Another +1 for this. A person can (sorta) do something like that with an e-target system, but a phone app would be vastly more useful for the majority of folks 👍
Coming from a Statistical Process Control experimental designs profession, and avid shooter and wildcat enthusiast, this is good stuff. I appreciate you sharing with us. Not everyone will use this , but you can rest assured i will. I have new 25 creedmore and 25 prc builds and this will be used.
Had to hit the Like button before I even finished the video. As a proverbial “stats guy”, this is the kind of info I love hearing. Keep up the good work, gents!
As someone who understands statistics, this makes me trust hornady more than I typically would. You know what you are talking about. Now, get an overlap function for multiple groups and you absolutely win the shot group app!😉
Basically, what you're saying is that we are not firing laser rifles. A bullet leaves the muzzle and flies inside a cone of dispersion, and the dispersion of each rifle is unique to itself, based on the components, and the accuracy/quality of the sum of the parts. If one was to draw a cone of where the bullet might travel, showing the path of the bullet as it leaves the muzzle, all the way out to the target, and then finish the diagram by drawing a circle the size of the cone once it reaches the target, one would expect that bullet to fly to the target inside that cone, and impact within that circle - not accounting for any outside influences such as atmospheric conditions. The extreme deviation shows us the outside edges of that circle - the diameter of the cone that we drew on the target/paper, and the mean radius is the area where the majority of the bullets left holes, in relation to the middle of the target - the mean radius shows us where to draw the dot in the middle of the cone - or if you prefer, where the middle of that cone is to be placed, and then the outermost holes would show us how big to draw the circle around that middle point. If I understood correctly, considering a bell curve, 60% of the bullets will create holes within the smallest grouping area, but some will land outside that, but with less frequency. I have 4DOF and have paid for Group Analysis, but haven't gotten to try it yet - but I think I understand... Even without the software, a large enough group can tell you a lot, just visually, regarding what your chances are at hitting your target, relative to its size, and your potential for dispersion, in perfect conditions. Adding Group Analysis and 4DOF zero angle take this up a couple of levels. You have invented fire, or the wheel, or sliced bread - or flight - this information is of that magnitude for those of us who appreciate ballistics and want to hit our targets, and to hunt ethically. Thank you for all of the work you're putting in. I realize it is also fun/enjoyable, but it is work - and I'm grateful.
This is great information. The system I had been using was a scoring in which I averaged the extreme spread with the best four out of five in a five shot group. I’ve checked some of those groups with the Hornady ballistics app and it’s interesting how close some of those scores are to the mean radius. Appreciate you guys.
I think that has a lot of potential for helping people understand what is really happening with their gun/loads. I will be adding it to my load tracking from here out out. Helps that with an app it adds no extra steps for me.
The app has a few bugs I have reported. Waiting on an update, hopefully soon. I like it and am still trying to figure a few things out. I love these podcasts!
inputting angle and head tail wind gives some crazt results, i have messaged emailed and commented on a few videos about it and consistently been intoned
While breaking in my new 6mmBR after getting a fairly good zero I had four rounds to shoot a group. Here are the results: Powder: 30 gr Varget Bullet: 105 gr Berger Range:100yds MOA: .548 Mean Radius: 0.199 (0.188 MOA) So if I heard correctly this is a good mean radius?
Thankyou. To my challenged mind, mean radius calculation gives statistical analysis of shot dispersion much more utility than standard deviation and extreme spread.
Standard Error of the Mean (SE) is how you calculate the needed sample size. The more variation you have, the more measurements you need to meet the probability of making a Type 1 or Type 2 error.
I did a good 15 round group and figured out my zero angle once. Worked like a charm. I had to take the barreled action out of the stock and clean the gun good after a wet hunt and when I put it back together all my impacts are now .4 miles low. I thought as long as the scope and barreled action stay together the zero angle stays the same? Do I have to re-do the whole process now that i re set the barreled and scoped action in the stock and the “zero” is now .4 mils low?
