Circular error probable, as traditionally used for characterizing ballistic missile performance, has advantages over the c-t-c measures most of use to characterize our shooting systems. I've written a short paper,not too mathematical) entitled Characterizing rifle performance using circular error probable measured via a flatbed scanner that you can find at www.statshooting.com. I'd be interested in comments.
Using circular error probable to characterize rifles
- Thread starter cfmcmillan
- Start date
BoydAllen
Gold $$ Contributor
If ones hobby is primarily shooting and not statistics, and one wants to be able to characterize the accuracy of a rifle or load at the range it would seem that your system would be of little use.
Also,this system virtually guarantees that there will be a very low probability of being understood when communicating information about accuracy to a listener or reader who has no interest in taking a statics course or reviewing one taken years, or decades earlier.
It has been my experience that the farther up the road of technical complexity one travels, in the hobby of shooting, the fewer people there are with which one can have a conversation that has the prospect of being mutually illuminating. Given this state of affairs, and the desire to maintain a social component, it would seem prudent to limit complexities to those that are absolutely necessary to the pursuit of accuracy, lest one be reduced to having a conversation with oneself.
Also,this system virtually guarantees that there will be a very low probability of being understood when communicating information about accuracy to a listener or reader who has no interest in taking a statics course or reviewing one taken years, or decades earlier.
It has been my experience that the farther up the road of technical complexity one travels, in the hobby of shooting, the fewer people there are with which one can have a conversation that has the prospect of being mutually illuminating. Given this state of affairs, and the desire to maintain a social component, it would seem prudent to limit complexities to those that are absolutely necessary to the pursuit of accuracy, lest one be reduced to having a conversation with oneself.
Body's point is well taken - however, I can think of a number of folks who might find this useful.
1. Those of us,I put myself in this camp) who wear propellers on our beanies, have a pocket protector for all our pens and carried,at some point in life) a calculator on our belts - the geeks. Those for whom science fair projects did not end with grade school.
2. Those who are worried about the details of accuracy - the competitors - who are selecting among rifles, scopes, hand loads and the like.
3. Those buying expensive custom equipment - it would be nice to know whether the piece of hardware I just plunked down 2-3K for really improved my accuracy or not.
4. Those making and selling custom equipment - from a QA perspective it would be nice to be able to convincingly show prospective customers what they are buying.
5. Those trying to get accuracy from hand-loads. It pains me to see guys at the range using 5 shot groups to try to discriminate between various recipes for hand loads. If the performance is close at all, they probably have a 1:3 chance of picking the load that is worse.
Having said the above, this is approach is clearly not for everyone.
1. Those of us,I put myself in this camp) who wear propellers on our beanies, have a pocket protector for all our pens and carried,at some point in life) a calculator on our belts - the geeks. Those for whom science fair projects did not end with grade school.
2. Those who are worried about the details of accuracy - the competitors - who are selecting among rifles, scopes, hand loads and the like.
3. Those buying expensive custom equipment - it would be nice to know whether the piece of hardware I just plunked down 2-3K for really improved my accuracy or not.
4. Those making and selling custom equipment - from a QA perspective it would be nice to be able to convincingly show prospective customers what they are buying.
5. Those trying to get accuracy from hand-loads. It pains me to see guys at the range using 5 shot groups to try to discriminate between various recipes for hand loads. If the performance is close at all, they probably have a 1:3 chance of picking the load that is worse.
Having said the above, this is approach is clearly not for everyone.
In defense of the statistical approach mentioned here, it gives 2.5 times as much as information from a 5-shot group as you get by measuring center-to-center,which only contains information from 2 of the 5 shots). Further, the CEP summary statistic is really more useful than a center-to-center measure, because it is independent of the number of shots fired. Further, it is possible to determine whether the CEP from, say, two different loads, is really statistically,i.e., meaningfully) different, using fewer shots that would be required if using c-t-c. Saves a lot of barrel wear during load development/testing.
It's really just a scanner/computer update of the old "string-measure" used a century or more ago, where the displacement of every shot from the center was made by wrapping a string around wooden plugs put in each bullet hole,starting and returning the string to center for each bullet hole), then measuring the total length of the string. Every shot is a data point.
