Standard Deviation (SD)

[Rizzo]

I use a chrono on my ladder tests and do not understand the SD number I get and how to interpret it.

Wikipedia says it is the square root of the variance in data points.
What?

Can anybody give me an explanation that is understandable about how or what SD is, in regards to interpreting the chrono results?

Thanks

[micro911]

I think this article explains it in understandable terms.

http://www.rifle-accuracy-reports.com/chronograph.html

[bsumoba]

In simplistic terms, SD will be close to about half of your ES, which is your "Extreme Spread," meaning the difference in your highest and lowest velocity recording.

Most people will shoot for a single digit SD number if they are shooting precision competition like F-Class or Benchrest or something similar, or they just like to get a consistent load. Most people in turn, will shoot for an ES that is low-mid teens or less for precision shooting. This is what I shoot for. Most factory ammo will most likely be in the 20-50+ fps extreme spread range.

My 6 dasher is currently sitting at a SD of around 5 and ES of 12 fps for 5 shots.
My 284 Shehane has a SD of around 8 and ES of around 15 fps for 5 shots.

The reason this is important is one, it tells you if your ammo is consistent from round to round, whether it is factory ammo or handloads. Second, it generally helps at long distances and results in better vertical dispersion, which is a big thing that long range shooters look to minimize.

The way to lower SD and ES is to have a good shooting rifle and to have the upmost consistency in your handloading (how you prep the brass, bullets, seat primers, weigh powder, etc). If you are shooting factory ammo, then you are stuck with what the manufacture can produce. Most quality, match ammo I have seen from the factory will usually be around the mid-/high teens to high 20's for ES.

[QuarterBoreGunner]

In layman's terms, SD will be close to about half of your ES, which is your "Extreme Spread," meaning the difference in your highest and lowest velocity recording.

Most people will shoot for a single digit SD number if they are shooting precision competition like F-Class or Benchrest or something similar, or they just like to get a consistent load. Most people in turn, will shoot for an ES that is low-mid teens or less for precision shooting. This is what I shoot for.

My 6 dasher is currently sitting at a SD of around 5 and ES of 12-14 fps for 5 shots.
My 284 Shehane has a SD of around 8 and ES of around 15-16 fps for 5 shots.

The reason this is important is one, it tells you if your ammo is consistent from round to round, whether it is factory ammo or handloads. Second, it generally helps at long distances and results in better vertical dispersion, which is a big thing that long range shooters look to minimize.

Nicely stated.

[Divernhunter]

To add to that I have several hunting loads that are higher SD but more accurate than other same bullet loads with a lower SD.

Single digit loads are usually excellent but many very accurate loads are in the teens and sometimes very good one are in the 20's. His is probably more so with hunting bullets and loads. That said I do love it when I get a SD of under 10

[bsumoba]

To add to that I have several hunting loads that are higher SD but more accurate than other same bullet loads with a lower SD.

Single digit loads are usually excellent but many very accurate loads are in the teens and sometimes very good one are in the 20's. His is probably more so with hunting bullets and loads. That said I do love it when I get a SD of under 10

Agreed.

Low SD and ES, like I mentioned, will generally get you better vertical dispersion at longer ranges, but is only a piece of the puzzle. Normally though, if you have a load that is shooting great groups at 100 yards and has low ES/SD, then chances are good that you have a load that will shoot well out to even 1000 yards.

If you are a hunter or recreational shooter, my suggestion would be to go on JBM, take your atmospherics and plug it in, then plug in your lowest velocity and then plug in the highest velocty recorded and see what kind of drop (theoretical) you get at certain distances between the two. If it is within the range that is acceptable to you, then run with it. Remember, JBM is only theoretical......

[LynnJr]

SD or standard deviation is a waste of time.
Extreme spread will give you your vertical from your load while standard deviation tells you nothing of use.

[Fjold]

Simplistically in shooting terms:

It's a measure of the variation in velocity from the average velocity of all the shots.

[cindynles]

Standard Deviation is a statistical method used to tell you how much your load will move off your average. In very simple terms you use it for the following:

- 68% of your ammo will be within 1 SD of your average
- 95% of your ammo will be within 2 SD of your average
- 99% or your ammo will be within 3 SD of your average

So for example if your data shows 1000 fps with a SD of 5 fps:
- 68% of your ammo will be between 995 and 1005 fps
- 95% of your ammo will be between 990 and 1010 fps
- 99% of your ammo will be between 885 and 1015 fps

[Fjold]

SD or standard deviation is a waste of time.
Extreme spread will give you your vertical from your load while standard deviation tells you nothing of use.

What if you're extreme spread is due to one reading?

If you shoot 100 rounds and 99 0f them are with 1 fps of 3000 fps and the one other round is at 2900 fps your extreme spread would be 100 fps but your SD would be about 1.

Then take the case where 50% of your rounds are at 2900 fps and the other 50% are 3000 fps. Your extreme spread is the same 100 fps but your SD is huge.

[LynnJr]

If you have four rounds at 3000 fps and one round at 3010 fps you have 4 good rounds and one round ruining your group.
If you look at the mean and the standard deviation you would think your ammo is good when it isn't.

As nobody shoots 100 round groups with 100 feet of variation I don't have an answer for your hypothetical question.
That said your slowest round and your fastest round tell you your vertical spread all else being equal so standard deviation is just a waste of time in my humble opinion.

[Fjold]

If you shoot a ten shot group for score at 1,000 yards with 9 rounds at 3,000 fps and one round at 2900 fps you get 9 Xs and a 9 for a score of 99

If you shoot a ten shot group at 1000 yards with 5 rounds at 3,000 fps and 5 rounds at 2900 fps you get 5 Xs and the other 5 are 9s for a score of 95.

The same extreme spread but different SDs and different scores.

[Fastattack]

Standard Deviation is a statistical method used to tell you how much your load will move off your average. In very simple terms you use it for the following:

- 68% of your ammo will be within 1 SD of your average
- 95% of your ammo will be within 2 SD of your average
- 99% or your ammo will be within 3 SD of your average

So for example if your data shows 1000 fps with a SD of 5 fps:
- 68% of your ammo will be between 995 and 1005 fps
- 95% of your ammo will be between 900 and 1010 fps
- 99% of your ammo will be between 885 and 1015 fps

This. If you aren't into math then don't worry about it. However it is very useful.

[Thoughts]

If you have four rounds at 3000 fps and one round at 3010 fps you have 4 good rounds and one round ruining your group.
If you look at the mean and the standard deviation you would think your ammo is good when it isn't.

I'm not sure how you define "good ammo" but the standard deviation is about 4.5 fps for your example. The standard deviation tends to be more useful with larger data sets, but I don't know how large the average sample size is for reloading.

[bsumoba]

If you have four rounds at 3000 fps and one round at 3010 fps you have 4 good rounds and one round ruining your group.
If you look at the mean and the standard deviation you would think your ammo is good when it isn't.

As nobody shoots 100 round groups with 100 feet of variation I don't have an answer for your hypothetical question.
That said your slowest round and your fastest round tell you your vertical spread all else being equal so standard deviation is just a waste of time in my humble opinion.

I think a 10 fps ES is great!