Mean Radius all the way. I only use group ES for matching POI centroid to POA. For everything else, I'm only concerned with MR. Mean Radius tells me everything that is necessary to know about my rifle/ammo/shooter combination, what I can expect from a probability perspective &, not send me off on tangents of questioning normal dispersion. MR always shows the dispersion from the POA (when POI matches POA) & not the almost meaningless group ES comparison. Mean Radius is the elephant in the room that everyone ignores.
I draw a 4 sided box around the outside edges of the group. Then I draw an X corner to corner across the box. I use the center of the X as my group center measuring the legs of the X to determine my group size.
What is the shape of the group is diagonal and most of the bullets are clustered in one corner. The center of the rectangle is no longer the center of the group. But I like your thinking.
The mean radius does not follow a normal distribution, but rather a Hoyt distribution. So while the radius does have a standard deviation, the SD does not mean (pun intended) the same thing it means in the normal/gaussian case. I.e., it does not mean that 2/3rds of the shot will fall within +/- 1 SD, 95% within 2 SD, etc. I assume this is why they don't report it in the app.
That's awesome! I tried out the group analysis yesterday on my PRC. 20 shots and got a .55 at 100. Not great but not bad. Yall should add a grading feature with the group analysis.
just pulled up my daughter's last targets in the group analysis section of the Hornady app, saw the mean radius #s. didn't know what it was when we first put in the targets. now we do :-) very cool!
This is great! Thanks so much. Could the app give you a standard deviation for that mean radius that you could use to predict the max size of say 95 or 99.6% of shots?
@hornady how do y'all measure the spread of the group with the radius method? And how do you measure statistical significance? In other words, if I shoot a 10 shot group with MR 1" and a different load shoots 10 shots with MR 3/4", do y'all have a way of telling if the difference is meaningful vs simply a random sampling effect?
Around 13:40. Yes, the 4DOF app calculates mean radius for you in the group analysis function. I just checked. Granted, it was only a two shot group for hunting with my 7 PRC, but the distance was .41 inches (.39 MOA) and the mean radius was .20 inches. So, on a whitetail deer, my primary target, my first two and probably only shots on a deer are going to hit nearly the same spot. Or, for example, I hit the spot behind the shoulder and it shudders and moves. And then stops, I could aim at the same spot and get within in inch. But a bigger sample would give a more usable mean radius. That was my next question. Which sample size for which job. 5 for game hunting? 40 for competition?
A podcast or podcasts dedicated to load development would be awesome. After listening to episodes 99, 50, & 52, I would like to hear Miles and Jayden's process on load development. How do we pick powders? (the Hornady load data lists about 10 per projectile), Seating Depth? (before finding charge weight/after/unimportant?). Miles said if a combo doesn't work, make big changes. Does that mean try out different projectiles with the same powder to determine the best combo. The combinations of powder & projectiles with 20 round groups would wear out the barrel of some calibers. Anyway, you get the idea. Thanks for all the thoughtful topics, I really look forward to listening to the new topics every week.
Pick a single base high consistency powder with low temperature sensitivity. That's it. Generally they're not the fastest powder for a given case, that's where double base comes in with the trade off of higher sensitivity and lower consistency.
This is a nice way to have a brag-worthy figure and more confidence in guessing follow up shot POA, but I still mostly care about group size since it’s really what determines if you can even hit a target with a correct distance and wind call. That probability better be 100% or I’m working up a new load. Both are important. 🎉
the problem with taking 20-35 shots for a single group: if you've got a tight groups, you'll get one or more big holes where you can't ID individual shots. not needed for measuring group size but hard to get individual radii. I've got target with a single ragged hole representing 2 boxes of ammo, and there's no way I could ID individual shots. Is there a way to combine multiple targets electronically/mathematically within the Hornady app to get a mean radius from, e.g., 6 5-shot groups or 10 3-shot groups?
Love the group analysis part of the app but it would be nice if mean radius was also output in moa. The range I go to, the closest target is 130 yards. I can do the math but it would be nice if I didn't have to.
