This morning I took a second look at the results Joe recently posted in his thread “SOME ACCRACY THOUGHTS” . He was reporting on three different load levels of one powder and was shooting a string of four 5-shots for each load. Joe often reports the size of each individual group in a string as well as the average of that string, an admirable practice IMHO.
I noticed how much the size of his groups varied within each string. I scribbled some numbers and found that the average percentage that the largest group in each four shot string exceeded the smallest group in the string was well over 100%, or the biggest groups were more than twice a big as the smallest groups in the same string.
If the wide variation between groups with the same load was noticed at all, a reader might assume a shaky old guy in Florida caused the variation in group sizes. My groups vary similarly – or course you might say OK, two shaky old guys. Or the reader might assume that the old guys cast very poor quality, are too lazy to weigh sort them, and bullet quality is responsible for the wide variation from group to group as well as the fliers in the groups. (In fact, that is the kind of assumption many of us erroneously make when we notice more variation than we like in where our bullets hit.)
However, if you haven’t noticed similar variations in your own groups, take another look or take a look in the test results in “Dope Bag” section of the American Rifleman. The AR standard testing standard is five 5-shot groups and they report both the smallest and largest group in each string. If you average 8 or 10 of these results you will find that the average that the biggest groups exceed the smallest in the same string will be pretty close to 90%. It seems unlikely that the AR editors are all old and shaky or are shooting defective bullets. This variation occurs in the testing of pistols and inaccurate rifles as well as in the testing of ugly “tactical” rifles that sometimes shoot much better.
I think this little factoid is more that just idly interesting. It might be productive to think about this surprising and unavoidable variation in group sizes in relation to the common practice of finding optimum loads by shooting a one 5-shot, or even one 10-shot, group for each load being tested. Yes, 10-shot groups vary less but still a lot.
And because this variation seems to be independent of the quality of either the rifle or ammunition it is also worth thinking about in relation to fliers.
John
Think About It
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- Last Post 05 January 2016
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John, Joe Gifford, Russ Harman and I were working on some Ransom Rest test with Ed Harris on his 38/200 articles. The picture below is the common backer for 102 record shots from the same revolver. Just above the center right you see an area totally shot away. This is from 4 of the loads used. The other holes are from 6 loads that did not group well. (Please note several profiles of bullets tumbling.) However, they are almost all low and left. They are not flyers, but part of the normal group dispersion for those loads. They are just the outliers of that load's group. All loads that shot small groups, shot them to the same point of aim. And by the machine, not by hand. My point is that a flyer should be outside of the normal group, not just one on the edge of normal. And you don't have enough data points with 5 five-shot groups to tell you anything. Actually I an surprised that only 100% larger groups are made with that number of groups. .jpg?width=690&upscale=false” alt=)
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Assume that shot x and y are distributed normal and we can model distributions of group sizes. We find that with sets of five, 5 shot groups, on average, the largest is 1.91 times the smallest. Recording group size data in EXCEL, the spreadsheet includes LARGEST/SMALLEST for sets of 5 groups-sometimes there are less than 5 groups shot-lack of bullets or??? Anyhow, for the Savage FV in 223, there were 83 sets of five, 5 shot groups fired. The average LARGEST/SMALLEST = 2.103, close to 1.91. This real world DATA suggests to me that the assumption of normality and the 1.91 estimate are supported pretty well.
Modeling group size and monte carlo repeats allow us to tell about anything about groups. We can answer about any question about group sizes.
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Something that I would like to bring up, regarding this subject, is “conditions".
If it's groups shot indoors at 50 ft, I can see discounting them but, at 100 yards and especially 200 yards, I believe they play at least a moderate if not a big role in ES's of groups.
In my sport, the reading of conditions is extremely important and that would hold true for Mil, Hunter and Production classes, too as most of them are shot at simular velocity 13 - 1600 fps) Heavy and UN classes are less effected but, still a factor.
I think most will agree that the shooters that win the most (therefore shoot smaller groups) are those that can gauge conditions the best.
I truly wish that I was a lot better at doping conditions than I am and I almost always ascribe my fliers to NOT calling a condition.
Frank
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Ric, It is obvious that if we are to get anywhere in discussing “fliers” we have to agree on the definition. Joe usually uses the term “outliers” to mean shots that are probably out there for some physical reason (individual defects of all kinds, gusts of wind, mirage,etc.) This as opposed to shots that are out there just because random variation put them there. Joe suggests that for five shot groups that is usually a shot that increases the group size by 70% if I understand him correctly. In a recent post he seemed to use the term flier as the same thing as outlier. Your post also seems to use flier the same way. That would be fine if we could all agree on that definition.