It's probably a good thing that most people don't bother to understand statistics -- otherwise, we'd have to raise taxes to make up for the lottery ticket sales we get now.
It's like the guy who heard that most car accidents happen within 25 miles of home. So he moved.
Toby Bradshaw
baywingdb@comcast.net
It's really just a scanner/computer update of the old "string-measure" used a century or more ago, where the displacement of every shot from the center was made by wrapping a string around wooden plugs put in each bullet hole,starting and returning the string to center for each bullet hole), then measuring the total length of the string. Every shot is a data point.
It's probably a good thing that most people don't bother to understand statistics -- otherwise, we'd have to raise taxes to make up for the lottery ticket sales we get now.
It's like the guy who heard that most car accidents happen within 25 miles of home. So he moved.
Toby Bradshaw
baywingdb@comcast.net
BoydAllen
Gold $$ Contributor
Cfmcmillan,
Assuming that everything else is working up to snuff, on a day with good testing conditions,using a rifle that has demonstrated its accuracy to be in the low ones to high 0s with the best ammo, conditions, and operator input, if you were starting from scratch with a new bullet and powder that were both working well for someone else shooting a similar rifle in the same caliber, how many shots would be required,with your method, to find the best load possible with those components, including neck tension, seating depth, primer preference, and powder charge, as well as that powder's, barrel and pressure requirements for cleaning frequency and method, with the understanding that all testing is to be done by a shooter with only slightly better than average trigger pulling and wind reading skills? Also,just out of curiosity, what is the most accurate centerfire rifle that you regularly shoot?
Assuming that everything else is working up to snuff, on a day with good testing conditions,using a rifle that has demonstrated its accuracy to be in the low ones to high 0s with the best ammo, conditions, and operator input, if you were starting from scratch with a new bullet and powder that were both working well for someone else shooting a similar rifle in the same caliber, how many shots would be required,with your method, to find the best load possible with those components, including neck tension, seating depth, primer preference, and powder charge, as well as that powder's, barrel and pressure requirements for cleaning frequency and method, with the understanding that all testing is to be done by a shooter with only slightly better than average trigger pulling and wind reading skills? Also,just out of curiosity, what is the most accurate centerfire rifle that you regularly shoot?
Bryan Litz Ballistics
Site $$ Sponsor
Mr McMillan,
Thank you for presenting your work. We all care about rifle accuracy and precision but we have such a poor standard of measure in c-to-c. It's so refreshing to see such a rigorous approach to measurement. I've often thought that a CEP or similar approach would be better for determining winners of target shooting matches,BR in particular) but some disciplines are so steeped in tradition that the method probably wouldn't catch on.
Short of changing the measure of winning accuracy/precision, your methods are certainly of great use to shooters wishing to make more informed decisions about what variables really affect the precision of their equipment, and by how much.
One benefit of the approach is that it gives one the ability to quantify the accuracy/precision of a shooting system in a way that allows 'probability of hit' analysis for a given size target at some range. For example, if a rifle shoots 1.5 MOA c-to-c at 800 yards,12"), and a target with an 8" vital area is presented at that range, what is the probability of hit against that target?
,of course this requires a slight departure from the CEP approach because CEP only identifies the '50%' radius...)
I've read your paper linked above, and intend to read the rest of the material on your golden nugget of a website in time. For now, here are some specific comments on the one paper:
-I appreciate you only presenting methods best suited for N<=20. The paper could have easily been cluttered with other irrelevant methods.
-My biggest criticism is your assumption that there is zero aiming error,scope is adjusted to remove all aiming error). Shooters who are serious enough to undertake this level of analysis will be shooting extremely accurate rifles, capable of 1/4" 5-shot groups,c-to-c) at 100 yards. Most scope adjustments are 1/4 MOA, which means there can be up to 1/2 of the groups size in aiming error. Even for the 1/8 MOA scope clicks, this still allows for 1/4 of the groups size in aiming error. It may be better to ignore the accuracy of the aiming, and focus on the precision of the shooting system. In other words, disregard the actual aiming point and instead determine the center of the group and assume that was the aim point.
-I also have a critisism of the target design, in particular, the many aiming points. Real shooting matches,BR-50 is an exception) use only one aiming point for the whole group or string. By having multiple aiming points, you introduce the variable of repositioning the rifle between each shot in the test, a variable that's not present in actual shooting contests.