Is there a similar process for finding velocity. Mean average velocity seems to suffer from the same problem as traditional group size. I shot a string that had five shots all within 25 FPS but then I also had one that was 100 FPS high and another that was 100 FPS low. I don't think those two flyers are indicative of the ammo. Do I include them in my average, do I just throw them out or better answer is there a equation that will give me a better velocity probability output.
Awesome podcast. Not much of a stats guy, but could you provide a "suggested"/recommended Mean Radius appropriate for different game size. For example, I'm primarily a moose hunter - what Mean Radius (assuming perfect shooting conditions and sniper-level ability") should I aim for when developing a load for moose. If relevant, my personal distance limit would be 450 yards. Currently, I use 18" as the diameter of the moose I hunt (Eastern Canadian moose).
Yep. Using extreme spread as a metric of precision is like doing 10 runs to figure out how fast you run 100 yards and then only keeping the data from your fastest and slowest runs. Not only is that obviously extremely wasteful, but it also only keeps the data from the two runs most likely to be outliers. Mean radius on the other hand is like taking your average run time.
Once you’ve established a reliable mean radius; could you then create a high confidence interval such as 90-95% about what your group size might be or how likely you’d be to impact a target that’s “X” size?
This sounds similar to what I use. I look for and measure where my group lands from center across my powder charges and select the most consistent powder charge.
Question, if I shoot a group size at 1" at 100 yards on 20 shots how do I do make sure the shots I can't track on paper are accurate the the mean radius measure ment because I will for sure not be able to judge a number of shots and where they hit?
Not sure why y'all are saying MR is a "new" thing, it's been a thing for at least 175 years that I know of, and used to be the main method of evaluation shooting stuff for anyone who took it seriously. It used to be known by a couple of other names, one of the most popular being Figure of Merit.
What if you're not zeroed to your test load and your shots land a half inch off point of aim? Does this affect your radius negatively? But you're shooting a bug hole?
It strikes me that as we talk about optimizing tiny variables in rifle systems, we expend almost no effort in analyzing the effect of wind, which may have much larger effects. Do we test how much drift comes from a 5, 10, or 20 mph wind? Do we measure wind speeds and develop a good feel for how windy it is? I suspect that most shooters do not. How many shooters have and use an anemometer? Most shooters enjoy buying and playing with equipment but have less interest in going out in varying wind conditions and testing. If you're about hitting targets you need to spend more time on wind and less on load development.
Hornady: If I shoot (6) separate five shot groups (all at the same style target) in order to gain 30 relevant shots, thus I have 6 M.R. Measurements, do I just have to average those 6 M.R. Measurements to get the M.R. Relevant to my 30 shots?
I think there’s one element that could throw that off. That is, the “average center” might change from one group to the next, which could give you a more precise estimate than the actual estimate would be. Technically you would need to overlay the groups so that a proper group “center” could be estimated. Realistically, you probably wouldn’t be far off by just averaging the averages, but you are definitely introducing error via your calculation method.
@@phild9813i deleted my previous response because i see what you are saying. A true average center would be calculated off of the full 30 shots. Vs having 5 average centers. I bet the results would be close either way with that many data points. I was getting betwen .2 and .3 MR at 100 yards.
@@phild9813 Makes zero sense.. If you shoot a 5 shot group your spread is going to be smaller than shooting a 6+ shot group because the barrel is going to be hotter regardless point of aim. Say you aren’t hitting your point of aim your sights/scope is off…
Wouldn’t group size give enough info to approximate mean radius with a Gaussian distribution algorithm? …and vice versa? I’ve never seen a tiny group with only 1 “flyer” that wasn’t shooter induced.
