Brent,

I am very intrested.  I think it depends on what match you shoot. Mimimum Group size is very important to the bench rest shooter particularly if shooting re-entry matches.

But I try to only shoot the Hudson 100 shot offhand match.  I think Standard deviation is the best measurement to determine potential scores and more important see what is required to improve.

Although many years ago I had one Statistics class Most of what I know about SD as it relates to shooting is from " The Russian Book"  Competitive Shooting by A.A. Yur Yev.  He does not call it SD but Bullet Dispersion.  Yur Yev makes the case for a analysis of targets on departure from the center.

Couple of years ago I took my 10 10 shot Hudson postal targets and overlaid them one by one on a fresh target. I put a pencil mark in the center of each hole. Then I took a hole puncher about bullet size and punched out all 100 shots.

It it intresting to look at and could be measured and analizyed. So far all I have done is figured the center of impact and size of the group in total and for the majority of shots as Yur Yev recomends.

I droped my P/S subscription a few years ago but will try to look that one up. And anything you post on the subject I am sure will be interesting

Boats

This post is not a disputation of anything, rather just a statement of thought on this subject. I am certainly a believer in science and in statistical analysis but there is a nagging memory when it comes to applying them to cartridges and rifle performance, etc. For probably twenty-five years the world of modern BR shooting was ruled by the .222 Remington (only to be displaced by the PPCs). The .222 was not (according to much I have read) a low SD cartridge and yet delivered extreme accuracy. The PPCs ARE better in terms  of SD, yet beat the older round by only a tenth or two of minute of angle (and I know that is more than enough in BR competition). I guess that where I am going with is that the proof still remains in the shooting.

PS: If anyone knows from actual shooting experience that what I have read re: the .222 Rem is incorrect, I would llike to know.

DonH,
Your comments are entirely correct in so far as small SD's in some measures are no guarentee of high scores.  This is especially true when measuring velocity.  For a good example, you may find that you can achieve a near zero SD with regards to velocity when shooting an 800 gr bullet out of a .38-55. But obviously, there is little chance that it will be accurate because a bullet that long will probably not be stable once it leaves the muzzle.   

But suppose we are to measure SD's for the radial dispersion of a group shot at a target.  The article I indicated describes this rather well - but it's sorta like doing a string measure, only rather than measuring from the center of the target, it's measured from the center of the group.  A small SD in this case is a good  indication of precision.  In fact, it is proof of a level of precision.  Nonetheless, if the group was shot ignoring the wind, or with the sights consistently misaligned or any of a host of other things, it may well be that this very precise group (small SD) is off in the 17 ring on a 25 ring target - in other words a great group in the wrong place.   

How many times have you said, "if I just centered that up on the target, it would be a great score"?  Happens to me all the time because I screw up with regards to one or more steps along the way.   

So, SDs are just a tool that helps, but not a magic cure all that will instantly make you into a world-class shooter.  Accuracy on the target is the summation of a huge number of variables and steps, each one having some degree of influence on the final outcome.  And while one or two of those steps may be executed close to perfection, if the rest of them are done poorly, the result is bad scores.   

So, never confuse a smaller SD with a guarentee of higher scores, but rather with having improved the steps involved in that one process that is being measured.   

Brent

I started analyzing my groups (or maybe patterns) years ago, when a fellow schuetzen addict and I took a couple of university courses in statistics.  Here is our method.  If you have an Excel (or other) spreadsheet it saves time.   

Lay or construct a grid over your target. A T-square & triangle will be helpful.  If you are shooting at a bull, it may better not to use the bull or x-ring as the center of the grid.  Just number the bullet holes and assign them horizontal (X) values and vertical (Y) values from an arbitrary point (the center of the grid).  I use inches & 1/100s for my measurements, but anything should work as long as the measurements are consistent from hole to hole.  The mean of the Xs and the mean of the Ys will give the X & Y coordinates for the center of the group.  Then compute the difference between each individual X and the mean X and the difference between each individual Y and the mean Y.  Then square each difference (individual X and corresponding individual Y), add each pair of differences together, and take the square root of each pair.  (The Pythagorean Theorem revisited).  That gives you a measurement of radial dispersion from the center of the group.  Now calculate means & SDs on the radial dispersion figures.  I use this to evaluate the effects of changing lubes or powder charges, or just about anything else.

I think one of the first things to understand about Standard Deviations is that they are a measure of the variability of whatever it is you are measuring.  Whether it's distance from the center of a group for each shot, or the velocity of each shot, the SD is the measure of the amount of variability.  The square of the SD is called the VARIANCE and it is similarly a measure of the variability of the measure.  If you know SD then you know Variance, so let's just stick with SD as they tell you exactly the same thing.   

Below is a sample of something that you might find when using your chronograph.  These two strings produce the same average velocity.  They both produce exactly the same ES too.  But you can see that the SDs are considerably different.

        Load #1      Load #2
     1282      1282
     1307      1301
     1298      1302
     1295      1303
     1307      1300
     1306      1301
     1293      1302
     1305      1302
     1307      1307
Average      1300      1300
St. Dev      8.233      6.633
E. Spred      25      25

Now, of course, there is no way of knowing which of these loads will shoot best, but first indications are that the second load is more predictable from shot to shot that the first load.   

The bottom line is that ES does not contain much information, it is also highly sensitive to sample size (number of shots per load or group), and does not well characterize the precision (repeatability) of whatever is being measure.

Of course, you can often get by using ES because they tend to run the same direction more or less as SD, but because they are less informative, when you are trying to make small improvements, ES can be very misleading and even SD can sometimes not be as perfect as you would hope. 

I'll try to post something about how to statistically determine if two loads are shooting differently in another post.

Brent

Waterman, 
I really don't follow much of what you posted.  There is a historic connetion between Guinness beer and a well renowned statistician, but frankly, in the big picture of stats, it doesn't go very far.  And it had even less to do with counting beer drinkers.   

That aside, I'm willing to wager that anything you feel will make a 0.005" difference in group size is really just a figment of your imagination and not actually happening in the real world.   

And that is the problem with folks that do not understand nor use statistics.  Many are happy as clams and many will out shoot me, but they would shoot even better and be even happier if they used statistics constructively.

There are two basic errors to be dealt with when using statistics.  Not surprisingly, they are called Type 1 and Type 2 errors.   

