Mean Radius Alone is Meaningless
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- čas přidán 19. 05. 2024
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Favorite Short-Range Load development targets:
Shotmarker circle-cross target: cdn.shopify.com/s/files/1/052...
OCW Target (circles with orange diamond): accurateshooter.net/pix/ocwta... - Sport
That's why it is nice that the OnTarget software lists MR and SD radius, as well as CEP50, CEP90, and CEP95.
The information everyone needs but doesn't want to hear. Good stuff!
I think that your groups look real for 10 shots and this is why we need 20 or 30 shot groups for final decisions. Love your videos. Thanks for what you do.
....in WW2, according to some history I read, for a bolshevik to qualify for Sniper duty he had to put 50 rounds into a certain size target at whatever the given distance was which I do not recall, that said, the point is 50 rounds, I read that like 40 years ago & found that to be interesting aswell as living proof of reality imo, & apparently many other military's world wide that have adopted similar tactics.
The individual radii for each shot which were used to calculate the mean radius can also be used to calculate the SD, and therefore used to determine if the MR for load A is different than load B . This presumes an adequate number of shots were used for each based on how small of a difference one desires to detect.
I partially solved the misleading MR issue about 2 years ago. You simply take the ratio of MR to group size. So 1"MR/2"group size = 0.5 ratio. It mathematically describes the distribution of the group for quick reference. A ratio of 0.5 is a perfect donut, roughly 0.350 to 0.250 is fairly evenly distributed, under about 0.250 is indicative of a tight cluster in the center of the group. So closer to 0.5 = more like donut, closer to 0.0 = more tightly clustered in the center of the group. I use this for analyzing shotgun patterns too. Depending on your application, depends on what ratio, you may want to target in load selection. Not the end all be all, but a very useful reference tool when looking a a group analysis spread sheet.
Mean radius alone gives you the same quality of information as group size alone. Neither tell the whole story.
The value of mean radius is that it more efficiently predicts the spread of the underlying distribution (which is what we really care about). In other words, if you shoot 5 groups and measure the mean radius of each, you'll be able to more accurately predict how spread out the underlying distribution is than if you shoot 5 groups and measure the group size of each. Frank Grubbs proved this in the 60's, although his message doesn't seem to have come through very well to modern shooters.
Ultimately any type of averaging (be it MR or group size) is going to be less informative than the full set of data so it’s not surprising that several groups of various shapes/fliers could be formed with the same MR. From Monte Carlo simulations of groups I’ve done I find one advantage of MR is that as the sample size increases the MR asymptotes out to a constant value where as group size steadily increases. Further I found that applying SD to a group is tricky with small samples (even 10 shots). To get an accurate SD value that is truly representative of the population requires groups in excess of 50 shots - otherwise you just don’t know if those fliers are 2-sigma or 3-sigma events.
Perhaps applying a sort of mean radius to just the horizontal component and another for the vertical component of the dispersion could help quantify the group shape.
Thank you!
Thank you
With the sample sizes 99% of shooters fire, why we don't focus on median values, instead of mean values is a mystery to me. Median values are resistant to outliers, and are especially preferred when sample sizes are small. In a perfect world, mean = median. In reality, outliers, good or bad, drastically affect the mean of the sample, until sample sizes are significantly large. It would be nice if analysis apps and software provided the median and mean values for all metrics, along with all applicable SD's. Generally, the sample median values are more representative of the population, more sooner than the mean of the sample is.
Keith, I feel SD would be a good metric, but not relative to MR as I believe you as doing. What I mean is, why not use SD relative to the the point of impact. It seems to me if we shoot a large enough number of shots we can pin down the point of impact which is just the mean. Then with that same information we can come up with the standard deviation from that mean or point of impact. I think this would be simple enough for people to use as a metric on how precise their gun is. This would make things much easier to compare. Of course one can go much further than this, but this seems way better than what we have now where folks say they have a half minute gun for instance. Instead we say we have a gun with a half minute SD. Why not just do something like this?
I’ve been seeing more and more of this nonsense lately. Thanks for calling it out.
Agree, what a joke !!, - the shots combined INSIDE the total diameter is the group size,.....how hard is that right !!.....the world is getting more & more retarded, not simplified, ......simplified seems to be incomprehensible nowdays.