13:20 - looks like the Hornady group analysis doesn’t calculate mean radius based on the point of impact relative to the point of aim. It looks like it’s based on the point of impacts relative to the center of the group. So you’d first need to calculate the center of the group as a whole before you could calculate the mean radius based on that center point
Yes, the mean radius is centred around the calculated centre of the group & not the point of aim however, the POA is input into the group analysis picture & we can simply use the vertical & horizontal offsets listed in the stats to see where our true group centre is vs the mean POI. The POA could be used but this would skew the MR around the POA giving an erroneous result unless the POA matched the POI. The calculated mean centre of POI is used to measure the pure dispersion of that group without the bias of the POA if POI is different to the POA.
@@rotasaustralis I was pointing out how you’d actually need more data to calculate the mean radius that what they described at this point in the video. As I mentioned in my comment, and as you eluded to in your comment, you’d need to calculate the center of the group before you could actually calculate the mean radius.
The app calculates the centre of POI. The Hornady app is quite good IMHO compared to others like Range Buddy or Ballistic X. The seamless integration of the Hornady app into their 4DOF app is a gamechanger in my opinion.@@TheParkingLotGarage
I measure a Mean Radius 0.62 Centimeters at 100 Meters ~ 1/4“ at 110 yards for a 10 shot group out of my RPR in 6,5 PRC pushing a 130 gn CX with 58 Grains Vihtavuori 565 at 948 Meters or 3100 ft. I’ ll leave it like that. Thank you for 4 Dof 👍🏻
Please make it so we can overlay multiple targets (combine targets based on the selected POI). This feature would set the 4 DOF app above the rest and make the paid feature valuable. Without the ability to combine targets… I’ll stick with excel 😅
Using a mean radius has been actually been around for a long time. The British referred to it as 'Figure of Merit'. This video discusses more and has a method with excel spreadsheet to calculate: th-cam.com/video/zAntq2M0o30/w-d-xo.html In the U.S. back in the muzzleloading days the 'string measure' was used. After several shots were fired on a target a string measured the distance from the center to each bullet hole. The sum of all strings was the 'string measure'. So it's mean radius times the number of shots. J.R. Chapman's (1841) The Improved American Rifle and Ned Roberts (1940) Muzzleloading Caplock Rifle books talk about this method and how many competitions between gunsmiths to see who's rifle as more accurate used this method.
Mean radius from the group center tells you how good the ammo/gun/shooter is. Distance between the mean point of impact to the aim point tells you how far to move the crosshairs.
The 4DOF group analysis function needs work fellas. It still produces erroneous expression of angular group size in MOA when inputting target distance in meters instead of yards… this is dead simple to fix. I am mildly annoyed that it is taking a long time between 4DOF software updates. I would actually prefer to pay money for 4DOF if it meant you could hire an extra geek to white glove that app and turn around bug fixes and updates weekly. I now use the 4DOF group analysis function bloody every time I go to the range… it has become an essential tool for me… it is TREMENDOUSLY USEFUL! One thing that would be very nice would be the ability to delete individual impacts when building a group in group analysis… when I make an oopsie during input… I have to delete the group and start over instead of just editing the errors. I have way more positive and constructive feedback to share but not sure of the best way to communicate to the 4DOF team at Hornady.
@@hornadyQuestion.. How many shots are you intending to take with a particular rifle consecutively? You never once mentioned barrel heating up by taking 10 to 35 shots you are talking about. Each round you shoot is going to cause the barrel to get hotter which is going to effect where the bullet impacts. Like hypothetically say you buy a new rifle and you find a round it likes that shoots 5 .50 groups consistently and you draw a circle around the group with an X in the center and sight the rifle in on that X. If you go and shoot 35 rounds at the same size target I bet you will have a lot of rounds outside of it because the barrel is hot. I mean it can be useful if you are shooting a lot of rounds consecutively, but as far as hunting goes I don’t see how it’s useful. I’m not a match shooter so I won’t pretend to know how many rounds are shot consecutively in a match.