As we all know, any of us will shoot two targets with ammunition as perfectly indentical as we can make it, under conditions as unchanging as we can hope for, and with technique that is as unwavering as possible, and yet get two very different results.  Why is this?  pure chance is of course the simplest answer and easy to understand.  A rifle/ammo/shooter/conditions combination that averages 1 MOA will not shoot exactly 1 MOA every time.  That is the nature of the beast and the reason why we need statistics.

So, what are these types of errors that we need to avoid?  Type 1 (T1) is the most commonly considered.  It is the probability that the difference in two observations (think of them as two different targets shot with two different loads) are in fact, the result of a true difference.  That is they really do perform differently and the difference is not just pure chance.  Statistics, in it's most precise definition can tell us that the likelyhood that the two observations (targets) have the same properties (come from a system with the same accuracy), is of a given probability.  If that probability is small enough, we might conclude that they are, indeed different, and proceed from there.  If the probability is not especially small, then we might be wary of concluding anything.  We could decide to test some more or to decide that they are the same.   

Type 2 (T2) is the probability that the two observations are indeed different, but we can't see detect the difference.  This is less commonly considered explicitly, but here is an example.  Suppose that you have two loads that differ only in primers.  But the loads, or the rifle, or you or the wind when testing, are not particularly good so that both loads shoot in the neighborhood of 4-5 MOA.  If one of those primers is actually contributing a 0.25 MOA inprovement in accuracy, you are not likely to detect the difference under these conditions unless you shoot extremely large numbers of targets.   

On the other hand, suppose your normal load and shooting system is running right around 1 MOA and now you make that same change of primers and get that 0.25 MOA improvement.  Now, in relatively few targets, you will be able to detect that difference with a high degree of confidence.  This "confidence" is called statistical Power and it is directly related to T2.   

So, having bored most of you, and for sure, turned off a few folks, how do you apply all of this to shooting directly?  I think there are two ways.

One is the direct methods that I can describe in gory detail if anyone cares.  I could even make up an Excel spreadsheet I think that would do most of it for anyone willing to trouble with it.  But I suspect that most ASSRA folks are pretty unlikely to do that so I won't waste my time or anyone else's if no one is going to use it anyway.

The other use is to at least understand the general principles, some of which I've tried to lay out here and use them in an informal and implicit method.  Many of you already do, including the most anti-statistics shooter of them all (and he knows who he is, because I've beat him over the head with this dead horse a million times to no effect).   

Some of those general principles would include using SD's instead of SE's to make decisions.  The best thing you can do with the SE is to throw it out!  The one exception to that is if you cannot calculate the SD.  It's a crutch that is better than nothing but that's all it is.   

The second thing you can do is to think about how you decide what constitutes an improved load.  If you are in the early stages with a recalcitrant rifle (as I am with my .38), then all you can hope to find shooting a few groups with each load, are differences that are relatively large improvements.  Those things that seem to have no effect or perhaps even a backwards effect need to be revisited after you have refined the load a bit more.

I could write more, but this darn thing won't let me.  This website has a few strange properties to be sure.

Brent

" Many of you already do, including the most anti-statistics shooter of them all (and he knows who he is, because I've beat him over the head with this dead horse a million times to no effect). "

Brent,
  Gee! I didn't know you cared!! 

  Actually tho I hope you keep discussing this SD thing even tho the Forums program seems to be giving you fits. Keep hacking away at it.

  I'll go along with the SD thinking as being valuable, and I'm beginning to see that it is more important than ES in figuring out if one load is better than another.

  I think our disagreement is in the statiscal analysis part where you've told me you need a 100 shots to be meaningful, statistically, when I figure three or four five shot groups will tell me all I need to know about that load.

  The way I'm seeing it now is that SD will tell me more postively that what I see with those three or four groups is true. Thus if on succesive days under varying conditions I'm not able to shoot up to the norm the SD's will tell me that, in fact, it's me, or the conditions, and not the load.

  The work I just got done doing with the .38/55 tho shows how you can have nice SD's that should indicate that you should be shooting around that MOA mark or under, but in reality are getting 5 + MOA. You just can't use SD's, or statistical analysis to figure out where the problem is. You can only use it to verify when you have the problem under control.

PETE

Brent,
  Well, I see we're getting closer and closer to agreeing on the same points. Glad I'm geting you trained! 

  Seriously.... Will you be setting up that Excel program on your web site, and will it be set up so we can use it?

PETE

Brent,
  Well, didn't mean to upset you so much with my statement of coming around...... partially ..... to your way of thinking.    Hope you didn't hurt yourself!! Between your explanations here and that FAIRLY clear article in PS I can see where SD would be better than ES's. I'm not gonna commit on statistical analysis (SA) being useful in all phases of shooting tho, so don't get your hopes up to far.

  I realise that setting up a web page with all the things you need in order to show us the "true way" is not gonna be an easy task. I have no idea how you're gonna do it, and I've set up my own web site. But figure if it can be done you'll be able to do it. We ain't going anywhere so do what you can, when you can.

  On your .38/55. Your problem is the part where I think SA really falls down. As you say, your SD's are great, but the results on the target aren't. There is no way SA can help you there. It can only show you what you can expect from the loads you have prepared. Your problem is just gonna have to take a lot of grunt work to figure out. Hopefully we can find some of the answers this weekend.

PETE

Joe, 
If there is controversy in the stats world, it surely is not with respect to sample sizes for simple tests such as we do.  Baysian statistics vs standard parametrics might yet be considered a "great" controversy, but we ain't there.

Next, how do you know if your groups are not round?  If one group is a 1.5" by 2.5" group unround? Could SDs give you a hint about that?  You bet.  But to know that a group is unround is something that can be dealt with statistically and it's not even that hard.  - essentially, you would compare the mean displacement from the group's center in the horizontal dimension with the mean displacement in the verticle dimension.  A conventional two-sample t-test (comparison of means) would suffice nicely.   

Since you have taught statistics - you know that distributions have infinite tails, and you know that the probably of finding a datum in any sample of size whatever from the extreme of either tail is totally dependent on sample size.  Hence it is not a very useful measure.  Also, having obtained a range or ES, you then procede to do what?  You cannot use it in a t-test, or an Anova, or much of anything.  You could use a bunch of range estimates in a formal statistical test, but the distributions of such tests are not known to me, and I have never seen anyone do such a thing.  You will not find it in any stats text that I'm aware of.  Think of it this way, an SD uses all the information contained in each and every shot to characterize a variance (square of the SD).  Variance is a property that is very very well understood but statisticians.  SEs use information from only 2 shots regardless of how many you shot.  And, it tells you nothing about any distribution-defining parameter.   

