I am new to competitive shooting and reloading. I reload for my varmint rigs,223, 22-250). I am now reloading for a F-class 6.5/284, and read alot about ES and ED. How do you calculate ES and SD. I under stand extreme spread, the difference between the high and low velocity, but how do you figure standard deviation. Is it the average? My chrono is plan jane and only gives me velocity. Thanks guys for the help.
ES and SD
- Thread starter spadforme
- Start date
Hi,
Standard Deviation is basically the dispersion around the mean of the velocities. I figure my S.D. by using the windows calculator, just bring up the scientific view of the calculator. You need to go into the statistical mode, enter your velocities, then press the ave. button, then the S button to get the standard deviation. The following link might be helpful.
http://www.techbookreport.com/tutorials/stddev-30-secs.html
Good Luck,
Jack
Standard Deviation is basically the dispersion around the mean of the velocities. I figure my S.D. by using the windows calculator, just bring up the scientific view of the calculator. You need to go into the statistical mode, enter your velocities, then press the ave. button, then the S button to get the standard deviation. The following link might be helpful.
http://www.techbookreport.com/tutorials/stddev-30-secs.html
Good Luck,
Jack
Lets say you have a data set like 3204, 3222, 3216, 3200
First find the average:
Avg =,3204 + 3222 + 3216 + 3200)/4= 3210.5.
The variance,sigma squared) is the measurement of the squared deviations. The variance is calculated as:
σ^2 = {,3204-3210.5)^2 +,3222-3210.5)^2 +,3216-3210.5)^2 + 3200-3210.5)^2 }/4= 78.75
Finally, the standard deviation,sigma) is equal to the positive square root of the variance:
σ = SQRT,78.75)= 8.87
Hope this helps. You can do it in Excel too but Micro$oft uses the n-1 method,slightly different result best for large data sets). All you would do there is type in your data set and then use STDEV,A1,A2,A3,ect...).
Cheers,
DG
First find the average:
Avg =,3204 + 3222 + 3216 + 3200)/4= 3210.5.
The variance,sigma squared) is the measurement of the squared deviations. The variance is calculated as:
σ^2 = {,3204-3210.5)^2 +,3222-3210.5)^2 +,3216-3210.5)^2 + 3200-3210.5)^2 }/4= 78.75
Finally, the standard deviation,sigma) is equal to the positive square root of the variance:
σ = SQRT,78.75)= 8.87
Hope this helps. You can do it in Excel too but Micro$oft uses the n-1 method,slightly different result best for large data sets). All you would do there is type in your data set and then use STDEV,A1,A2,A3,ect...).
Cheers,
DG
Spadforme....
Too many folks in the shooting fraternity get hung up over the mystic of the term "Standard Deviation". Don't become one of them. If you want all your shots in one hole, cut your Extreme Spread to zero. EVERYTHING ELSE BEING PERFECT, that is where they'd be. Cutting your Standard Deviation to Zero may not win you any kewpie dolls. For example:
Shooting at, say, 1000 yards you could come up with one shooting load which yielded a perfect Zero Standard deviation and under perfect conditions put all bullets in the same hole. And then you come up with another load that also yielded a perfect standard deviation that shot nothing but high-low impacts.
In the first instance, all recorded shots could have been at exactly 3000 feet per second.....no deviation. In the second instance 1/2 of the shots could have been at 2000 feet per second and 1/2 were at 4000 feet per second....again no deviation, but a huge extreme spread.
So, what Standard Deviation is giving us is a statistical degree of Confidence in our results. In the first example we can be perfectly confident that All of our shots will be at 3000 feet per second. In the second example, we will again be perfectly confident that 1/2 our shots will be at 2000 feet per second and 1/2 will be at 4000 feet per second.
Anytime your recorded shots fall outside the above, or any other perfect set of conditions, the Standard Deviation will become larger and impacts will become more scattered. The actual SD number will be pretty meaningless and you will need to review your target along with individual shot speeds to come to any conclusions. Atomic Cowboy layed out the math formula. Try it at 10 shots at 2000 fps and 10 at 4000 fps. Then again at 11 shots at 2000 fps and 9 at 4000 fps.