-I found your references and other 'support' material on the website to be very remarkable.
It's up to each person how they choose to quantify their shooting systems performance, and I suspect few common shooters will adopt this method, simply because of the complexity, and the effort required to properly measure the targets. I think that manufacturers of shooting components,barrels, bullets, tuners, etc) would be compelled to use more rigorous measurement techniques to demonstrate the improvement offered by their product,IF it's genuine)
Again, thank you for sharing your excellent work. I'll probably be in touch with you guys in the future to discuss statistical methods.
-Bryan
Thank you for presenting your work. We all care about rifle accuracy and precision but we have such a poor standard of measure in c-to-c. It's so refreshing to see such a rigorous approach to measurement. I've often thought that a CEP or similar approach would be better for determining winners of target shooting matches,BR in particular) but some disciplines are so steeped in tradition that the method probably wouldn't catch on.
Short of changing the measure of winning accuracy/precision, your methods are certainly of great use to shooters wishing to make more informed decisions about what variables really affect the precision of their equipment, and by how much.
One benefit of the approach is that it gives one the ability to quantify the accuracy/precision of a shooting system in a way that allows 'probability of hit' analysis for a given size target at some range. For example, if a rifle shoots 1.5 MOA c-to-c at 800 yards,12"), and a target with an 8" vital area is presented at that range, what is the probability of hit against that target?
,of course this requires a slight departure from the CEP approach because CEP only identifies the '50%' radius...)
I've read your paper linked above, and intend to read the rest of the material on your golden nugget of a website in time. For now, here are some specific comments on the one paper:
-I appreciate you only presenting methods best suited for N<=20. The paper could have easily been cluttered with other irrelevant methods.
-My biggest criticism is your assumption that there is zero aiming error,scope is adjusted to remove all aiming error). Shooters who are serious enough to undertake this level of analysis will be shooting extremely accurate rifles, capable of 1/4" 5-shot groups,c-to-c) at 100 yards. Most scope adjustments are 1/4 MOA, which means there can be up to 1/2 of the groups size in aiming error. Even for the 1/8 MOA scope clicks, this still allows for 1/4 of the groups size in aiming error. It may be better to ignore the accuracy of the aiming, and focus on the precision of the shooting system. In other words, disregard the actual aiming point and instead determine the center of the group and assume that was the aim point.
-I also have a critisism of the target design, in particular, the many aiming points. Real shooting matches,BR-50 is an exception) use only one aiming point for the whole group or string. By having multiple aiming points, you introduce the variable of repositioning the rifle between each shot in the test, a variable that's not present in actual shooting contests.
-I found your references and other 'support' material on the website to be very remarkable.
It's up to each person how they choose to quantify their shooting systems performance, and I suspect few common shooters will adopt this method, simply because of the complexity, and the effort required to properly measure the targets. I think that manufacturers of shooting components,barrels, bullets, tuners, etc) would be compelled to use more rigorous measurement techniques to demonstrate the improvement offered by their product,IF it's genuine
)Again, thank you for sharing your excellent work. I'll probably be in touch with you guys in the future to discuss statistical methods.
-Bryan
A couple of points. Just because a rifle HAS shot in the zeros does not mean that it WILL shoot in the zeros for an agg. There are two alternative explanations for comparatively rare groups in the zeros:
1. The rifle COULD agg in the zeros if the shooter is sufficiently skilled and the conditions,or lack thereof) permit. This is what most people seem to believe. From the Houston warehouse we know that this explanation is at least possible, though apparently not all that common.
2. The groups in the zeros represent the left tail of the distribution of group sizem with the mean,agg) group size somewhere to the right,larger). A thousand monkeys at a thousand typewriters for a thousand years = Shakespeare. A thousand shooters with a thousand 0.250 rifles will shoot in the zeros from time to time. ,And we can calculate that probability easily if we know the CEP or group size distribution for a particular rifle, load, shooter, and conditions.)
Personally, having shot some competitive benchrest, including some match winners in the zeros,and many practice groups in the zeros), I like to think that Explanation #1 is closer to correct, when talking about top shooters and top equipment. But conditions are such a big part of the game that the equipment's and shooter's capabilities can only be known with any certainty by shooting in dead calm or "warehouse" environments.