Perhaps the best thing for you to do sometime, besides pulling out your old stats texts and looking at simple parametric comparsions of means (t-tests being the most obvious and simple, ANOVA being a possibility as well I suppose) would be to shoot 100 rounds or so, and plot SD for the first 2 shots, the first 3 shots, the first 4 shots, etc. up to 100 shots, and see what happens.  It is not "crazy".

FWIW, I have now written a program that will allow you to enter all the shots from a pair of targets and provides mean and SD estimates for the distances of each shot from the group center and also calculates a simple t-test comparison of means for a 1-tailed hypothesis testing (is my new load better than my old reference load?), estimating approximate confidence you can have that the two loads do indeed differ.

I will eventually post that software and a tutorial, example and description of what and why this is done on a website.  But right now, I'm going to go out and make a 100 shot comparison of Lapua Midas L and Wolf Match Extra ammo to decide once and for all, which is better.

Adios,
Brent

Dale, perhaps you are right.  I'm not so sure that lot to lot variation is quite as real as it often is credited for.  Again, because I'm not confident, or even aware of the data from whence these conclusions come.   

But I am pretty sure that different BRANDS of ammo are quite different.  For one thing, Lapual Midas L uses an oversize bullet relative to all the other ammo that I'm aware of.  Wolf Match Extra hits about 4" higher on the target at 100 yds so it is presumably considerably faster.  I'm willing to wager that whatever the batch to batch variation, the brand to brand variation is greater, and that is where I'm going to start.   

FWIW, I got in 45 rounds of each brand of bullet this morning before the rain arrived and with it wind.  Until then, it was darn fine shootin'.  Now to see what I actually go for results.   

Brent

Joe b.,

  I pretty well agree with your summation as I've argued that math isn't altogether useful for determining accuracy or reliability of any given load.  Personally I've never seen the best load SD-wise shoot the best. You have to have a good SD/ES but that doesn't mean it shoots the best.

  But you're losing me when you say if a group isn't round the process isn't in control. What do you mean by process or control..... The load isn't good, or I'm not in control for having shot a non round group?

  I'll freely admit what you guys are talking about is WAY beyond my 8th grade education, but if I get what you're talking about as far as "round groups" go, it means to me an actual group that's round. Doesn't happen that often in the real world just thru normal distribution of the shots, and the myriad other factors effecting a group. A case in point is target #1 that I put up on my web site. The measurement shown is 9/16" but if you measure across the next widest C to C it's also 9/16", yet that is far from being a round group.

  The SD of target #2 suggests that all other groups shot with this load/alloy have a pretty good confidence level that it will repeat. And in fact it does, most of the time, thru using that combo as a reference for all other testing. SD also bounces around quite a bit, as a group I shot with that combo had half the SD of the above, and the group shows it, being about half the above, altho it is strung out horizontally.

  So somewhere you're leaving me behind here, unless round to you means something it doesn't to me.

PETE

We say that the process (shooting the gun) is "in control" when the measurement of the output is kind of distributed normally, the bell curve. For groups, that would mean that the groups are round. Now round is sort of subjective, but we all know exactly what I'm talking about. You know a round group when you see it, and a non-round group too. Wednesday I shot a M54 Winchester 30/30 at 100 yds with 311299, and a contender 7TCU at 50 yds with 139 Hornaday. The 30/30 load is what I shoot in my SS bench gun/martini. The M54 averaged 1.192" for 8 "round" groups, the contender shot 1.975", 2.0" and 2.15" groups that were maybe twice as high as they were round. 
The 30/30 was "in control", the 7TCU was "out of control". Something other than random variation was affecting the pistol, my guess is that there isn't enough powder-the ignition is varying, and MV varies. The pistol doesn't have one process going on, it has a maybe 1400 fps process, a 1450 fps process, a 1500 fps process.....
There's no statistics applied to the pistol that makes sense.
The process is out of control.
The traditional CBA/ASSRA "oh shit" group has 4 in a single hole, and the fifth out toward Cleveland somewhere. The process is out of control-something happened, and if we can find out what that something is, we can fix it. Exotic measurement techniques won't help.

joe b.

Brent;

>>>But I am pretty sure that different BRANDS of ammo are quite different.  For one thing, Lapual Midas L uses an oversize bullet relative to all the other ammo that I'm aware of.  Wolf Match Extra hits about 4" higher on the target at 100 yds so it is presumably considerably faster.  I'm willing to wager that whatever the batch to batch variation, the brand to brand variation is greater, and that is where I'm going to start.   <<<

I am certainly in agreement here. My previous statement was predicated on the fact that I have considerable problems trying to fine tune my .22 ammo selection. I buy a small quantity of various brands and lots of ammo. By the time I get to the range on a "good" day, select which is best, no more of that particular lot is available. Sheesh!!

With a tuner on a bolt gun, at least you can "help" a "not so perfect" selection. However, with Single Shot rules , I cannot use a tuner so I am stuck with brand selection. I finally give up in disgust and just buy a case or two of what "looks good". Not really the best way around it, but there it is - the REAL world.

Dale53

Joe B,
I wrote another long dissertation concerning each of your points.  Of course, it was "too long" to post, according to the damn websoftware.  Told me to go back and modify it, and, of course, there was nothing there to go back to.  

But really, it was a waste of my time anyway, since you already know all about statistics and how they are so damn useless.  

But since you know all this stuff that I surely don't, perhaps you can tell me which of the targets on this webpage were made with a gun that was "in control", or out of control - horizontal, or out of control - verticle?  Cause w/o stats, I surely cannot tell...

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Brent

Brent et al;
I love the range. The calculated standard deviation from a sample of data is an estimate of the population SD. The range, corrected for bias, is also an estimator of SD.
One may use either estimate of SD in any calculation.
On your targets; 3 and 5 are round looking groups, 2,6 and 8 are not. I don't think that we can say that the process is in or out of control based on 5 shots = 1 group. Statements about control maybe need 5 groups or so for validity. What I will tell you is that if those targets were shot with the same equipment/load in about the same conditions, then the shooting process is out of control and something other than statistics needs to be done.
I don't dislike statistical analysis, don't  think I know it all (Anybody who thinks they do should look at "Bias in Mental Testing" by Herrnstein?).
Have at it, enjoy yourself, I was once a true believer myself, and I know how it feels to be able to change the world. 
Did you look at the Ed Wosika stuff?
joe b.