Work first on getting your ES down and SD will follow. Then, if you are lucky or very very good, you will find a low ES-SD combination which groups your shots well.
Frank
Too many folks in the shooting fraternity get hung up over the mystic of the term "Standard Deviation". Don't become one of them. If you want all your shots in one hole, cut your Extreme Spread to zero. EVERYTHING ELSE BEING PERFECT, that is where they'd be. Cutting your Standard Deviation to Zero may not win you any kewpie dolls. For example:
Shooting at, say, 1000 yards you could come up with one shooting load which yielded a perfect Zero Standard deviation and under perfect conditions put all bullets in the same hole. And then you come up with another load that also yielded a perfect standard deviation that shot nothing but high-low impacts.
In the first instance, all recorded shots could have been at exactly 3000 feet per second.....no deviation. In the second instance 1/2 of the shots could have been at 2000 feet per second and 1/2 were at 4000 feet per second....again no deviation, but a huge extreme spread.
So, what Standard Deviation is giving us is a statistical degree of Confidence in our results. In the first example we can be perfectly confident that All of our shots will be at 3000 feet per second. In the second example, we will again be perfectly confident that 1/2 our shots will be at 2000 feet per second and 1/2 will be at 4000 feet per second.
Anytime your recorded shots fall outside the above, or any other perfect set of conditions, the Standard Deviation will become larger and impacts will become more scattered. The actual SD number will be pretty meaningless and you will need to review your target along with individual shot speeds to come to any conclusions. Atomic Cowboy layed out the math formula. Try it at 10 shots at 2000 fps and 10 at 4000 fps. Then again at 11 shots at 2000 fps and 9 at 4000 fps.
Work first on getting your ES down and SD will follow. Then, if you are lucky or very very good, you will find a low ES-SD combination which groups your shots well.
Frank
+1LongRanger said:
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Bryan Litz Ballistics
Site $$ Sponsor
Standard Deviation is a very useful number for quantifying velocity uniformity. Using ES, you're only using 2 of the shots in the group to quantify the variability of velocities. However, SD uses all the information available.
Here's an example of how to use SD to estimate velocity spread. Using 'Confidence Intervals', you can make predictions such as the following:
Let's say that a particular load has an average speed of 3000 fps, and an SD of is 10 fps.
1. You can say with 67% confidence that a future shot will be within +/- 1 SD of the average, in other words, between 2990 fps and 3010 fps.
2. You can say with 95% confidence that a future shot will be within +/- 2 SD of the average, in other words, between 2980 fps and 3020 fps. This 95% measure, the +/- 2 SD case, is the most commonly used for shooting since 95% is 19/20 shots.
3. you can say with 99% confidence that a future shot will be within +/- 3 SD of the average, in other words, between 2970 fps and 3030 fps.
Combined with a ballistics program, the above information can be used to predict how much vertical dispersion,due to velocity variation) can be expected with a particular load. For example, if the above example was for a Palma rifle shooting 155 grain bullets at 1000 yards, having a SD of 10 fps means that each shot has a 95% chance of being between 2980 and 3020 fps. This is roughly +/- 5" of vertical, which is 'X-ring' elevation,the X ring is 10" in diameter). Hence the common rule of thumb that an SD of 10 fps is the goal for LR shooting.
The above calculations cannot be done with ES alone. ES is not repeatable group to group, where SD is more repeatable. Furthermore, the previous post that said the SD of 2000 fps and 4000 fps shots was zero is incorrect. The SD of such a velocity set is 1054 fps.
ES is a good number to get the 'gist' of a loads potential. It represents something easy to understand, and should not be discarded. However, SD has it's place in shooting as well. It's not as obvious what it is, physically; and it's harder to calculate, but it allows you to make some pretty useful predictions.
-Bryan
Here's an example of how to use SD to estimate velocity spread. Using 'Confidence Intervals', you can make predictions such as the following:
Let's say that a particular load has an average speed of 3000 fps, and an SD of is 10 fps.