0.67 SD radius - so your real world (3 SD radius) group is ~4.5 times bigger. 50% group size is basically what NATO ammo qualification used for half a century. They are all switching to SD, because of their real world application. I get it, for most ammo/rifles it will give you a sub-MOA sounding 'number', for your no where near 'sub-MOA' "precision" ammo/rifle... "guaranteed". Will be a lot of upset customers when they measure their mathematically correct accuracy in SD and go toward ~99% group size.
not really, mean radius describes the group mathematically. "Group size" could be viewed as an ES, but to be accurate, you always have to take the largest size you shoot, and update it every time you shoot a larger size group with that load and gun combo. Doing this allows you to say that ALL of your shots from this load/gun combo fall into a 4 MOA circle at 100 yrds for example. Mean radius lets you say 50% of my shots from this combo are inside of a radius of 1.5 MOA, that means 50% of your shots are inside of a 3 MOA diameter circle. So using both better describes the group. In this example, 100% of your shots are in a 4 MOA diameter circle at 100 yrs and 50% of those shots are inside of a 3 MOA diameter circle, and by default, the other 50% fall outside of the 3 MOA circle but inside of the 4 MOA circle. MR also helps identify TRUE "fliers" if you calculate the SD of the MR. Most scientists consider anything beyond +/- 1.5 to 2 standard deviations of the mean to be a "true outlier". By applying this shot groups, true outlier = true flier. So back to our example. You work up a load, and over a few months shoot 200 rounds of it. The widest it ever shoots is a 4 MOA diameter circle, you know this because you have tracked every shot with extreme OCD. This seems odd to you, because the groups "looked" better in development. You look at the MR and see that it is 0.75 MOA, so 50% of your shots are inside of a 1.5MOA diameter circle, the other 50% are outside of the 1.5MOA diameter circle, but inside of the 4 MOA diameter circle. You calculate the SD of the MR, and see that it is 0.25 MOA. You decide that anything beyond 2 SD of the MR is a true outlier. So, 0.75 MOA + 0.25 MOA + 0.25MOA=1.25 MOA radius, X2 = 2.5 MOA diameter circle. So based on a normal distribution, 97.7% of your shots fall in a 2.5 MOA diameter circle, 2.3% are true fliers and fall outside of the 2.5 MOA diameter circle, but inside of the 4 MOA diameter circle, and 50% of all shots are in the 1.5 MOA diameter circle, while 47.7% of all shots are outside of the 1.5 MOA diameter circle, but inside of the 2.5MOA diameter circle. So 100% of all shots = 4 MOA diameter circle 97.7% of all shots = 2.5 MOA diameter circle 2.3% of all shots are true fliers and will land outside of 2.5 MOA but inside of 4 MOA 47.7% of all shots will fall outside of a 1.5 MOA diameter circle, but inside of a 2.5 MOA diameter circle 50% of all shots will fall in a 1.5 MOA diameter circle You can do more with it but that's a general overview of the basics
Standard Error of the Mean (SE) is how you calculate the needed sample size. The more variation you have, the more measurements you need to meet the probability of making a Type 1 or Type 2 error.
@@joearledge that is not correct. ES will only be useful in your example if the sample (number of shots) is high. SD can become useful at 8 shots or more. ES from only one group needs to be way bigger than that, or it is just the ES of that one group, which we call "Group Size", which as established in the Hornady discussions is not a good measurement. When your cut off is 50% that is 0.67*SD. To get to "100%" ~ 3*SD the size goes up from 50% to 100% by 4,5 times (the say it in the video themselves). So your 1.5MOA@50% circle is 6.75MOA@100%. 4MOA ES no where near 100% in that case. For criteria to remove outliers refer to Chauvenet or Grubbs and Student or Graf-Henning respectively, depending on how you want to check for outliers. Also a big problem with using just the "radius", but not the X and Y direction, is that you cannot see from the mean radius if you have accuracy problems like bad support (X) or high Velocity deviation (Y). The "mean radius" is way better than "group size", but is like going from rifleman rule to advance rifleman rule for inclination. The result is more precise, but it is still not correct.