Well, Brent, I'd refer you to 
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or
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or search on "range standard deviation"
or 
control chart
or statistical process control
The range has been used as an estimator of SD since at least 1931, when Shewhart sort of invented SPC.
When I entered graduate school (Economics, MA, 1972, Northeastern University, Boston, MA) several math and stat teachers balked, as you did-saying it ain't so. About 10 minutes with "Statistical Quality Control" by Grant, now Grant & Leavenworth last I looked, boogered their minds. 
Quality and Statistical Process Control
Here's a little info:
Prof. Sid Sytsma – Ferris State University
Statistical Process Control 

"Shewhart's discovery statistical process control or SPC, is a methodology for charting the process and quickly determining when a process is "out of control" (e.g., a special cause variation is present because something unusual is occurring in the process)."
A few minutes on the computer will explain all about using the RANGE as an estimator of SD, and what "in control" and "out of control" mean. 
Perhaps, Brent, you don't know quite everything that you think you know?
Look it up, Brent, do the work
joe b.

JoeB;

>>>Perhaps, Brent, you don't know quite everything that you think you know? 
Look it up, Brent, do the work 
joe b. <<<

Disagree all you want. You do NOT have to insult everyone who disagrees with you. You nearly ruined the last forum before you were removed. How about "chilling down" a bit?

You and others have a lot to contribute. We need this forum to remain civil for ALL of our benefits.

R. Dale McGee

Perhaps my manner is offensive. When I read that "The range is NEVER...", that is kind of offensive. I used and taught SPC/SQC for 40 years, and telling me that it ain't just gets me riled up.
As I said when I entered the fray, my interest is in the variability of group size.
For instance, Pete says that his rifle shoots into 9/16" for 5 shots at 100 yards on a quiet day. 
I don't know what he means by that. 
Is this the best group, or 1 in 5, or an average, or what?
In 2002 at the CBA Nationals, for an average of 4 five shot 100 yard groups, one of 41 shooters shot less than 9/16" = .5625", and only 4 shot under .6"
In 2003 4 of 49 shooters averaged under .6".
I record group sizes for every group shot. I find that my groups vary widely from group to group on the same day, and from day to day with identical loads, and they seem to get smaller the more I shoot on any given day.
In the 1997 Handloaders Digest, "Let's put some numbers on accuracy" by Paul Schiffelbein, PhD  says that 185 five shot groups are required to get a variability estimate that is good to within +/- 5%.
Maybe this is true, I hope not. My shift from IMR4227 to AA#9 in my Martini 30/30 bench gun was driven by far fewer groups, although the question was slightly different.
My query is kind of f-testy, variation within the data vs. variation between the data. If my gun shoots from .25" to 1.25"  over a long run, is that to be expected or is something wrong?
I hope that this hasn't been overly offensive.
When is the next ASSRA Journal coming?
joe b.

joe b.,

"For instance, Pete says that his rifle shoots into 9/16" for 5 shots at 100 yards on a quiet day.  
I don't know what he means by that."

 Ok... I can see I need to be a little more specific for you. So here are the last ten group sizes.

3/4" - 5/8" - 9/16" - 9/16" - 9/16" - 7/8" - 1/2" - 11/16" - 3/8" - 9/16".

 Out of these ten I would say only two are "round". The rest have at least one shot that at least increases the group by half.

 Of course, in my opinion these mean nothing without the conditions they were shot under. No more than one of these groups was shot on any given day, as I was using this load as a control for other testing. The smaller groups all were shot under "ideal" conditions. 7 AM in the morning, dead calm, target and ground in shade with no sign of mirage. The larger groups were shot on days at about the same time but some wind was present, varying from 7 to 3 o'clock depending on the day. The same condition was tried for but I can't say I hit it exactly every time.

 Since I shoot every day I don't record every shot, but do keep the targets till I have decided that a particular load combo is the best or not worth pursuing. But I do agree with you that groups will vary within the same day, and day to day. When you reach a certain level with you gun/load you need some way of confirming that it is the best load. This is where I think some math program would be of benefit.

 Both GWarden and myself are both having a hard time figuring out whether..... in my case a 1-25 or 1-30 alloy is best, and GWarden has the same problem with 1-20, & 1-25. What we need is something SIMPLE that can tell us over a fairly decent interval of shooting which would be the best. Both of us, I think have fired enuf of each alloy that we should be able to tell, but one day one will be better, and the next the other. Seems like we can go on forever like this and not be able to decide.

PETE

P.S.  Since Brent is a personal friend of mine I won't get into who's manner is most offensive. I'll only say that it's not how you perceive yourself, it's how others perceive you that counts. Both of you should state your case and leave the personalities out!

Ah, another great weekend in the books only to return to this sort of junk.   

Joe, 
If you don't like it, don't go there.  It is as simple as that.  If you want to hang on to range rather than SDs as an estimate of SDs - great.  More power to ya.  But it won't fly anywhere in any science I'm familiar with.  It surely won't get you published in my field.  If you wish to bandy about references and qualification on traditional and universally accepted statistical techniques, I have on my shelf right now,...

Design and Analysis of Experiments by John Gill.  I spent an entire year in Gill's courses (3 volumes).   

Then there is another perennial favorite, Sokal and Rolf's Biometery - about 850 pages of quite basic traditional statistics, 

And, let's see, Conover's Practical Nonparameterics -another semester spent on dissecting that.  Nonparameterics could be a quick good fix to the lack of statistical rigor in shooting.  But then you would see that immediately.   

There were several course in multivariate statistics that I spent my time (and money) in.  No texts handy, but multivariate stats would be an interesting way to go for a lot of load development, but no way that I know to make it easy for the average shooter.  Oh wait, yes, Multivariate Statstical Methods by Manly.  And a couple devoted to the arcane field of community ecology that would have little utility here.   

Then, lest we dwell on just the applied stats, I spent a year working through Hogg and Craig's Introduction to Mathematical Statistics, deriving the theoretical underpinnings of stastitical methology and probability theory.  Worked under Larry Shear on this.  he is fairly intense and more than slightly competent by most standards (standards of statisticians, not rank amatures like me).

And last of the general theoretical stastictics books, Noel Cressie's Statistics for Spatial Data.  Noel was/is pretty much a spatial stats diety.  He makes Larry look like milk toast for breakfast.  I spent a semester with him and a dozen of his and other Stats PhD students learning how to work with spatially organized data.  Application of spatial stats to shooting would be an interesting idea since a group on a target is nothing less than a map of events in space and time, but point-process analyses, or some sort of cludged variogram/kriging technique might be a whole lot more work than it's worth.  It would be great, I think, for diagnosing an potentially busted scope however, and probably other things as well.