All the variables in group shooting,e.g., neck tension, seating depth, type of sand in the bags, direction/intensity of wind info from each wind flag, powder type/lot/charge, ad infinitum) could be plugged into an analysis of variance to gauge their effect on CEP,or, with more shots, group size). Detecting a difference produced by any of these factors depends entirely on the magnitude of the difference and the sample size. To detect a small effect,in a game where small effects really do matter) takes a large sample size. CEP gives a larger sample size than c-t-c for the same number of shots, and so would be superior for any kind of statistical analysis. A power analysis could be done to figure out how many shots would have to be taken to find a statistically significant difference of a predetermined magnitude, given a known,estimated, really) CEP for the initial setup. Surely the number of shots is larger than most non-statisticians would expect, since so many people will make decisions based on one or two groups,2-4 shots of information, if c-t-c is used).
Most competitive shooters don't do a full-scale statistical analysis -- they take shortcuts based on experience,including the experience of thousands of other shooters who pass on information in forums like this one) and intuition. In my experience,which doesn't include ever winning an agg!) perhaps half the rifles on the line COULD win if steered by the right shooter. I.e., most of the rifles, loads, and equipment are good enough, and the top shooters beat the trigger pullers by doping the conditions better. A match winner can be shot by almost anybody with decent equipment in a relay where conditions are right, which is why there are a lot more people who can win a match than can win an agg, and only a handful of people who can CONSISTENTLY win an agg.
FWIW.
Toby Bradshaw
baywingdb@comcast.net
1. The rifle COULD agg in the zeros if the shooter is sufficiently skilled and the conditions,or lack thereof) permit. This is what most people seem to believe. From the Houston warehouse we know that this explanation is at least possible, though apparently not all that common.
2. The groups in the zeros represent the left tail of the distribution of group sizem with the mean,agg) group size somewhere to the right,larger). A thousand monkeys at a thousand typewriters for a thousand years = Shakespeare.
A thousand shooters with a thousand 0.250 rifles will shoot in the zeros from time to time. ,And we can calculate that probability easily if we know the CEP or group size distribution for a particular rifle, load, shooter, and conditions.)Personally, having shot some competitive benchrest, including some match winners in the zeros,and many practice groups in the zeros), I like to think that Explanation #1 is closer to correct, when talking about top shooters and top equipment. But conditions are such a big part of the game that the equipment's and shooter's capabilities can only be known with any certainty by shooting in dead calm or "warehouse" environments.
All the variables in group shooting,e.g., neck tension, seating depth, type of sand in the bags, direction/intensity of wind info from each wind flag, powder type/lot/charge, ad infinitum) could be plugged into an analysis of variance to gauge their effect on CEP,or, with more shots, group size). Detecting a difference produced by any of these factors depends entirely on the magnitude of the difference and the sample size. To detect a small effect,in a game where small effects really do matter) takes a large sample size. CEP gives a larger sample size than c-t-c for the same number of shots, and so would be superior for any kind of statistical analysis. A power analysis could be done to figure out how many shots would have to be taken to find a statistically significant difference of a predetermined magnitude, given a known,estimated, really) CEP for the initial setup. Surely the number of shots is larger than most non-statisticians would expect, since so many people will make decisions based on one or two groups,2-4 shots of information, if c-t-c is used).
Most competitive shooters don't do a full-scale statistical analysis -- they take shortcuts based on experience,including the experience of thousands of other shooters who pass on information in forums like this one) and intuition. In my experience,which doesn't include ever winning an agg!) perhaps half the rifles on the line COULD win if steered by the right shooter. I.e., most of the rifles, loads, and equipment are good enough, and the top shooters beat the trigger pullers by doping the conditions better. A match winner can be shot by almost anybody with decent equipment in a relay where conditions are right, which is why there are a lot more people who can win a match than can win an agg, and only a handful of people who can CONSISTENTLY win an agg.
FWIW.