1. You can say with 67% confidence that a future shot will be within +/- 1 SD of the average, in other words, between 2990 fps and 3010 fps.
2. You can say with 95% confidence that a future shot will be within +/- 2 SD of the average, in other words, between 2980 fps and 3020 fps. This 95% measure, the +/- 2 SD case, is the most commonly used for shooting since 95% is 19/20 shots.
3. you can say with 99% confidence that a future shot will be within +/- 3 SD of the average, in other words, between 2970 fps and 3030 fps.
Combined with a ballistics program, the above information can be used to predict how much vertical dispersion,due to velocity variation) can be expected with a particular load. For example, if the above example was for a Palma rifle shooting 155 grain bullets at 1000 yards, having a SD of 10 fps means that each shot has a 95% chance of being between 2980 and 3020 fps. This is roughly +/- 5" of vertical, which is 'X-ring' elevation,the X ring is 10" in diameter). Hence the common rule of thumb that an SD of 10 fps is the goal for LR shooting.
The above calculations cannot be done with ES alone. ES is not repeatable group to group, where SD is more repeatable. Furthermore, the previous post that said the SD of 2000 fps and 4000 fps shots was zero is incorrect. The SD of such a velocity set is 1054 fps.
ES is a good number to get the 'gist' of a loads potential. It represents something easy to understand, and should not be discarded. However, SD has it's place in shooting as well. It's not as obvious what it is, physically; and it's harder to calculate, but it allows you to make some pretty useful predictions.
-Bryan
This example holds true when the SD is calculated for the population of all shots fired with the load, and under uniform conditions. Additionally, there is an assumption that the population is randomly distributed, and that special cause variation has been culled.bsl135 said:
For any string of a finite number of shots, and using the given SD as that of the population, what we can say is that the ES will be 60 or less with 99.4% confidence. Saying anything more about a three or five shot string is highly presumptuous. A 20 shot string will tend to conform to a random distribution, but only within the confines of sampling analysis. i.e., randomness is implied.
I agree.
.
Winchester 69, I am not trying to butt in however I just got my first chronograph and have been absorbing as much as I can about ES and SD. My rifle isnt a 1000 yard rifle but I do want to shoot at 600 when I can find somewhere nearby. I fired 20 rounds over my chrono and my ES is 35 and SD was 10. I am not sure what I can do to lower these numbers and I dont want to do too much because the load I am shooting groups great at 100. I just need access to more yardage to better evaluate the load.
but its still a good intro for the average shooter.CR, allow me to quote from Glen Zediker:crbrumbelow said:
I don't think standard deviation is near as important as the "range," which is the lowest and highest speeds recorded. ...extreme spread is the difference between this shot and the next shot. [Zediker is here making his own point, not defining ES.]
I watch the speed on every shot and do not wory about calculating a number to brag about or fret over, because that's about the ultimate function of knowing sd. There is no saying that a load that exhibits low standard deviation is going to group small, and I honestly don't think it's ever been shown that extremely low standard deviation is a divine bestowal of accuracy. I do know that it is no measure of accuracy, by any stretch.
Here's the payoff for you:
A tolerable sd is 12. Anything more than that is not good; anything less than that probably doesn't perform any, if at all, better than a 12.... One two. The twelvster. That's it.
I knew that'd make you feel good. :thumb:
Thankfully, Zediker's contribution to mathematics doesn't compare to what he's done for the English language. :tounge:
To illustrate this point, the following material is excerpted from his conclusion to the SD discussion.
I also thought about a device that numerically-challenged folk should pay atention to. My calculus tutor...told me that sometimes it's very helpful to picture something tangible of one's own devices to help understand the true values of mathematical high-falutations.
So, here's the way I look at standard deviations. I use the example of a large extra-pepperoni pizza, cut into twelve equal slices. Take six of the slices away at equidistant points and eat them. Now, take two more from each side, folding each of the two-slice sets over into pizza "sandwiches" and eat them. That leaves two slices remaining along the vertical axis. Eat those. Do this at midnignt and then go to bed. You will then wake up at three o'clock in the morning in a cold sweat after dreaming that you've just caught what should be the game winning touchdown pass in the Superbowl, and, with seconds remaining, are ten yards from the endzone with only Elton John standing between you and all the better endorsements, and you are afraid to hit him. Calculating why makes no sense and the entire endeavor wasted the better part of an otherwise restful evening.