None of these, btw, rely on range or semi-interquartile range to do anything useful.   

So, there you have it.  My "library" as it were (and is) and my background.  For an ecologist, I'm probably in the middle of the pack with respect to using stats, but a good bit ahead of the pack with respect to statistical training.  I'm surely no professional statistician, but I play with them (professional statisticians every day  

So, I'll stick with that.  Something like 10 courses in statistical training and 25+ years of doing it is quite enough to get me down the road to better shooting analyses. 

End Part I   
Brent

  Good! I'm glad we're movin' on.

  Three of us had a little fun with this... at Brent's expense this past weekend..... which is why he's probably a little owly today! 

  Without boring you with the details todays shooting really pointed up the "out of control", or the more commonly called "flyer". Some of the groups were REALLY out of control and it was interesting, with our messages on this as witness, that the really bad shots would show up on the chronograph with big changes in MV's, and a final large SD/ES.

  But.... All these would have been pretty obvious without the chronograph data.

  I had one tho that would have had some thinking maybe there was something wrong with that bullet. The group was 2 1/8", with 4 in 15/16". Without the chronograph I would probably fire this a coupla more times to see if that " flyer" was just a fluke shot. But the chronograph showed that altho the MV averaged in that sweet spot of around 1405 fps, the SD was 33.9 and the ES was 90.3. Since I know with this gun I need to get the SD's below 10, I can pretty safely say this load isn't worth expending anymore time on.

  To me it's cases like these that make Statistical Analysis a shortcut to finding the best load.

  But, what's really needed is something that can take a series of tests, with nearly identical results, and compare them to see which is best, such as I mentioned where I was having trouble determining whether 1-25 or 1-30 was the best alloy to use. Something that doesn't take a rocket scientist to apply.

  To me this is why I don't think SA is a practical option for most people to use. Taking the group above as an example, if I didn't have a chronograph it would have been a lot easier for me to just fire a coupla more groups to get the answer rather than to spend hours(?) using SA to come up with an answer, IF I even understood which part of SA to use in the first place. What we need is a better mousetrap!

PETE

GWarden;

How about a "practical", non-scientific answer to your question? A good number of years ago (when the .222 ruled modern benchrest) I decided that, as a rifleman, I needed at least one REAL rifle to work with. A REAL rifle's definition was created for ME . It turned out to be a heavy varmint class .222 with metalwork by Ferris Pindell and a benchrest fiberglass stock "glue-in" stocked by me.

The rifle was a success. It turned out to be a genuine one-quarter minute rifle (thank you, Ferris). I had no intention of limiting my shooting to benchrest. However, I had determined that to further my shooting education I needed a rifle that did not lie to me.

After some use, in working up loads I determined that three shot groups were useless. A single five shot group was useless. It took three consecutive five shot groups before I decided to either discard the load or it needed further testing. I learned that a single ten shot group was about three times as useful as a five shot group (as far as determining the quality of the load - what we would now call determining the "probabilities"). I also learned that it is derned difficult to maintain absolute concentration for ten straight shots. I suspect that is why modern benchrest shooting is done five shots at a time.

So, I have concluded that 3-5 five shot groups for load development. Then when I have my load, I have learned that I need to practice, during ALL conditions with ten shots on score targets if that is what I shoot at the matches (the ASSRA Schoyen match, for instance). Since it is so hard to shoot ten perfect shots, it is a MUST to practice with ten shots. 

I'll say it again, you must practice in BAD conditions if you want to win matches in the real world. Excellent conditons seldom happen at Etna Green, for instance, and shooting only when the conditions are good is NOT good enough to learn how to win...

FWIW
Dale53

Dale, If you want to compare groups like that, you might think about using binomial testing - commonly called a sign test.

In such cases, you wish to compute the probably that you could get one load to be better than the other for every group, just by chance alone (i.e., assuming there is not a true difference in accuracy between the loads).   

To do this you want to shoot enough groups that you can be sure that when all of them favor one load in particular, that the chances of that happening by chance alone is small.   

This is EXACTLY the same as judging the fairness of a coin in coin toss.  If you tossed a penny three times and it came up heads each time, would you be confident that this coin was NOT fair (ie, that it was biased towards heads)?  The possibility of this happening is 1/2*1/2*1/2 = 1/8 or about 12.5% of the time when you fire three groups of each about 12.5 times out of one hundred such trials, you will get this result.   

Generally, I advocate at least 5 such comparisons.  This gives a probability of 1/32.  But you may have to choose what level of confidence you want.   

Now, if you shoot 5 such pairs of groups and one load wins out 4 out of 5 times what are the odds of that happening even if there is no difference in the accuracy of the loads?  It's a bit more difficult to compute, but some calculators can do it for you (like my ancient HP 15C) or I can give you the figures to compute this quickly in a spread sheet.   

This sort of calculation is exactly what I was thinking about when I suggested that nonparametrics may have a wide range of application to shooting.

Brent

I won't address this to GWarden or Brent, or even Dale53 since they probably know what I think about GWardens question anyway. So this is for the rest of you.

  What I do is to shoot a 5 shot group first. After all, if it shoots an 1 1/2" with 5 shots it's not gonna get any smaller with 10 shots. If a group looks promising then I will repeat it the next day, or, if the chronograph shows it might be promising I'll repeat it. After I have tested a 5 shot group load at least 5 times I'll then try for 10 shots to see if it holds up. But this only comes after I have several promising loads.

  As Dale hints at, the more shots you put into a group the bigger the chance for error to creep in. 5 shots will at least tell you if a load has promise, and if not will allow you to move on to other bullets, loads, and powders. I hate casting, so the fewer I send down range the better I like it!

  After you have selected what you feel is the best load then it's time to practice. Practice does not mean picking the best weather conditions. It means going out on any given day whether the weather is good or not. I do draw the line at getting rained on, but have shot many times when it was raining straight down and I'm under a roof. I've shot in fog, and rain, so heavy you could barely make out the target at 100 yds., and in wind so strong it was blowing things off the bench. I don't know how many times my chronograph has blown over, even with a facing brick attached to the tripod!

  Dale mentions keeping your attention span over a period of ten shots can be difficult. So true if all you're doing is practice! What I do is to always have an experiment of some kind to work with. For me, this forces me to pay attention or else the experiment is wasted. If you don't have something that keeps you interested practice very quickly gets to be boring and you'll soon give it up.