@@sheepshooter1424 Yep, that's why I said you have to update the "group size"(ES) over time. It's also in the second part of the example I said "you shoot 200 rounds over a couple months". Sample size matters... a lot. I'm not clear on what you're trying to say about SD. Generally in stats, there are 6 or 8 standard deviations under a normal curve. 3 or 4 above the mean and 3 or 4 below it. In shooting, you don't really mess with the SD's below the mean, unless you're playing with stats concerning the absolute tightest shots for whatever reason. Next, you can't calculate a SD of a mean, if you don't have the numbers in the sample population. Ex: your mean velocity is 2,700 FPS, you can't calculate the SD of that mean without the individual velocities. So you can absolutely have a sample population ES of 4 MOA, with a MR of 0.75 MOA(which is a diameter of 1.5 MOA) and an SD of 0.25 MOA. Furthermore, it was just an example, not a full on stats class, Mr. Sheeple. The numbers and concepts were kept fairly simple so that more people could understand it.... without sitting through a stats class... Yes the criteria for outliers is relatively subjective, and dependent on a lot of stuff. 4DOF does give you XY coordinates... so if you want to use those to analyze accuracy problems, you can. MR is concerned mainly with precision, not so much accuracy. I'm glad to see you are starting to learn stats Mr. Sheeple, keep at it!👍
Statistics is hard. LOL’s Skewed distribution statistics are even harder! The real math becomes difficult. The issue with just using a generic mean radius versus an aim point radius is the world in my opinion. In other words the mean radius HAS TO BE measured from the aim point and NOT the impact center to mean anything. Maybe that’s what you are trying to say. I took it as the center of the group is the measurement point for radius.
Hey let’s talk about how when you go to load your first load of 7mm PRC with your red Hornady funnel and end up dumping powder in your lap! Good thing I’ve bought all this Hornady shit that doesn’t work together! Fuck!
27:00 - I think it could be argued that the more conservative approach in terms of deciding whether to take the shot would be to use group size instead of mean radius. Your group size number will always be larger than mean radius, unless you have a magic laser shooting perfect single hole groups.
Using Mean Radius calculation gives the shooter a view of the probability of the imagined outcome vs overall group size. Mean radius is not an alternative measure of extreme spread. Mean Radius calculates the MEAN of the radius of all the shots which, is a statistical representation of the probability of placing a bullet within a certain size target. If you use extreme spread to analyse a 10 shot group, 9 of which shoot within 1MOA with the tenth shot pulling the group extreme spread out to 3MOA, then, by that measure, you would base the rifles repeatability on 3 MOA. If Mean Radius calculation is employed, you will assess the rifles repeatability by the far more representative probability of placing a shot at or within 1MOA. In the above example, there is a 9/10 chance of meeting the 1MOA criteria of the target. Using extreme spread would cause you to abandon the 1MOA target based on a 1/10 probability of missing the target.
@@rotasaustralis I don’t dispute anything you’ve said, but my point was that your hit probability is ~100% within your group size (assuming you’ve validated your group size with a sufficient number of shots. And of course that’s not considering any other environmental factors). So if you solely relied on group size to determine whether or not you engage an animal, it is a much more conservative approach than using mean radius.
I supose you could look at it that way however, I think you would be limiting yourself unnecessarily. All rifles have dispersion & the point of mean radius is to express a more representative outcome using probability which, mean radius gives us, provided an adequate number of samples are used in the calculations however, sample number applies to every statistical calculation with ES being by far, the least efficient. Since ES does not give a probability beyond that which any random group could suggest, the limits of ES become particularly apparent. The point is that whatever number of sample shots you use would be far more beneficial if used to calculate mean radius because this gives a probability factor based upon whatever sample number you have rather than the reliance of an ES which could be the result of a 1 in 1000 shot dispersion. I've been using Mean Radius for many years & I can assure you that it really does work. @@TheParkingLotGarage
Mean radius just "smooths" the data. If i shoot an 1.5" group with one odd ball and a bug hole the odd ball has less weight on the over all group. Second, I would not extrapolate mean radius for a guaranteed hit at distance if it's only a 50% chance ,in a hunting situation, i would go full group size. Third, you should be able to see a good mean radius with your eyes, a 20 shot bug hole is awesome, a bug hole with a couple flyers, good, shotgun blast bad. Just dick swinging to say numbers.