I am with those who disagree. If you have 9 shots in .250 and the 10th makes the group 2 inches you have a 2 inch group. The MR takes all the good ones AND the bad one for an average. It tells a enormously better truth of the state of your load.
I’m old enough that when I did the rifle shooting merit badge, the range master demanded all shots be under a dime, not touching, under.
Yes Sir - Reality of group size.
Mean radius tells you… the mean radius. Yes you still have to look at the data. I normally compare a mean radius of 100% of the shots to the mean radius of 80% of the shots. There is a ratio between these calculation and if that ratio is greater than the average of all of my groupings it indicates that the group I am analyzing likely has errant shots due to wind/technique/etc. Usually you can tell if there is something strange with your grouping just by looking at it, for example my SU16 likes to vertically string. But in 95% of my cases I get consisten circular groups with 1 in 20 shots being a flyer due to either bullet deformation, shooting technique or something else.
Works for me and is better than simple extreme spread analysis which inly measures 2 shots.
What causes variations is very important. If one bad shot is form related and one shot is component related, what exactly is being measured? Keeping things simple can free the mind to do more important things.
Well said !! - this holds probly the most merit on hitting targets - simple.
Watch out, there is another CZcamsr that may be lurking around to do a drive by.
LMAO !
Ideally we should be looking at actual distribution curves. The problem is getting large enough datasets literally changes the deterministic aspects of our systems like temperature, cleanliness, etc.
I will be called a Hornady fanboy. So be it...
1. There are 2 hypotheses on load (charge weight) development in the general case: a) there tends to be “accuracy nodes” (traditional approaches such as ladder tests and OCW) and b) as a rule, dispersion increases linearly with muzzle velocity (Hornady’s claim based on their large data set testing). It would be fascinating if Hornady were to make their test results public so it can be scrutinized. I would find it even more fascinating if someone can point any higher load producing a lower mean radius than a lower (safe) load with all other things being held constant and with sample sizes of 35 or more shots. That would be a significant blow to Hornady’s claim, but I’ve not seen that yet.
2. Drawing conclusions about future performance based on 10-shot groups isn’t statistically defensible. I just earned 17 Hornady fanboy credits for saying that, but I do think that’s true.
3. Any complaints about the expense involved with 35 shot groups only make sense if we have a high confidence that there are accuracy nodes to be found (see 1 above). If Hornady is correct (that dispersion increases with velocity), then we should think about LOAD VALIDATION, instead of load development.
4. Using a target analysis app allows us to easily determine mean radius (MR). R95 is the radius around the group center than guarantees that 95% of shots will land inside of that radius. Assuming a normal distribution and a statistically significant data set (35 shots or more), then R95 is approximately MR x 2.1. Which means that the predicted diameter that will account for 95% of future shots is MR x 4.2. (I suspect that if most hunters validated their pet loads with 20-35 shot aggregates and used that to computer their 95% diameter, they would be forced to rethink their maximum distances for ethical shots.
5. The Hornady process as I heard it and extended it...
1. Establish your performance needs in terms of dispersion and impact velocity.
2. Pick a powder proven effective for the cartridge and barrel length.
3. Identify a set of bullets suited for your downrange goals.
4. Pick the minimum charge weight needed to achieve your desired impact velocity.
5. For a given bullet, VALIDATE the load by shooting composite targets using strings similar to planned use (course of fire pace for matches and 1, 2, or 3 shots strings for hunting). Abandon the validation if the dispersion exceeds your pre-established criteria (powder/bullet combos don’t get better) or you reach the most statistically valid composite target you can afford. 35 is golden. 20 is sorta. 10 and below is nothing.
6. If a powder/bullet combo fails to meet your criteria, change bullets, as different barrels are know to like different bullets (chamber/ogive+construction).
7. Lastly, aggregate groups that are not round in shape and shot at normal testing distances (e.g. 100 yds) indicate problems in the gun (or bench), the shooter, and/or the weather conditions and should be fixed before drawing conclusions.
Great topic. Like most things theres usually no shortcut to the answers sought, and decisions are best made by considering as much data as possible and all its metrics.
In theory, radial SD is actually ALL that matters when evaluating groups... MR of the predicted population is entirely defined by its radial SD. MR is just the more digestible metric for those graduating from looking at small sample size groups through the lens of ES
What do you mean by saying that the mean radius of the predicted population is entirely defined by the radial standard deviation?
@@adamwilson8559 look up the Rayleigh statistical distribution.