PETE

I've had trouble with variation in group size-sometimes I get small groups and sometimes I get big groups, with the same loads and under the same conditions. 
I did statistics to the problem, and got the solution. The topic, and title of the article, is: Detecting Accuracy Differences."
The answer is a table showing how many five or ten shot groups must be shot to be either 90% sure or 95% sure that there's a difference in two different loads-all varied by the percent of difference.
As I suspected, for small differences in group size a hell of a lot of groups must be shot to be reasonably sure that one load is REALLY more accurate than another.
I've got the article done and am working with The Fouling Shot folks to get it printed there. I will also offer it to the Journal Editor. 
I'm writing this to bring what I previously wrote on this topic to a close, and to offer to e-mail the article to any interested parties.
You won't like the answers, but that ain't my fault.
joe b.
joeb33050@yahoo.com

Joe
I sure would like to get a copy of your paper.
Bob
rthsrdr@iowatelecom.net

Brent,

  Well, you ask a good question. I won't argue that with enuf of the "proper design" in the test it might yield results that can be counted on....... maybe! I don't doubt that SA can be very useful when the conditions of the test can be controlled enuf to get reliable data. I just don't believe this can be done under normal shooting conditions by the average shooter.

  In my last post I mentioned some things that we have no control over that would skew any data results. The other side of the coin is shooter error, unless of course you do all your shooting from a machine rest. That combined with shooting in a vacuum would probably give you meaningful data. Since few of us have access to those two conditions any results you get would be very suspect. It would be like tossing a coin.... Every toss is a 50/50 chance that it will come up heads or tails. No amount of tossing will change those odds in favor of one or the other. The same goes for any group you shoot. No matter how many thousand you would shoot, the odds will be 50/50 that you will have a "good" group for analysis, or not. The question is...... How do you separate out those "good" groups from the "bad" ones?

  So...... I would imagine that everyone "replaces" statistical analysis the way they have for hundreds of years when it comes to shooting. They go out on several decent days and shoot some groups to establish which combo works the best in their guns.

PETE

Joe,

  Perhaps you don't understand my comments because I don't really know what I'm talking about. I am trying to understand, and the comments I make are probably thoughts that many have also, but which you don't connect with since you seem to believe that Statistical Analysis is the only true way to find out a most accurate load.

  To me shooting a dozen, or whatever number you, or anyone else, seems to think needs to be fired in order to get a valid set of data in order to be certain load A is better than load B, just seems to be a waste of time in most cases.

  Now I realise that Statistical Analysis is a very useful tool under the right conditions. I just don't believe that it can be usefully applied to shooting just due to the myriad of factors you have to deal with that can skew the results. Possibly you're right that if I fire enuf groups I will be able to statistically determine that one load is better than another.

  But most anybody on here that has been shooting for a few years can tell within one group whether a load has possibilities. If they have several groups that look good, they can tell within three or four groups on several different days, which is the best and most consistent one. And..... If more than one load is equal to another most would pick the one that's easiest and cheapest to assemble.

  To me there's just no sense blowing off a hundred dollars worth of components to prove statistically what you knew with the expenditure of a coupla dollars worth.

  Bench rest shooters pretty well determine the best load for their guns with as few groups fired as possible since the maximum accuracy life of their barrels is measured in the hundreds of rounds. If they shot as many groups as a Statistical Engineer felt was needed to determine with 95% certainty they had the best load, they would never be able to really find out because their barrel would be shot out long before that 95% certainty factor was reached.

PETE

  Now Joe.... You're confusing what I'm saying. I didn't say Statistical Analysis wasn't useful. Far from it. I'm only saying that I'm not positive it's "reasonably" useful for shooting.

  I've read your purposed article and find it very interesting and hope both the CBA and ASSRA see fit to publish it. It does point up a few of the arguments I've tried to present here. In your articles first example where the average group size difference is 1/4" or 20% difference, you say that a total of 9 groups must be shot in order to attain 95% surety that one load is better than another. This seems reasonable, but experience would tell me in a far shorter time than that which was best for that big a difference. Next you say that if the difference is 10% then 38 groups would have to be shot to achieve 95% certainty. Again. Probably not to  bad. Then you go down to 1% difference in groups where you mention 4050 five shot groups are needed in order to be 95% certain one load is best. Now as you mention this is bordering on the ridiculous and no one would try to achieve it.

  The premise for my whole argument is where do you draw the line between what can reasonably be achieved and what becomes impossible to test for?

  I feel that God gave me a brain to differentiate between what is reasonable, as far as accuracy is concerned, and what is ridiculous in trying to seperate out. If several groups sizes for two different loads are within 1% of each other then a myriad other factors are present that will cloud any difference and would probably cause a greater disparity than 1% anyway.

  What I would like to hear is what is a REASONABLE number of groups that I need to shoot in order to be REASONABLY certain I have the best load.

  Your mention of one guy at a match dancing around because his scores/groups are great, and another is down in the dumps because his are terrible, is exactly what I'm trying to see if Pressure (PA) & Density (DA) Altitude has a bearing on. These good and bad scores/groups are not due to a bad load, because the very next day the emotions of these two shooters might be exactly opposite...... and I've seen that happen. I'll even go so far as to say I've seen it happen before and after lunch, and between early in the morning and late in the afternoon!!

  If you have ever kept an eye on PA & DA you will have seen that it changes from minute to minute, and the changes can be rather astonishing at times. How much of a change is needed in order to affect score/group size at Schuetzen ranges I don't know, but is one of the things I want to find out in the near future. I know it affects sight elevations, but I also want to see if these conditions have a bearing on group size. I think they do, because some experimentation done by Ed Stutz many years ago show that a change in temp. and humidity can mean you need to change your load to compensate in order to maintain the same accuracy. PA & DA are just a refined version of the testing Ed did.

PETE

Joe,

  I guess you could say I'm fully aware of what the nuclear regulatory agency wants as I spent quite a few years as a nuclear welder and having to qualify yearly under Section 8 & 9 of the ASME Boiler and Pressure Vessel Code, using positions 1G thru 7G.

  But you're right on about flight calculations being a part of Pressure (PA) & Density(DA) Altitude. A pilot who shoots quite a bit of LR is where I got the idea. He uses this method for sight setting changes. I'm not sure whether this method will work at Schuetzen distances since changes will be quite small compared to 1000 yds., and might be lost in wind and mirage and other factors. 

  But I want to take it a step further. As you know bench shooters will often change their powder charges between relays because they felt their groups weren't going like they should. In all the years I've read about these shooters I've never heard mention of "how" they knew which way to go. Is this by chance, long experience, or have they some "formula" that tells them which way to go?