Quotations taken from Handloading for Competition: making the target bigger.
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Fred Bohl
Gold $$ Contributor
Monte
I've attached the histogram from the article you provided as a sample of a real but NOT NORMAL distribution and the NORMAL but not real distribution.
These illustrate quite simply the risk of assuming normal distribution and putting too much faith in SD.
I've attached the histogram from the article you provided as a sample of a real but NOT NORMAL distribution and the NORMAL but not real distribution.
These illustrate quite simply the risk of assuming normal distribution and putting too much faith in SD.
Attachments
memilanuk
Gold $$ Contributor
Fred,
Interesting. I look at that as a good example of how +/-2 SD covers pretty much everything you would normally care about, regardless of the 'dip'. +/- 3 SD gets you the extra 4.7% to get you out to 99.7%
I see people get way too excited over a short string of shots with an ES of say, 19 but and SD of 6. Their ES is under 20, so they are ecstatic. They don't seem to grasp that all they measured is a small sample. The SD indicates that their long term ES for the total population,all the shots fired from that barrel with that load) will be something in the mid 30's,or higher) per the +/-3SD, but they don't want to hear that. The more shots you fire, the closer you come to a normal distribution, and the more closely SD applies. A person can fool themselves into believing that it doesn't by only shooting short strings,samples) and only looking at each sample, not the overall body of data...
Anywho, do as you like.
Interesting. I look at that as a good example of how +/-2 SD covers pretty much everything you would normally care about, regardless of the 'dip'. +/- 3 SD gets you the extra 4.7% to get you out to 99.7%
I see people get way too excited over a short string of shots with an ES of say, 19 but and SD of 6. Their ES is under 20, so they are ecstatic. They don't seem to grasp that all they measured is a small sample. The SD indicates that their long term ES for the total population,all the shots fired from that barrel with that load) will be something in the mid 30's,or higher) per the +/-3SD, but they don't want to hear that. The more shots you fire, the closer you come to a normal distribution, and the more closely SD applies. A person can fool themselves into believing that it doesn't by only shooting short strings,samples) and only looking at each sample, not the overall body of data...
Anywho, do as you like.
Good info Winchester. I think I am gonna try to narrow my ES more and by what I have seen SD has to follow. I use Lapua brass Varget CCI BR2 primers and 168 gr Berger VLD. The hotter the charger the better my rifle likes it. I am at 46 gr. of varget which is max by the book and this is fine because I am really just tweaking a hunting load down to see how small it will shoot. I seat the bullet on the lands and its pretty firm contact so I set my seating die to seat the bullet .005" deeper to see if maybe land contact is too much. We'll see.
CR, Let your targets tell what is necessary. If your lateral dispersion,windage) is greater than the vertical dispersion, what are you improving? Longer distance shooting will tell the story.
As an addendum, maybe this will interest you:
www.snipershide.com/forum/ubbthreads.php?ubb=showflat&Number=725031&gonew=1#UNREAD
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As an addendum, maybe this will interest you:
www.snipershide.com/forum/ubbthreads.php?ubb=showflat&Number=725031&gonew=1#UNREAD
.
Good info I’m also new to reloading and long range shooting. I got my best load down to 8 sd and es of 23 With a .467 Moa at a 100yards. I think you guys are missing the point of having a low sd #.you can have a sd of 2 and es of 6 in a group. And all of that doesn’t matter if your leaving out moa.If your gun doesn’t like that ghost of a perfect sd or es. Why does it matter. Well that’s my two cents worth up on the soap box.
jepp2
Gold $$ Contributor
My Chrony gives me both, but when I shoot round robin I have to calculate them myself. I just created a simple Excel spreadsheet that I use to input the velocities. It calculates them using the same formulas as my Chrony. PM me if you want a copy.
10 year old thread, spad looks long gone, lol
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