Standard Deviation and Spread Question

[rwt]

When dealing with springers and nitro pistons, I'm curious as to what SD is considered good or indicative of a healthy gun?  Also, I've heard some say the spread is a better indicator of gun health.  If that's true, what percentage of avg. velocity would be considered healthy for spread?  What are the key indicators that show that a gun needs a rebuild or seals, etc.?  Yes, I've searched the forum and found bits and pieces of information, but nothing that addresses what I'm asking concisely and directly.

Another observation that I find curious is that the pellet that my RWS 52 shoots most accurately doesn't have the lowest SD or spread of all pellets tested.  It's sort of in the middle of the pack. 

Presently, I'm evaluating a Crosman Vantage NP refurb that I received.  After roughly 300 pellets, it's shooting 125 - 150 FPS slow no matter what pellet is selected, the SD ranges from 10 - 22, and the spread is 5 - 7 percent of average FPS.  SD on my RWS 52 ranges from 3 -8.  With 30 days to evaluate if the Vantage is really in refurbished condition, any assistance would be helpful.  I have no desire to rebuild a gun that is supposed to be factory refurbished.  If it needs that kind of work, they can have it back.

[TC]

A spread in the 15-20 fps range has only impacted my precision on longer distances, say past 35 yards. One unexpected observation on my springers is that when I changed lubes from moly to Krytox, I saw significant reduction in velocity spread of 30-40%. With Krytox grease, my Stoeger X20S now posts a 10 shot spread of 8, and a 20 shot spread of 11. If your rifles are new, clean the barrel and take some shots to condition the barrel and break in the moving parts.

[rwt]

The first thing I did was clean the barrel before firing any shots.  I fired 50 - 100 pellets before taking any measurements whatsoever.  Is that adequate?

[TC]

The first thing I did was clean the barrel before firing any shots.  I fired 50 - 100 pellets before taking any measurements whatsoever.  Is that adequate?

I would say more than enough. I fire off about 25-50 shots in between pellet changes or barrel cleaning with good results.

[Booger]

I usually fire at least 1000 pellets before I do any chrony testing. You want to break in the rifle and spring before the tests really mean anything. Also leading of the rifle helps accuracy. JMHO 

[QVTom]

A good and healthy gun will produce an ES of less than 10 and will spread the deviation evenly throughout the string.  Guns that have an ES of of greater than 10 and less than 20 can still shoot very well but is a sign that some improvement is possible through a good tune.

A gun that gives a good ES for several shots and then produces a a wildly high deviation is most likely over lubed and/or may have a marginal piston seal.  Every few shots some amount of lube is passing the piston seal and burning off.  When the excess has burned of the ES will stabilize until another slug of lube passes the seal.

A gun that shoots all shots with wild deviation most likely has bad seal, broken spring and/or a lube problem and needs to be tore down and sweetened up.

Magnum springers generally have larger deviations than the low or mid-range guns.

Tom

[MicErs]

Question for all the old timers here,  "Pellets, both weight variation and bore seal don't impact SD?"

[DOKF]

Question for all the old timers here,  "Pellets, both weight and bore seal don't impact SD?"

I have looked at the SD of pellet weight and diameter, and compared them to both SD of velocity and momentum for my rifles.

Some of the pellets I tested had a correlation between weight and momentum, or weight and velocity, others correlated diameter and momentum.  Most pellets I tested did not correlate at all.

[MicErs]

Question for all the old timers here,  "Pellets, both weight and bore seal don't impact SD?"

I have looked at the SD of pellet weight and diameter, and compared them to both SD of velocity and momentum for my rifles.

Some of the pellets I tested had a correlation between weight and momentum, or weight and velocity, others correlated diameter and momentum.  Most pellets I tested did not correlate at all.

Have you ever compared SD for the same pellet with and without sizing the skirt?  It seems to me that a sizing tool (pellet seating tool used to spread the skirt before loading) reduces the velocity SD substantially.

[DOKF]

Yes, I've checked wt against vel without sizing, and wt + dia against vel.

Have not checked dia without wt against vel.

I found in most cases that the SD for vel was greater than the SD for wt or dia.  In some select cases the pellet vel had a strong correlation to wt, such that momentum and wt correlated.

After all that, I looked at 15 m accuracy (limit of my back yard range), and found insignificant practical correlation between wt~momentum and accuracy.  I could still hit quarter sized objects with most pellets.

[rwt]

Thanks for the replies so far.  I was hoping for a simple "rule of thumb" that could be applied such as: A healthy springer/nitro should have a SD of 10 or less, and a spread of 3% (or less) of Avg. velocity.  This is assuming that pellet deformation, or some other pellet problem isn't the cause of a poor SD or large spread numbers.  Is something like this true and available?  The reason I put it in terms of a percentage of average velocity is that it has been stated that a spread of 10 for a gun shooting 500 FPS is quite a bit different than a spread of 10 for a gun shooting 980 FPS.

[HYspd]

spread of 10 at 500 is 2%...10 at 980 is 1.020408163264% (I'm plenty sure that calling it 1% is acceptable, but the math jocks out to get a kick from the power of 2 progression of the factional reaminder)

[Scotchmo]

When I see an SD of 1% for muzzle velocity, I'm happy.