  I'm figuring that since changes in group size are due to changes other than MV/SD/ES if you haven't changed anything in your load, then, if a load starts to go "bad" during a match it must be due to some exterior influence.

  As we know humid air is less dense than dry air, so as the humidity level changes from the early morning hours to late afternoon, might not this difference make a difference in the bullets flight? If this is so then we would have to change our load slightly to get back on track.

  To take an example..... Where I live is 970 ft. Above Sea Level. Doing the calculations I've seen PA go as low as 805 ft. to 1008 ft. in the course of half a day. Doing the calculations for DA I've seen that run from 1000 ft. to 3010 ft. within the same time frame. Of course since temp. (C.) is a part of figuring DA that has to be taken into consideration.

  So, a lot going on when we shoot and it all has a negative effect on our shooting unless we can learn to deal with it.

  As for SD being a respected way of testing things..... I'll certainly agree with that. I'm just not sure that considering the variables we shoot under, that it can be used to generate 95% certainty for a load. As Joe pointed out, if the average group size for two loads is within 1%, not an unreasonable expectation when determining differences in two loads, you would have to fire over 4000 five shot groups in order to reach the excepted 95% accuracy level to be sure you have the right load. Even for a difference of 10%, firing 38 groups is bordering on undoable.

  So far no one who supports Statistical Analysis (SA) has said what is a reasonable number of groups to fire. That's all I ask! If a number can be brought forth that is reasonable, then I can use SA as a method to predict load confidence. Otherwise I don't believe it's totally applicable to shooting unless you want to spend that kind of time and money to prove things out, and I will continue to do it the "old fashioned" way.

PETE

Joe,

  Sorry to read you think I'm prejudiced against SD and SA, and have your mind set that anything I have to say is not valid. Einstein was right!    Guess we better drop the whole idea.

  I guess if you don't know what PA and DA is then you have some more to learn. That's the part I like about shooting. There are so many things I don't know, and so many avenues to explore. Short of giving a lesson on how to calculate both these conditions, what I wrote in my last message gives a general idea of what they are and a little on how they are, and possibly could be, used in shooting.

  Besides it should be put into another thread if there was any interest!

PETE

Forrest,

 Glad you chimed in on this, as I'm sure I might not have gotten things exactly right in this PA, DA thing. "Cuss and discuss" is right!   Lots of cussing on my part before I got it thru my thick head what had to be done. PA almost had me giving up!

 Just sitting here reading your message and note that you said you've never shot below a DA of 2000 ft. For the record Forrest lives at 4000 ft. It got me wondering, so I figured out my PA & DA right now. PA is 324 ft. and DA 1328 ft.

 But then a thought hit me. That's using an inside temp. of 72 deg.'s F. and the outside temp is 35 deg.'s. So figured that out and it comes to a PA of 314 ft., and a DA of 1140. When you know that my actual altitude is 970 ft. you can see how the changes are, and how they can affect POI, and possibly group size because of the different air resistance.

 For those not up to speed on this you can see the changes in DA and that's what Forrest uses, as it changes, for changing his sight settings.

 You might wonder why we have PA in there. The calculation for DA is determined by the PA and the current temp. in deg.'s C. PA is figured by adding or subtracting a set amount from the actual barometric pressure using the "Standard" of 29.92 inches of mercury as your base. This figure is then used on the "computer" to figure the DA.

 Sounds kind of complicated, and I'm probably not explaining it exactly right, but it's pretty easy once you get the hang of it. OR..... You can buy a Kestrel 4000 and it does the figuring of both for you!  

PETE

Keith,

  That's why I suggested buying the Kestrel 4000. It's advertised in Precision Shooting. It'll do everything you mentioned and a whole lot more. But, you'll have to calibrate it for a known barometer setting and the altitude of your current location, in the right order. Not for the faint of heart either as the instructions aren't any to clear in that area.

  Another very big BUT. The Kestel costs about $325 and a flight computer costs $12. If you can afford the former, go for it. If not, a person can do a lot of calculating for $300.

  It sounds complicated because I'm not a very good teacher. But once you grasp the idea it just takes a minute or so to come up with DA. Less when you get the hang of it, as when I do it things seem to be backwards of what they should be so it takes a little time to be sure I've got it right.

  Grasping PA was what got to me and only because I was assuming things that weren't true so my calculation for that was skewed. One of the problems of trying to get an idea across over a period of several days emailing. As you can see by what we've got here now, and we haven't even got into doing any "work"! 

  Once you have PA then you just plug that and deg. C. into the computer and DA is the result. The only other known you need is the altitude of the range you're shooting at. Those can be gotten frorn USGS topo maps that are free for the downloading off the web.

PETE

Forrest,

  Looks like there is some interest considering the number of views. But like most other threads on here, everybody wants to "suck" the info up without contributing to it by offering info or asking questions. Seems to be a real lack of curiosity on here.

  That's why I've been purposely vague on how to do the figuring, and what you do it with. Us two know what we're talking about yet we're the only ones participating. Not much sense going over what we've hashed out in private email if there's not enuf interest for people to ask.

PETE

Pete has been explaining it to me, and it is another thing that can possibly help with our shooting. After he explained it to me, I remember one Sat. last summer we were shooting in our league, took a lunch break. When I shot my next relay I though someone had messed with my scope, as it was shooting higher than before lunch. I know that Brent didn't mess with the scope as he was with Pete and I. This DA really sounds like it can help if one wants to get with the program and keep a record of conditions. We're not all just sitting back. If Pete doesn't share his Kestrel, probably have to dig up the jar in the back yard and gete some money out to buy one( always need another toy)
Bob

Bob,

Bob: If Pete doesn't share his Kestrel, probably have to dig up the jar in the back yard and gete some money out to buy one( always need another toy)

F:  Pete doesn't have a Kestrel I don't believe. He went out and bought a E6B at his local airport. Cost: $12

This is a simple mechanical computer, no batteries, two moving parts and some numbers around the dial.

This, a thermometer, one calculation and a spin of the wheel and you've the DA displayed under the little arrow. 

It will save you from the high/low miss if the temperature changes over the course of your lunch period or any other delay.

Good morning,
Forrest

Gentelmen,

The question continues as per how much change in elevation may be expected as DA changes.

I have not done any shooting at the relativly close ranges such as I know are the norm for easterners. Like I said above, the shortest distance I shoot over is 395 yards.