Makes zero sense to me.. They are if I’m understanding correctly saying you need to shoot larger sample sizes. Each round you shoot consecutive the barrel gets hotter, and hotter the barrel gets the less accurate.. I guess it all depends on how many rounds you typically shoot conservatively.. Like say I buy a new hunting rifle.. I find a load the rifle likes by shooting a 3 to 5 round group and then set my sights/scope in the center of where the impact was. Seems to me they are trying to overly complicate things and looking for computers to solve basically a mechanical problem.
We need an option in the group analysis that combines separate groups!
Strongly second that!
Make an Overlay with transpering “paper”
This would set the 4Dof app apart and make the paid feature have real value!
Completely agree !! Please do this!
Another +1 for this.
A person can (sorta) do something like that with an e-target system, but a phone app would be vastly more useful for the majority of folks 👍
Coming from a Statistical Process Control experimental designs profession, and avid shooter and wildcat enthusiast, this is good stuff. I appreciate you sharing with us. Not everyone will use this , but you can rest assured i will. I have new 25 creedmore and 25 prc builds and this will be used.
Had to hit the Like button before I even finished the video. As a proverbial “stats guy”, this is the kind of info I love hearing. Keep up the good work, gents!
Glad you enjoyed!
Gotta love hearing intelligent people speaking clearly about complicated ideas.
As someone who understands statistics, this makes me trust hornady more than I typically would. You know what you are talking about. Now, get an overlap function for multiple groups and you absolutely win the shot group app!😉
Basically, what you're saying is that we are not firing laser rifles. A bullet leaves the muzzle and flies inside a cone of dispersion, and the dispersion of each rifle is unique to itself, based on the components, and the accuracy/quality of the sum of the parts. If one was to draw a cone of where the bullet might travel, showing the path of the bullet as it leaves the muzzle, all the way out to the target, and then finish the diagram by drawing a circle the size of the cone once it reaches the target, one would expect that bullet to fly to the target inside that cone, and impact within that circle - not accounting for any outside influences such as atmospheric conditions. The extreme deviation shows us the outside edges of that circle - the diameter of the cone that we drew on the target/paper, and the mean radius is the area where the majority of the bullets left holes, in relation to the middle of the target - the mean radius shows us where to draw the dot in the middle of the cone - or if you prefer, where the middle of that cone is to be placed, and then the outermost holes would show us how big to draw the circle around that middle point. If I understood correctly, considering a bell curve, 60% of the bullets will create holes within the smallest grouping area, but some will land outside that, but with less frequency. I have 4DOF and have paid for Group Analysis, but haven't gotten to try it yet - but I think I understand... Even without the software, a large enough group can tell you a lot, just visually, regarding what your chances are at hitting your target, relative to its size, and your potential for dispersion, in perfect conditions. Adding Group Analysis and 4DOF zero angle take this up a couple of levels. You have invented fire, or the wheel, or sliced bread - or flight - this information is of that magnitude for those of us who appreciate ballistics and want to hit our targets, and to hunt ethically. Thank you for all of the work you're putting in. I realize it is also fun/enjoyable, but it is work - and I'm grateful.
Thanks gentlemen. The app and tools are very useful. Using this with my first new rifle and learning to re load. Please keep the information coming.
Ohhhh yeah baby back on track!!!
This is great information. The system I had been using was a scoring in which I averaged the extreme spread with the best four out of five in a five shot group. I’ve checked some of those groups with the Hornady ballistics app and it’s interesting how close some of those scores are to the mean radius. Appreciate you guys.
I think that has a lot of potential for helping people understand what is really happening with their gun/loads. I will be adding it to my load tracking from here out out. Helps that with an app it adds no extra steps for me.