[SagaciousKJB]

I had a lot of questions about this too when I first heard the 10 rule of thumb as well.  Now, what I learned, I soon found myself way over my head in theory of statistical analysis...  And actually way down the line in a digression of used oil analysis.

Long story short, I believe the rule of 10 to be applied to "Standard Deviation" in a way without sufficient information to really be valuable at all.  What I mean is that, if the statistical data you feed comes back with a Standard Deviation of 10 that isn't a mathematical formula that can tell you the health of your gun, it's simple a statistical analysis of the data you input and nothing more or less.  You have to know how to interpret it.

Standard Deviation comes back to something called "sigma" or something or other...  Like I said it was way over my head.  What I basically concluded though is that what you're trying to measure here is predictability.  Most people when they think of an average, they think "Well that's what it's going to be most of the time."  That's not what an average actually is, it doesn't figure into odds.  The rule of sigma or whatever they call it says that you actually need at least 30 some odd points of data, and three sets of data, to actual form a statistical prediction, but that once you do the standard deviation essentially becomes a "factor" by which your highest or lowest expected value can be expected to well, deviate from.

I actually found a forum for powder burners and was talking about handloading.  Basically what they were trying to measure from the data was what the actual lowest muzzle velocity they could predict with great certainty.  So they would input their chronograph numbers, then get the standard deviation...  This is where it gets weird.

Say that after a string, their average muzzle velocity is something like 1600 fps but they have a standard deviation of 10.  What the sigma theory actually dictates, is that the lowest velocity you could predictably count on is going to be three times less feet per second than the Standard Deviation.  So if you have an SD of 10, you would multiply that by 3 to  subtract 30 fps from the average and you could expect that 90% of the time you're going to be at that velocity or greater.

So when you think of it like that it starts to show why a larger standard deviation is indicative of poor health, because what it actually means is that if you have an SD of 10, you can actually count on the pellet coming out of the barrel at 30 FPS lower than your average--higher numbers and the predictability starts to fall off.  Thats good information to have, because if you have a large spread and don't know whether to count on the lowest velocity or the highest, the standard deviation may show you a happy "middle ground" and is essentially a statistical function to find the most predictable number--some people think that this is what the average is for, but without falling on my face trying to explain that just trust me it's not.  If a good predictable number can't be found, that's a good indication something is wrong because it means the data entered is too inconsistent.  When that's relative to muzzle velocities, that's when you can infer there is a problem.

Only problem is it counts on more than just one set of data to work right.  You need at least 30 data points, and at least 3 sets of data for it to actually make certain predictions.  When you see people talk about the numbers they run, and you see only 5 or 10 shot groups that figure for Standard Deviation may not really be representative of anything we expect it to.  All it means is out of the data given, it's just a way to figure out which value is the most likely to show up.

Now take all that with a grain of salt because like I said I'm not sure if I got it all right, but what I gleemed is basically that the Standard Deviation is less of a formula-based number like an average or a mean, but more of an actual statistical-analysis tool.  Without proper knowledge of how to use it and how to apply it, there's also not knowledge of how to properly interpret it.  But for our purposes, I'd be comfortable saying not that a low standard deviation is an indicator of good health, but that a HIGH standard deviation is an indicator of inconsistent velocities--and like someone else said that could come down to things like pellet fit.  Don't think anything more or less should be inferred, especially not without heaps and heaps of data--way more than just a 10 shot string.

[DOKF]

Standard deviation (sigma, stdev) is a mathematical tool to predict probability of an outcome based on a small sample of measurements.  Normal distribution is based on a probability of 97% of data occurring within +/- 3 stdev of the mean.

The more data used to calculate stdev, the more accurate the prediction of outcome for "true" normal distribution.

With a small sample size, it is often simpler to just measure the range of values, min ~ max.  With a larger sample, the stdev can be used to determine if high or low values are "fliers" that can be ignored, or statistically legitimate values that have to be to be considered in further calculations.

[MicErs]

Read the thread, none of it seems to be directly answering your question.

So here is an answer... (Executive Summary)
Ok, so what is a small SD? I'd say 2% +/- is probably suboptimal, 1.5% +/- is acceptable, 1% +/- is good and 0.5% +/- is exceptional.  If I could not get any pellet to hold an SD of +/- 2% in my rifle, it would be troubling.

Here is why I chose these values...  (Details)
When you take the SD of a list of shots you are measuring the distribution of those shots around the average velocity, or energy, or whatever it is about those shots you are measuring.

You can't know whether that number whether large or small may be telling you more about the pellets you are shooting than the gun you are using.  Crappy pellets may give you a large SD, even though everything is just fine in your rifle. On the other hand a small SD tells you that neither the pellets nor the gun are preforming poorly.  Why?  If the gun is performing poorly it will show up in the SD.  If the pellets are performing poorly it also will show up in the SD.  If both are performing poorly it will REALLY show up in the SD; however, both of them have to be performing well for the SD to be small.