Anyway, the elevation differences are unmistakeable, running to 5 or even 6 minutes during the course of normal daily temerature changes.

When we are all shooting on our hill-top range, starting in the cool of the morning, it is possible to identify the increasing DA as the day heats up and it becomes necessary for everyone to lower their sights to stay on the steel.

Keep in mind that I do not know how the differeing DA will show up at the typical 200 yard Scheutzen match! Sure it'll be there but how much I can not say.

Pete himself is on that particular road and he'll let us know I'm sure.

Good morning,
Forrest

  Well, yes I do have a Kestrel. Got that a few days back. we've been on other topics and forgot to mention it to you.


Pete,

Whoe! That is real commitment!

P:  This might be where the discrepancy you noted came in. When I saw it I wasn't satisifed with the reading either because the temp. on the Kestrel didn't match what my out door thermometer read (very accurate). So just went with the reading on the Kestrel as I figured it knew what it was doing with any condition it was recording internally.

F: I wonder if the machine tells you clearly if the DA reading is above or below sealevel. That is a plus value or minus indication. I noted that the number was pretty close, it just didn't say if it was above or below SL.

P:  One thing I'd like to go over with you again, which I'm sure some have thought about. That is where does humidity come into the formula. You think it isn't needed, as temp. will bring the widest swings in DA. I'll take your word for it, as you've had more experience with this idea. But, considering the considerable amount of humidity changes in the Midwest and South during the Summer, I'm not to sure about this. You live, and shoots, in country with low humidity, where I think if it gets about 50% it's considered very humid, whereas in my part of the country 50% would be considered a "dry" day. I routinely see changes of 40% difference in the course of a days shooting. What's your thinking on this?

F: Well, I've never figured it in. The performance charts in the flight manuals I use do not address it, not that it does not have an affect! There must be something to it as you say.

All I can say is that I'll look into it more closely.

Good evenng,
Forrest

AHHH....Statistics....the art of intelectual Mystical exercises in futility!! They will tell you what has, was, or did, but they cannot tell you what will. They might tell what could, or may or might.

Ed,

  Well said!

  Probably the hardest thing I have to do is explain to people why the chronograph is not the " be all, end all" of working up a load. It is just one of the tools you need to become good at shooting.

  Once you work up that final load then, as you put it, you need to work up a memory data base for that particular gun and load. Personally I feel I'm weak on wind and mirage, and plan to spend all the next years Schuetzen matches shooting nothing but the .22. That experience, I hope, will make me a better "big" bore shooter. Can't hurt! 

  What I am hoping is that using Density Altitude will be another tool in being able to shoot better. We know it works at the longer ranges, but even if it doesn't work at the shorter ones we will at least have a better understanding that there are other conditions besides wind and mirage that affect the bullets flight.

  Right now I'm trying to work over in my mind whether we will have to use humidity, altho how we can run that into the E6-B I don't know. Forrest doesn't think so, but I'm not sure. There has to be a reason why, in the test I ran, that the Pressure Altitude between the Kestrel and E6-B were reasonably close, yet the Density Altitude had such a wide spread, except for the 11 & 11:30 readings whiuch weren't to far apart.

  The only two possibilities I can think of are I'm not as good with the E6-B as I would like to imagine, or else the Kestrel is using other inputs in addition to PA and temp. Humidity???

PETE

  Once you work up that final load then, as you put it, you need to work up a memory data base for that particular gun and load. Personally I feel I'm weak on wind and mirage, and plan to spend all the next years Schuetzen matches shooting nothing but the .22. That experience, I hope, will make me a better "big" bore shooter. Can't hurt! 

PETE,

Your mention of the 22RF is interesting to me as per the discussion about Density Altitude. 

Since the 22RF is bound to be more sensitive to any changes in the air, let it be wind, temperature and/or your interest in humidity (plus being cheap) perhaps we can show data using it over the close ranges you have available back there.

What do you think?

Good evening,
Forrest

Forest and Pete,

Can't figure out how to quote from a message, oh well.

Forest looking at your chart showing Kestrel and E-6b values for PA and DA, baro pressure, temp and humidity I can see no correlation what so ever. As I understand somehow Pa is calculated from baro, and temp then you get DA from ..what?

What am I looking at with your chart, what is it telling me?

Ed 

Pete, 

I think I understand, you will calculate the DA for every target shot and enter the sight settings, so that after a decent amount of data THEN you will be able to calculate sight changes based on the collected data.

At this point do you know which direction to change per data,
if DA goes up will the sights have to come down or up?

Did you say Forest has used this method? if so then he can probably answer my question.

Btw Brent is suspiciously quiet re my statistics comments 

Ed

Ed,

  I see Forrest has answered most of your questions pretty well. I'd like to maybe cover the "how much recording is enuf" angle.

  To be honest, at this time, I don't know what amount will be necessary to get accurate enuf data to be useful. Plus, how "fine" of DA do we need to use in order for it to be of use at the short ranges we use in Schuetzen. Forrest feels that a DA change of 500 ft. is sufficient for his puposes shooting at fairly good sized targets. He has the saving grace of only having to hit the target, whereas we have to hit a certain point on a target..... i.e. - the bullseye.

  Your idea of "every target" might work out, if you shoot one target per relay. That should be more than suffricient, as at our club we use 30 minute relays. Many of our shooters tho will shoot two or three targets per relay, but I think that keeping track of every target then would be overkill.

  Here's my plan. When practicing I will shoot a target, then go down and change it. I will keep track of the DA at the beginning of every target, until it's shown any differences in DA amount to less than 100 ft. At a match I will check at the beginning of every relay, unless it's shown on a given day that it doesn't need to be that frequent. We have to keep in mind that not every day will show rapid changes. Probably, on average, once an hour will be more than sufficient. But, we've all run into those days at a match when a front is moving in, or out, so it might be necessary to check more often at those times.

  That DA change of 100 ft. will be what I'll start out with at first. It might end up having to be smaller, or maybe I can let it be larger.

  What I feel right now is that we're cutting new ground here and can't have to much data. I can always back off on both the number of feet change in DA and the frequency of taking a measurement.

  Forrest's comments on gathering his data at Sheridan and then using the same data at other ranges because he feels that the difference in elevation between all of them isn't making enuf difference to matter. This got me thinking and I checked the USGS topo maps on their web site and found that all the ranges I shoot at locally have no more than a 100 ft. difference between them and my local range. Most are even less than that.

PETE

Forrest,

  What you said!  That's what I meant to say. Guess I didn't make it clear enuf. Glad you corrected it.

PETE