I get a natural variance in thrown loads that swings up and down several tenths of a grain. But with Power Pistol in the same press, I get much more consistent loads. This difference shows up in my chronograph data, specifically the SD & ES. Because SD & ES are dependent on the specific distribution from which they are drawn they really are not terribly useful comparing two powders to one another. About the only way you could approximate that would be to load for the same MV with two different powders (select a load for example that is intended to produce a consistent MV of 850 fps). Another way, and this is overkill, would be to collect a sample of SDs (shoot 10 strings with the same load) for each of two powders. Then you could convert the SDs to standard scores and compare them with something like a t-test. Like I said this is probably way over the top. In the final analysis, and assuming you are a reasonably proficient marksman, the real test is group size. Group size is dependent on a multitude of variables, all of which need to coalesce into a consistent and repeatable pattern. The load data is but one of those variables. If you are reloading to send more bullets down range, don't get too obsessive about load data. If your are shooting to maximize accuracy (e.g. benchrest) then all this becomes much more relevant. FWIW, your SDs seem about right to me. For fun shooting the TLAR principle works best (that looks about right). Tight groups.

August 21, 2010, 12:57 AM	#6
zippy13 Senior Member Join Date: August 23, 2008 Location: SoCal Posts: 6,442	Greetings aiming fluid and welcome aboard, As I recall my statistics, the power of knowing your SD and ES comes not from having a uniform method to analyze a sample's performance but as tool to predict the performance of future samples. To that end, I gotta go with peetzakilla on this one, data based on target impact is a better indicator than velocity, YMMV.

August 21, 2010, 07:07 AM	#7
FlyFish Senior Member Join Date: January 20, 2009 Location: Overlooking the Baker River Valley Posts: 1,723	In theory, the standard deviation is an inherent property of the population from which it is drawn and therefore should be independent of the sample size, i.e., should neither increase nor decrease with increasing sample size (more shots in the string). A shot that is +/- 1.5 sd from the mean would not be close to being considered an outlier by statisticians (about 14% of the distribution lies outside +/- 1.5 sd, so the probability that the shot is not from a different population is approximately 1/14100 = ~7%. The usual rule of thumb is +/- 4 sd, which would be a probability of about 0.1%, and some of the statisticians I work with would argue that even that isn't low enough. More importantly, distributions of velocities are inherently heteroscedastic, which means that the sd is correlated with the mean, so that you can't simply compare two sds and say which is "lower," nor is it possible to give a value for a "good" sd without knowing what velocities are involved. For example, you would expect the sd of a population of low-power pistol bullet velocities to be lower than the sd for a population of, say, .22-250 measurements. A better way to compare is to express the sd as a percentage of the mean, a statistic known as the coefficient of variation: sd/u100 = CV (where u is the mean). That said, I too tend to agree with peetzakilla. It's too easy to get wrapped around the axle with this stuff and if you're not a statistician you honestly don't really know what the numbers are telling you in any case.

August 21, 2010, 09:47 AM	#8
aiming fluid Member Join Date: July 1, 2010 Posts: 44	Thank you gentlemen for the outstanding information. You have given me much to ponder...... It still seems to me that there could be usable info gleaned from the SD and ES. As Ike explains it, these numbers ultimately gauge the consistency of your rounds, and it would seem to me that consistent ammo is important in any hopes of accuracy. Would it be safe to say that if your ES was 5% or less of your average velocity, the consistency of your ammo would be considered adequate? Thank you FLyFish for expanding my vocabulary. For the "unwashed Masses" here's a definition of heteroscedasticity http://en.wikipedia.org/wiki/Heteroscedasticity. It is a very cool word. Yup, I had to look it up. Also has anyone chronied factory ammo?

August 21, 2010, 12:27 PM	#11
farmerboy Junior member Join Date: May 16, 2009 Location: Central Texas Posts: 1,343	peetzakilla is right on, on both replies!