However, from observation I don't believe that most shooters use the term flier only that way. Holes that increase the size of the best four shots by much less than 70%. are called fliers all the time. I have heard shooters say that their rifle and load will shoot 1” groups if fliers didn't increase them to 1.4". That use of flier may not be “correct” if there is a correct definition, but that's the way it is used by most shooters.
I generally use the term as I hear people using it because I am trying to communicating with shooters not statisticians. I think these two different definitions are causing us to seem to disagree when we really don't.
John
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Something that I would like to bring up, regarding this subject, is “conditions".
If it's groups shot indoors at 50 ft, I can see discounting them but, at 100 yards and especially 200 yards, I believe they play at least a moderate if not a big role in ES's of groups.
In my sport, the reading of conditions is extremely important and that would hold true for Mil, Hunter and Production classes, too as most of them are shot at simular velocity 13 - 1600 fps) Heavy and UN classes are less effected but, still a factor.
I think most will agree that the shooters that win the most (therefore shoot smaller groups) are those that can gauge conditions the best.
I truly wish that I was a lot better at doping conditions than I am and I almost always ascribe my fliers to NOT calling a condition.
FrankHere “Wind” is what Frank calls “conditions". Absent data at least suggesting otherwise: Wind affects accuracy least, although much more as range increases. Skill affects accuracy more, but less than Equipment. It's hard to imagine an Equipment improvement, above the Heavy class equipment, that is as great as the difference between Production and Heavy equipment. These changes in group size don't simply add. The changes, in inches, must be squared, the squares summed, and the square root of the sum is the combined change. If the effects of Wind, .046", and Equipment, .345” were eliminated, and Skill improved from Second to First,
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"Wind” is what Frank calls “conditions". No, mirage is also included in “conditions".
"Wind affects accuracy least” Add mirage here.
I just can't get behind that statement and I don't think that competitive shooters, will either.
"Skill affects accuracy more", yes and when combined with “conditions” WILL, lead to smaller “fliers".
When you do you stats, you are also adding (w/o realizing it) the shooters ability at both holding and ability to gauge conditions.
I think the stats would be better served by using the first place finishers in match results.
Frank
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In the 5 five shot group testing are we ascribing any shot outside the “average” of the 5 groups as a “flyer"? or any shot outside the smallest group shot with a particular load?
I'm beginning to question if what we call are calling “flyers” (or “outliners") here aren't really flyers in the usual external ballistics sense of the word.
LMG
Concealment is not cover.........
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Let me take a run at this. If I fail to connect the dots, I apologize in advance. My hypothesis is that we are all looking for a valid way to isolate and quantify the variance in our results caused by less than perfect bullets. If i shoot a 5 shot group and 1 shot is not where I want it to be, I think we could all agree that it is not proof that the bullet was flawed. If I shoot 4 groups? 10 groups? 20 groups does it become easier? How about if our Heavy rifle national champion was doing the shooting? Do the basic answers we are seeking become easier to identify. His average group size will be smaller. The variance in his group size measured in MOA will get smaller. There is , however, no proof that his variance in group size measured relative to his equipment and his abilities would get any smaller. Simply put his variance as a percent of his group agg wouldn't necessarily vary one bit from that of a less accomplished shooter.
Now if our expert were to fire 100 groups with the most perfect bullets we can make, we will get a distribution of measurements that may well be a normal distribution as Joe suggested. If it is we now have a distribution of groups with a mean and with a standard deviation we can calculate. (1000 groups would be better). No shot was an outlier as we were using our most perfect bullets. The next day is an identical day. Conditions are the same, the shooter is the same, the equipment is the same, etc. We now substitute bullets that all have rounded edges on their bases. Our shooter fires his first group and there is one shot uncomfortably away from the rest. An outlier - not necessarily. We need to have all 100 groups. Now we can calculate a new mean and standard deviation .
Now we can see what impact our rounded edges had. No single shot or no single group helps us. The logistics of this approach are a problem of course. I suppose the most practical solution would be a single shooter alternating groups - lets say 40-5 shot groups. 20 with perfect bullets and 20 with similarly flawed bullets. These groups would need to be alternated and the actual order would need to be “blind” to the shooter to avoid bias. No single shot or no single group still will help us. It is only when we compare the two statistically valid sets of groups that we may be able to draw a conclusion.
Until then you may be assured that any shot I fire which does not hit where I want will be labelled a flier.
I am sorry this got too long.
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For the purpose of our discussion I propose that we define “flier” as any shot in a five shot group that increases the size of the group from 20 to 70% over the group size of the four closest shots. The great majority of these are caused by the natural variation as explained by Joe above and are seldom the result of defective bullets. My testing hints that this is true but to prove it solidly enough to convince more shooters we need more testing.
Shots that increase the size of the group of the four best shots over 70% in good shooting conditions (whatever that means) and all the holes that are clearly caused by bullet or load defects like the one pointed out by Ric in his 102 shot group should be called “outliers.” Outliers could be cautiously considered as possibilities for deleting from test data. Fliers should never be deleted from the test data.