Look up the Rayleigh distribution, SD is the descriptive sample statistic from which population characteristics can be inferred.
@@BelvidereGuy The Rayleigh distribution is often specified by the population SD of the underlying Cartesian bivariate circular normal distribution. But in the video the SD of the radius is presented - the difference is very important.
@adamwilson8559 agreed, sample radius SD will never exactly match population's true radial SD due to sampling distribution of the variance. Regardless, radius SD of the sample often still has merit in *estimating* a radius population, just as velocity sample SD has merit in estimating a population for things like WEZ analysis
👍👍
Dang. Blew my mind😂😂
I've never even looked at mean radius. All i have ever cared about is group size, center of group, velocity extreme spread, and velocity variance with temperature. (I guess the standard deviation of velocity has some value ti me as well, but not as much as the extreme spread.)
Could you point us to a way to calculate the SD for shots?
There’s nothing special about this SD. Same way you calculate SD in any other situation. SD is SD.
@@ClaytonMacleod It's true enough that SD is SD, but the SD of what is the key question. The SD of the radius (as presented in this video) is definitely not the SD of the group size, which is definitely not the SD of the horizontal or vertical locations, etc etc.
@@adamwilson8559 I’ll stick with CEP.
As presented in the video: First, find the center of the group (this can be done with various apps, or you can plot the xy coordinates and find the average of the x's and average of the y's, which together give you the group center). Second, compute the distance from the group center to each shot, which is the radius for each. Third, find the average of the radiuses. Fourth, find the difference between the radius of each shot and the average radius. Fifth, square each of those differences, sum them together, and then take the square root of the sum. That's the standard deviation of the radiuses.
It's worth noting that I've been studying statistical measures of accuracy for awhile now, and this is the first time I've encountered anyone talking about the standard deviation of the radiuses. Be cautious with this metric, as the radiuses do NOT follow a normal distribution and the typical rules of thumb (95% within 2 SD, etc) do not apply when we're talking about the radius.
@@adamwilson8559 Actually, it is a normal distribution. Specifically, a bivariate normal distribution, X and Y, elevation and windage. And in a bivariate normal distribution you see 39% fall within 1 SD/sigma, 86% fall within 2 SD/sigma, and 99% fall within 3 SD/sigma. CEP50, or typically just referred to as CEP, is 50% of shots, or a sigma of 1.18. Mean radius is 54% of shots, or a sigma of 1.25. I believe Keith's not quite understanding mean radius fully, as it does actually tell you more than he seems to think it does. I'll again mention this is one of the reasons I like the OnTarget software, as it lets you see MR, SD radius, CEP50, CEP90, and CEP95 at a glance. Printing out its targets, and then letting it scan and analyze the shot targets saves a whole whack of time.
Very excellent video. I’ve been thinking this ever since the hornady guys vids. Tho it’s all very interesting
Mean radius dictate group shape and group dimension. The number you choose to represent you explaination is quite huge. Do the same with 0.1/0.2/0.3/0.5 MR and then a 1 MR and etc and show the difference . It will be alot closer to reality and show people a proper representation of it.
I see what you're saying & I sorta, kinda agree. On the whole though, I beg to differ & I'd like to explain how I use Mean Radius (MR).
If you look at MR the way you explain it, there is some very basic merit to your logic however, there are several other considerations which grant MR far more power than many would think.
For example, MR is pretty much the easiest & most efficient way of matching POI to POA. Since the majority of shooting disciplines are inherently tied to a definitive reference point in space, i.e.; a target of some description, MR is a very powerful tool which shows the match or mismatch between POI & POA. Moving on logically from there, we can then calculate our hit probability at distance which allows us to determine the suitability of any rifle/load combination for our intended purpose.
Although we can choose to focus on group size & characteristics, this really only compares one impact in reference to another with one degree of freedom whereas, if we focus more heavily on MR, we uncover far more about the state on the combined impacts including the ability to calculate the validity or not of true flyers or anomalies & thus our error bounds or the error probability.
If we recognise the fact that each & every shot is an entity unto itself & not a product of the total relative placement of the other shots around it, we can begin to comprehend the power of MR over that of group size.
Imagine if you will a situation whereby during a 1000 yrd F class shoot, the target is replaced by a new target with each & every shot. Would you still think the same way as you do now?
Interesting thought, isn't it.