August 21, 2010, 09:02 PM	#13
Ike666 Senior Member Join Date: October 10, 2009 Location: SW VA Posts: 491	ditto on the Pizza Killuh - I also recently chronied some factory 357SIG loads. The only thing it did for me was tell me that my handloads were, um, "better." This was actually a little depressing b/c I thought I could use factory loads as some kind of standard. In the end, my handloads were faster overall, and they grouped better, had less felt recoil (very subjective), were quieter (also subjective), and generated less muzzle flash at EENT. I do think that running the factory loads through the 'graph was a worthwhile exercise. It gave me more confidence in my loading technique - even with the dreaded Unique powder. I was able to generate "factory" replica MVs best with a near-max load of Power Pistol. The SDs and ESs were also better but were not the deciding factor. BTW, FlyFish is on-target with his info. I still use to x1.5 SD to consider dropping a shot from the calculations - but that's my idiosyncrasy. Another technique is to drop the top and bottom quartiles if you've got a large enough sample - but I rarely shoot a string large enough for that.

August 23, 2010, 02:30 AM	#20
noylj Senior Member Join Date: October 21, 2007 Location: Between CA and NM Posts: 858	Standard Deviation S.D. just hasn't proven to be of much value in terms of predicting an accurate load. A truly accurate load (not a load that occasionally will produce a small group) will be accurate over a range of powder charge values. In other words, despite a variation in velocity, the harmonics of the barrel/gun are such that the bore direction is nearly the same over a range of velocities. This will be your most accurate load and a relatively large S.D. will not affect the accuracy much. This is where benchrest shooters work to find. Once this load is found, you can just throw powder by volume and not worry about each charge being ±0.3 gn or more. Now, Let's discuss S.D.: The S.D. doesn't mean anything without the mean value. You take the S.D. and divide it by the mean, multiply by 100, and get the Coefficient of Variance as a percent of the mean. In general, you want a CoV of 3% or less to consider a batch to be consistent, and even that depends on what parameter you are tesing. Of course, you really need to have a sample set of at least 20 values. The standard deviation is used to determine if, based on a sub-set sampling of units, do the units meet the specification requirement. The other use is when you make a change to one variable and you want to determine if the samples from the changed production lot are the same as the production lot without the change (the null hypothesis) or does it represent a statistically significant change in the tested parameter by running a t-test. The two main uses for a chronograph and the S.D. for velocity is to ensure that you are not significantly exceeding expected velocity (and you know you had better carefully inspect for high pressure) or if you will meet the target Power Factor for whatever game you are participating in. Your aim may be to ensure that your velocity is 2 standard deviation units higher then the required velocity to meet the power factor. You don't want too much velocity, but you also do want to fail and drop down to minor from major or out of the competition entirely. One other use I found was that some cartridges (those that run at 30-35k psi or higher) show an effect where, at max pressure, an additional increase in charge weight will not produce the expected increase in velocity. There is also the effect I found for the .38 special shooting a 148gn L-HBWC where a slight increase in powder would produce a large jump in velocity (generally with sudden pressure signs on the case, also). As soon as you see either condition, you know that you have reached the effective maximum for that gun and reload combination, and it is time to back off.

August 25, 2010, 12:04 PM	#21
RKG Senior Member Join Date: June 18, 2009 Location: Boston Posts: 562	As this thread demonstrates, you've asked a question that can generate complex answers and really complex answers. Whether you want to tumble into the subject of descriptive statistics (you can't really dabble in this subject), is up to you. However, here is a simple answer, so long as you don't ask any follow-ups: A) Load at least 10 rounds, using bullets and primers from the same box, powder from the same can, and brass with at least the same headstamp. B) Collect instrument velocities and compute mean and SD C) Ignore ES. D) Divide an SD derived from at least 10 samples by the mean derived from the same samples and express as a percentage. Less than 1% is good; between 1% and 2% is not uncommon and not bad; over 3% implies a fair probabilty that something is wrong that requires further investigation.

August 25, 2010, 12:07 PM	#22
temmi Senior Member Join Date: June 13, 2006 Location: Texas Posts: 531	Unless you have a large sample, the SD really is not helpful…. But the smaller the better

August 25, 2010, 06:45 PM	#23
aiming fluid Member Join Date: July 1, 2010 Posts: 44	Thank you members for your replies; outstanding info and great patience exhibited on my query. I did have the opportunity to go shooting with my chrony friend again today, and we evaluated some military .45 ACP with headstamps from the early 1940's. I will post the details soon as I tear the remaining bullets apart and get some pictures. One string of rounds had an SD of 8! Pretty cool for 67 year old ammo.