So what is a small SD?  One responder said he liked 1% of the average velocity.  So a pellet launched at an average velocity of 800 ft/sec would show an SD of +/- 8 ft/sec.  That sounds pretty good to me but what does it really mean?

It means that 68% of the shots fired will be inside the range of 792 ft/sec to 808 ft/sec.  That is "one sigma" or "one standard deviation".  If the standard deviation is 8 then two times the SD is 16 ft/sec.  That is "two sigmas" or "standard deviations".  Ninety five percent of the pellets shot will be shot within the mean plus or minus two sigmas.  So if the SD is 8 and the average velocity is 800 then 95% of shots will be between 784 ft/sec and 816 ft/sec.  Now it turns out that 99.7% of the shots fired will be within three sigmas.  For our example there is a 99.7% probability that any shot fired will fall within the range 774 ft/sec and 824 ft/sec.

Ok, so what is a small SD? I'd say 2% +/- is probably suboptimal, 1.5% +/- is acceptable, 1% +/- is good and 0.5% +/- is exceptional.  If I could not get any pellet to hold an SD of +/- 2% in my rifle, it would be troubling.

[nervoustrigger]

Seeing some examples here where an extreme spread of around 20fps is deemed to be reasonable, that would amount to only 2.5% for a rifle shooting a 14.3gr Crosman pellet at 800fps. 

At 50 yards, that would amount to a difference in elevation of 0.07".  Best wishes on shooting a springer well enough to detect that 1/16 of an inch.

[SagaciousKJB]

Interesting, I just loaded up some spreadsheets I made for my Kodiak.  Had to use a microphone as a chronograph so the numbers might not be very accurate.

Code: [Select]

Seconds Velocity
0.00453 699.043414275202
0.00451 702.143385070214
0.00444 713.213213213213
0.00443 714.823175319789
0.00435 727.969348659004
0.00458 691.411935953421
0.00453 699.043414275202
0.00448 706.845238095238
Average Standard Deviation
706.811640607661 11.541532164629


Code: [Select]

Seconds Feet Per Second
0.00404 742.574257425743
0.00406 738.916256157635
0.00422 710.900473933649
0.00414 724.63768115942
0.00409 733.496332518337
0.00412 728.155339805825
0.00408 735.294117647059
0.00407 737.100737100737
0.00401 748.129675810474
Average SD
733.244985728764 10.9495944439966


Code: [Select]

0.00426 704.225352112676
0.00403 744.416873449132
0.00419 715.990453460621
0.00423 709.219858156028
0.00417 719.424460431655
0.00412 728.155339805825
720.238722902656 14.4485987419213

Then check out the .177...

Code: [Select]

Shot End Shot Start Time Velocity
31.43764 31.434625 0.003015 995.024875622627
55.650135 55.64712 0.003015 995.024875622627
18.77503 18.771905 0.003125 959.999999999782
45.60621 45.60313 0.00308 974.025974026896
11.929085 11.92586 0.003225 930.232558139397
40.56219 40.559035 0.003155 950.871632329764
2.207145 2.20409 0.003055 981.996726677497
34.485475 34.482435 0.00304 986.842105263613
58.798399 58.79499 0.003409 880.023467291201
18.868185 18.864975 0.00321 934.579439252549
Average Standard Deviation
958.862165422595 36.291257105228
Now the itneresting story behind this is that even though when hunting I could not get the trajectory of the .22 out to hit pests, it would group a lot tighter than the .177 pellets.  Looking at the .177 pellets with a Standard Deviation of 36 and that starts to make sense...

The other interesting part is that there were couple of shots in the .177 string that came in pretty low, like 870, I took those out thinking they were just flyers from bad pellets.  Interestingly though if I take 958 minus three sigma I get 850 and 1066.

Since mine is a mutli-caliber platform it's easy for me to conclude the .177 pellets are not as consistent as the .22.  Also pretty easy to tell this by how random the fit int he barrel for the .177 is.

But what about the three data sets for the .22?  On the first two the stdev remains about the same, but the average velocities are pretty different.  Third one the average velocity is closer to the second, but then the SD goes way up.

[Rex]

My earlier reply doesn't seem to have been posted, so I'll try again.

You asked a difficult statistical question which came up in my days with TVA while monitoring environmental radiation, "how confident am I that two measurements of the same event are significantly different", as opposed to the usual "how confident that the event is greater than zero."  A rough rule of thumb turns out to be about 5 SD's.

Assuming that your two rifles should have very similar performances it looks like the measured values are truly significantly different.

[rwt]

Assuming that your two rifles should have very similar performances it looks like the measured values are truly significantly different.

Not only am I considering my other rifle, but I have personal experience with a springer version of the Vantage, and we have posted FPS measurements of the Vantage NP from others here on the forum.  My refurbished Vantage NP seems to be significantly different than all rifles in consideration since it only shoots a 7.9 gr. pellet at 760 FPS.  I would expect a healthy .177 rifle that advertises 1200 fps to shoot in the low to mid 900's with a 7.9 gr. pellet.  The slow shot performance along with SD's ranging from 15 - 22 makes me think that this rifle needs to go back to Crosman so they can truly refurbish it.