Toby Bradshaw
baywingdb@comcast.net
Bryan Litz Ballistics
Site $$ Sponsor
Toby,
Thanks for your insight into the short range BR world. I agree with your statements, and I've got a couple reactions:
1. I think it would only take one monkey a day or two to produce the equivalent of Shakespeare's collected works
2. Here are two of the statements you made,I'm paraphrasing): "many things make a small difference, and small differences matter". and: "good shooters can win with most equipment because skill in reading/managing conditions is more important than having equipment that's marginally better".
I think these statements are a strong argument in favor of a statistical analysis that can determine with some known confidence if one 'system' is better than another, or not. In other words, is there really a meaningful difference between 0.002" and 0.004" of neck tension? I suspect that many of these variables would be shown to have no real significant effect, at least not as much as we think. The logical conclusion would be to spend less time in search of that elusive and unrepeatable 1% gain in precision and spend that time at the range studying conditions and learning to shoot better.
3. 97.5% of all statistics are made up on the spot...
Take care,
-Bryan
Thanks for your insight into the short range BR world. I agree with your statements, and I've got a couple reactions:
1. I think it would only take one monkey a day or two to produce the equivalent of Shakespeare's collected works
2. Here are two of the statements you made,I'm paraphrasing): "many things make a small difference, and small differences matter". and: "good shooters can win with most equipment because skill in reading/managing conditions is more important than having equipment that's marginally better".
I think these statements are a strong argument in favor of a statistical analysis that can determine with some known confidence if one 'system' is better than another, or not. In other words, is there really a meaningful difference between 0.002" and 0.004" of neck tension? I suspect that many of these variables would be shown to have no real significant effect, at least not as much as we think. The logical conclusion would be to spend less time in search of that elusive and unrepeatable 1% gain in precision and spend that time at the range studying conditions and learning to shoot better.
3. 97.5% of all statistics are made up on the spot...
Take care,
-Bryan
Bryan,
Disagree on #1 -- I'm a fan of Shakespeare!
Agree completely on #2, and this is pretty much why I stopped shooting competitive benchrest. With top equipment,a Borden-smithed/Panda/Hart/Jewell/McMillan 6PPC -- sound familiar?) I learned to shoot well from a bench and to put together,and adjust) loads that were accurate enough to win at any local/regional event. This is the real reason I gave benchrest a try -- I just wanted to know if I could shoot a rifle to the highest standard of accuracy,sometimes). I very much enjoyed my time in the sport, and the people I met at tournaments are the salt of the earth. I also learned a heckuva lot about what it takes to make a rifle shoot, which is why I still smile every time I read a post about those 0.250MOA out-of-the-box factory varmint rifles.
But I realized that the guys who were beating me every weekend didn't really have a better mechanical system than I had. What they did have was superior wind-doping ability, and the skill to know when to shoot as well as where to point. It was always hard for me to hold in the 7-ring to put a bullet in the group in a reverse, but the good shooters thought nothing of this,or machine-gunned so they never had to think about it!).
To even hope to be competitive, I would have had to practice much more in typical,= BAD) conditions, to learn to read conditions and have the confidence to trust my reading when the "30 seconds!" announcement finds me with 4 shots fired in a different condition on the record target. I just didn't want to put forth the effort, because of other time commitments. I acquired tremendous respect for the shooters who HAVE made that kind of commitment.
I suspect, as you do, that far too much time is spent chasing 0.010 or 0.050 in group size by fooling with equipment,and without any statistically valid means of knowing whether the goal has been achieved), and far too little time practicing in conditions. It only takes something like a 0.5mph crosswind to move a 6PPC bullet 0.050 at 100 yards ... more to be gained by learning to dope conditions than by diddling around with ammo, for most folks shooting decent equipment. In fact, I've often wondered whether most shooters wouldn't be better off with slightly less inherent accuracy if they could shoot bullets with a higher BC to make wind doping less critical.
Wouldn't it be interesting to do an experiment at a BR tournament by randomly assigning a rifle to each shooter for one match, or even for all 5 targets at the 200yd range,which usually separates the wheat from the chaff)? I am very sure that the top shooters I know could whip my a** with my own rifle and ammo!
Finally, BR is enough of a mind game that if someone THINKS they have found that last 0.010 it could easily make a difference in their confidence level that could translate into better shooting. As long as the "tweak" hasn't HURT accuracy, the placebo effect might be an advantage.