My reason for suggesting the 20-70% be the criteria for the term flier is because I think that fairly well matches what a lot of shooters now call fliers. I think that unless we adopt some similar definitions we will have a hard time communicating.
John
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"Wind” is what Frank calls “conditions". No, mirage is also included in “conditions".
No Frank, “Wind", my definition, is what you call “conditions", your definition.
"Wind affects accuracy least” Add mirage here.
I just can't get behind that statement and I don't think that competitive shooters, will either.
It doesn't matter if you or anyone else can “get behind” that statement, until you or someone comes up with some DATA to refute it, it's there, out in front of you. Show us the data Frank, show us how shooters compensate for “Wind” = “conditions", and how much. Otherwise you're expressing opinions about facts, Frank, and that doesn't make sense.
"Skill affects accuracy more", yes and when combined with “conditions” WILL, lead to smaller “fliers".
When you do you stats, you are also adding (w/o realizing it) the shooters ability at both holding and ability to gauge conditions.
You have no idea how I did this analysis, Frank, you never read it. I think the stats would be better served by using the first place finishers in match results.
Show us how to do that, Frank. Please. Frank
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For the purpose of our discussion I propose that we define “flier” as any shot in a five shot group that increases the size of the group from 20 to 70% over the group size of the four closest shots. The great majority of these are caused by the natural variation as explained by Joe above and are seldom the result of defective bullets. My testing hints that this is true but to prove it solidly enough to convince more shooters we need more testing.
Shots that increase the size of the group of the four best shots over 70% in good shooting conditions (whatever that means) and all the holes that are clearly caused by bullet or load defects like the one pointed out by Ric in his 102 shot group should be called “outliers.” Outliers could be cautiously considered as possibilities for deleting from test data. Fliers should never be deleted from the test data.
My reason for suggesting the 20-70% be the criteria for the term flier is because I think that fairly well matches what a lot of shooters now call fliers. I think that unless we adopt some similar definitions we will have a hard time communicating.
John Shoot a gun that averages 1” 5 shot groups and some groups will be >1", some <1".
The more groups shot, the larger will be the largest and the smaller will be the smallest.
Shoot enough groups and start to see some few VERY big groups, with one shot WAY out.
BUT, the gun still averages 1” 5 shot groups.
Every group will have 1 shot that makes the group > the other-four-shot-group size.
WAY out shots are either the result of natural variation, or some STRANGE thing happening.
We can NEVER tell what caused one shot to be WAY out. We CAN say this: If 1 shot makes a 5 shot group ~ 1.7or more X as big as the other 4 shot group, we would expect this to happen only ~4.5% of the time by natural variation. Thus, ~95.5% of the time this shot location is caused by a STRANGE thing.
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Shoot a gun that averages 1” 5 shot groups and some groups will be >1", some <1".
The more groups shot, the larger will be the largest and the smaller will be the smallest.
Shoot enough groups and start to see some few VERY big groups, with one shot WAY out.
BUT, the gun still averages 1” 5 shot groups.
Every group will have 1 shot that makes the group > the other-four-shot-group size.
WAY out shots are either the result of natural variation, or some STRANGE thing happening.
We can NEVER tell what caused one shot to be WAY out. We CAN say this: If 1 shot makes a 5 shot group ~ 1.7or more X as big as the other 4 shot group, we would expect this to happen only ~4.5% of the time by natural variation. Thus, ~95.5% of the time this shot location is caused by a STRANGE thing. Joe, I am in complete agreement. Does that somehow conflict with my claim that we need definitions? John
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"We can NEVER tell what caused one shot to be WAY out. We CAN say this: If 1 shot makes a 5 shot group ~ 1.7or more X as big as the other 4 shot group, we would expect this to happen only ~4.5% of the time by natural variation. Thus, ~95.5% of the time this shot location is caused by a STRANGE thing.”
Joe, Why didn't you say it that way before? Now my little mind can get around that concept.
Ric
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I started this thread to discuss that the size of groups with the same load, rifle and shooter vary way more than most shooters think they do. Ric says he is surprised that they don’t vary more but most shooters apparently think nothing of the kind since they routinely report that they use one 5-shot group at each load level in finding best load and one pair of 5-shot groups to see which lube, seating depth, primer, etc. is best. They would have better luck if they used bigger samples. Because so many shooters are spinning their wheels and don’t know it I think this deserves discussion and an article in TFS to try to help them.
However, I also mentioned fliers. Fliers immediately took over the thread. I suppose that is some kind of measure of the interest in fliers. Talking about fliers is OK by me, I will start another thread about the variation of groups. Let’s keep on discussing fliers since we have had a lot of good posts. All shooters should read Joe’s explanation in post #12 over until they understand it.