Toby Bradshaw
baywingdb@comcast.net
Disagree on #1 -- I'm a fan of Shakespeare!
Agree completely on #2, and this is pretty much why I stopped shooting competitive benchrest. With top equipment,a Borden-smithed/Panda/Hart/Jewell/McMillan 6PPC -- sound familiar?) I learned to shoot well from a bench and to put together,and adjust) loads that were accurate enough to win at any local/regional event. This is the real reason I gave benchrest a try -- I just wanted to know if I could shoot a rifle to the highest standard of accuracy,sometimes). I very much enjoyed my time in the sport, and the people I met at tournaments are the salt of the earth. I also learned a heckuva lot about what it takes to make a rifle shoot, which is why I still smile every time I read a post about those 0.250MOA out-of-the-box factory varmint rifles.
But I realized that the guys who were beating me every weekend didn't really have a better mechanical system than I had. What they did have was superior wind-doping ability, and the skill to know when to shoot as well as where to point. It was always hard for me to hold in the 7-ring to put a bullet in the group in a reverse, but the good shooters thought nothing of this,or machine-gunned so they never had to think about it!).
To even hope to be competitive, I would have had to practice much more in typical,= BAD) conditions, to learn to read conditions and have the confidence to trust my reading when the "30 seconds!" announcement finds me with 4 shots fired in a different condition on the record target. I just didn't want to put forth the effort, because of other time commitments. I acquired tremendous respect for the shooters who HAVE made that kind of commitment.
I suspect, as you do, that far too much time is spent chasing 0.010 or 0.050 in group size by fooling with equipment,and without any statistically valid means of knowing whether the goal has been achieved), and far too little time practicing in conditions. It only takes something like a 0.5mph crosswind to move a 6PPC bullet 0.050 at 100 yards ... more to be gained by learning to dope conditions than by diddling around with ammo, for most folks shooting decent equipment. In fact, I've often wondered whether most shooters wouldn't be better off with slightly less inherent accuracy if they could shoot bullets with a higher BC to make wind doping less critical.
Wouldn't it be interesting to do an experiment at a BR tournament by randomly assigning a rifle to each shooter for one match, or even for all 5 targets at the 200yd range,which usually separates the wheat from the chaff)? I am very sure that the top shooters I know could whip my a** with my own rifle and ammo!
Finally, BR is enough of a mind game that if someone THINKS they have found that last 0.010 it could easily make a difference in their confidence level that could translate into better shooting. As long as the "tweak" hasn't HURT accuracy, the placebo effect might be an advantage.
Toby Bradshaw
baywingdb@comcast.net
BoydAllen
Gold $$ Contributor
Bryan,
Many things that get lost in the wind at longer ranges don't at shorter. Try it, you might like it. I should add that apparently the opposite is true. There are things that matter quite a bit at longer ranges that seem to make little difference at 1-200. My point, of course, is that making inferences about one from experience with the other, can lead one astray.
Most of what I know, I learned from more experienced shooters. They were kind enough to share their knowledge, and I was smart enough to listen and try what was suggested. For example, when discussing neck tension with a friend who is one of a long list of my betters, he told me that he and a friend of similar talent use quite a bit of neck tension when loading 133. Somewhat skeptical, I tried it, and my average group size shrank, measured the same way they are at matches.
BC wind drift, and projectile stability, and design may require a mastery of higher mathematical concepts, knowing that your groups have shrunk is a lot easier, and I have never seen a scanner at the range, which is where I do my loading and tuning.
As far as I know, the long range disciplines preload and while there a small record of success with this in short range, it the weather changes much, it is more likely a recipe for disaster. Changes during a match day are a semi educated guess, and the only opportunity for testing alternate loads is on the sighter target during a match where the changing wind and heavy mirage may make evaluation of the differences between loads near impossible, and of course there are no chronographs.
Many things that get lost in the wind at longer ranges don't at shorter. Try it, you might like it.
I should add that apparently the opposite is true. There are things that matter quite a bit at longer ranges that seem to make little difference at 1-200. My point, of course, is that making inferences about one from experience with the other, can lead one astray.Most of what I know, I learned from more experienced shooters. They were kind enough to share their knowledge, and I was smart enough to listen and try what was suggested. For example, when discussing neck tension with a friend who is one of a long list of my betters, he told me that he and a friend of similar talent use quite a bit of neck tension when loading 133. Somewhat skeptical, I tried it, and my average group size shrank, measured the same way they are at matches.
BC wind drift, and projectile stability, and design may require a mastery of higher mathematical concepts, knowing that your groups have shrunk is a lot easier, and I have never seen a scanner at the range, which is where I do my loading and tuning.
As far as I know, the long range disciplines preload and while there a small record of success with this in short range, it the weather changes much, it is more likely a recipe for disaster. Changes during a match day are a semi educated guess, and the only opportunity for testing alternate loads is on the sighter target during a match where the changing wind and heavy mirage may make evaluation of the differences between loads near impossible, and of course there are no chronographs.
Bryan -
Thanks for your thoughtful comments. Both of your points are well taken.
I've outlined an analysis that is referred to in the literature as CEP_MPI where MPI refers to the "mean point of impact". The issue of bias in CEP measurements is well studied in the Air Force literature on the subject. Thus, extending this work to account for the bias should not be difficult. When I do it, I'd like to couple it with a bit more Monte Carlo work to be sure I understand how the statistics are working.
The many aim points are not essential to the analysis. When I did the initial target design, I wanted to be able to correlate the POI with each shot fired. However, the analysis could work equally well if shots were fired at a single aim point. The key would be to have enough statistical spread so that the POIs for the different shots didn't overlap significantly. Again, something to take on in a next set of notes.
Thanks for your thoughtful comments. Both of your points are well taken.
I've outlined an analysis that is referred to in the literature as CEP_MPI where MPI refers to the "mean point of impact". The issue of bias in CEP measurements is well studied in the Air Force literature on the subject. Thus, extending this work to account for the bias should not be difficult. When I do it, I'd like to couple it with a bit more Monte Carlo work to be sure I understand how the statistics are working.
The many aim points are not essential to the analysis. When I did the initial target design, I wanted to be able to correlate the POI with each shot fired. However, the analysis could work equally well if shots were fired at a single aim point. The key would be to have enough statistical spread so that the POIs for the different shots didn't overlap significantly. Again, something to take on in a next set of notes.
Boyd -
You asked how many shots it would take to optimize under a certain set of conditions. Unfortunately, as posed, the question can't be answered because you have not said how large the effect on accuracy each of your variables represents. If the effects are large, the number of shots required to measure statistically significant differences is small. However, if the effect is subtle, then the number of shots will be large and, may in fact, be very large.
Even though I cannot answer your question as posed, I can offer one observation with confidence, the number of shots required to demonstrate statistically significant differences would be fewer using CEP than c-t-c. The right half of Figure 1 in our paper shows why. The variability in the measure,labeled "Percent Error") in the paper is always smaller for the CEP measures than it is for c-t-c. Thus at any level of difference in the independent variables you propose, the difference will be easier to discriminate with CEP.
You asked how many shots it would take to optimize under a certain set of conditions. Unfortunately, as posed, the question can't be answered because you have not said how large the effect on accuracy each of your variables represents. If the effects are large, the number of shots required to measure statistically significant differences is small. However, if the effect is subtle, then the number of shots will be large and, may in fact, be very large.
Even though I cannot answer your question as posed, I can offer one observation with confidence, the number of shots required to demonstrate statistically significant differences would be fewer using CEP than c-t-c. The right half of Figure 1 in our paper shows why. The variability in the measure,labeled "Percent Error") in the paper is always smaller for the CEP measures than it is for c-t-c. Thus at any level of difference in the independent variables you propose, the difference will be easier to discriminate with CEP.
BoydAllen
Gold $$ Contributor
That's the point. In the real world we don't know how much to weigh the variables. Some powders "care" about neck tension a lot more than others. Some bullets are more seating depth critical. That is why, in a world of limited resources and 1,200 round barrel life, experience and educated guessing based on anecdotal evidence is the rule. Come out and do the thing that your are writing about, in the real world. That is where the worth of any theory is really proven. That flier that is one in five probably has a real cause that needs fixing, and I assure you that at a match those scoring targets certainly won't disregard it is statistically insignificant.
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