Things I think people in the discussion understand include: We can’t ever be sure that the individual shot that enlarges the best four shot group has a physical cause or is just natural variation (see post #12). However, if the shot enlarges the four shot group a small amount it is more likely to be caused by natural variation than a shot that enlarges the four shot group more. Thus when the percentage increase is very small the chance that is just natural variation approaches 100%. Joe tells us that at 70% increase there is only 4.5 percent chance that it is natural variation. This is true for small groups (high quality equipment, shooter, and conditions) and large groups (not such high quality inputs.)
If I am wrong about my assumption of agreement in the paragraph above we perhaps need to discuss disagreement first.
John
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I'll butt out of this discussion but, first I'd like to address these two questions, since they are directed at me:
You have no idea how I did this analysis, Frank, you never read it.
Please tell me/us how that you resolved the “fliers” when shot in 5, 10, 15 and 20 mph variable winds and what direction the wind was, as well as how often the conditions occurred? You CAN NOT say that it doesn't matter as a 10 mph with at 90 deg the bullets direction will cause a .28 BC (a average 30 cal BC. 22 cal BC's are usually way lower) bullet shot at 1600 fps, to be dispersed by 2.91". Saying that it's accurate because it from a large sample, doesn't cut it, as you are just measure how that the majority of shooters can't read conditions, accurately and I believe that, that's what is being measured, is their inability to gage conditions. If your data was shot in a vacuum or a indoor range I will concede.
"I think the stats would be better served by using the first place finishers in match results." Show us how to do that, Frank. Please.
I would suggest that you take shooters scores that are record holders, and follow their results at all matches that they shoot and the first place finishers results from the last 5 years at the yearly National shoot and use that info for the flier stats. It won't be as accurate as groups shot indoors but, as they will be much better at calling all “conditions", it will be much more accurate than any other single or other groups of shooters and I would have much more confidence than saying that conditions mean little, it just a plain fact, that reading conditions is the reason that most, if not all matches are won.
In addition, if you will take my results, seriously, next time out, I will shoot 4 five shot groups, watching the conditions with my flags and in alternating targets, shoot the same number of groups in unfavorable conditions.
I'm NOT posting to be negitive, I'm posting for accuracy. I'm a competitive shooter and have to deal with these things at each match, that I shoot. For me, the most important thing in accuracy IS reading conditions and the better I do at reading the conditions, the better I place. What some people call “fliers” I call a missed condition!
Frank
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I bought 3# of Titegroup, got the 22-250 Striker shooting with it, easy and fast- then tried to get the Savage 12 FV going yesterday. Last time with the FV; 5, 5.5 and 6 grains produced big ugly groups, too big to measure. Loaded 3.5, 3.9, 4.3 and 4.7 grains and shot them yesterday. 3.5 grains, 3 groups of 2.85", 2.95” and 3.15” 3.9 grains, 1st group missing a shot, it just isn't on the paper. Then 4.0” and 1.7” 4.3 grains, 1st group is an even 8", see the picture 4.7 grains, no measurable groups I went home, unscrewed the varmint weight barrel off the gun and screwed on a 22” light sporter barrel. There's got to be something wrong for the gun to shoot so erratically. This brings up a caveat. In talking about groups and fliers and anything measured and statisticed, the process must be operating smoothly. Groups can be big, but they've got to be sorta round and sorta consistent. Not like mine. My results are telling me that something is amiss, something is causing wild changes in where them bullets hit. I've got to find and fix that before doing much more analysis.
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Joe, Have you checked your telescope and your mounts.Mike.
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Joe, Have you checked your telescope and your mounts.Mike.
Mike;
Yes, and checked everything else I can think of.
Yesterday, after the very poor shooting, I shot 5 shots of a known fair load into ~1.5". The rifle will shoot some loads fairly reliably < 2", but other loads, Titegroup so far, just wild.
Today I'll take everything apart and see if I can find the gremlin.
Thanks;
joe b.
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LARGEST OVER SMALLEST GROUPS IN SETS OF GROUPS
5 SHOT 10 SHOT
GROUPS LARGEST/ LARGEST/
SHOT SMALLEST SMALLEST
2 1.36 1.25
3 1.59 1.39
4 1.77 1.50
5 1.91 1.59
6 2.03 1.66
7 2.14 1.71
8 2.24 1.77
9 2.33 1.81
10 2.41 1.86
Here's the table. For 5 shot groups, when 7 groups are shot, the largest/smallest is 2.03. Means that if we were to shoot MANY sets of 7 five shot groups and measure the largest/smallest, the AVERAGE largest/smallest would be 2.03. OR, if we shoot 7 five shot groups and measure them, we would EXPECT the largest/smallest to = 2.03.
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