Best video I've seen on this topic. As a visual learner, working through the with diagrams, even drawing it n the podcast would be so helpful.
11:35 in terms of mean radius, every additional shot counts as another data point. Brilliant!
The app has a few bugs I have reported. Waiting on an update, hopefully soon. I like it and am still trying to figure a few things out. I love these podcasts!
inputting angle and head tail wind gives some crazt results, i have messaged emailed and commented on a few videos about it and consistently been intoned
While breaking in my new 6mmBR after getting a fairly good zero I had four rounds to shoot a group. Here are the results:
Powder: 30 gr Varget
Bullet: 105 gr Berger
Range:100yds
MOA: .548
Mean Radius: 0.199 (0.188 MOA)
So if I heard correctly this is a good mean radius?
Thankyou. To my challenged mind, mean radius calculation gives statistical analysis of shot dispersion much more utility than standard deviation and extreme spread.
Standard Error of the Mean (SE) is how you calculate the needed sample size. The more variation you have, the more measurements you need to meet the probability of making a Type 1 or Type 2 error.
I did a good 15 round group and figured out my zero angle once. Worked like a charm. I had to take the barreled action out of the stock and clean the gun good after a wet hunt and when I put it back together all my impacts are now .4 miles low. I thought as long as the scope and barreled action stay together the zero angle stays the same? Do I have to re-do the whole process now that i re set the barreled and scoped action in the stock and the “zero” is now .4 mils low?
Mean Radius all the way.
I only use group ES for matching POI centroid to POA. For everything else, I'm only concerned with MR.
Mean Radius tells me everything that is necessary to know about my rifle/ammo/shooter combination, what I can expect from a probability perspective &, not send me off on tangents of questioning normal dispersion. MR always shows the dispersion from the POA (when POI matches POA) & not the almost meaningless group ES comparison.
Mean Radius is the elephant in the room that everyone ignores.
I draw a 4 sided box around the outside edges of the group. Then I draw an X corner to corner across the box. I use the center of the X as my group center measuring the legs of the X to determine my group size.
What is the shape of the group is diagonal and most of the bullets are clustered in one corner. The center of the rectangle is no longer the center of the group. But I like your thinking.
It would be nice to be able to calculate the SD of the MR inside of 4DOF to ID true outliers instead of still having to do it manually.
I agree. StdDev should be reported along with mean. Then you can actually calculate the hit probability.
The mean radius does not follow a normal distribution, but rather a Hoyt distribution. So while the radius does have a standard deviation, the SD does not mean (pun intended) the same thing it means in the normal/gaussian case. I.e., it does not mean that 2/3rds of the shot will fall within +/- 1 SD, 95% within 2 SD, etc. I assume this is why they don't report it in the app.
That's awesome! I tried out the group analysis yesterday on my PRC. 20 shots and got a .55 at 100. Not great but not bad. Yall should add a grading feature with the group analysis.
just pulled up my daughter's last targets in the group analysis section of the Hornady app, saw the mean radius #s. didn't know what it was when we first put in the targets. now we do :-)
very cool!
This is great! Thanks so much. Could the app give you a standard deviation for that mean radius that you could use to predict the max size of say 95 or 99.6% of shots?
Seth throwing in the truck axle reference! At a boy! 😂
@hornady how do y'all measure the spread of the group with the radius method? And how do you measure statistical significance? In other words, if I shoot a 10 shot group with MR 1" and a different load shoots 10 shots with MR 3/4", do y'all have a way of telling if the difference is meaningful vs simply a random sampling effect?
Around 13:40. Yes, the 4DOF app calculates mean radius for you in the group analysis function. I just checked. Granted, it was only a two shot group for hunting with my 7 PRC, but the distance was .41 inches (.39 MOA) and the mean radius was .20 inches.
So, on a whitetail deer, my primary target, my first two and probably only shots on a deer are going to hit nearly the same spot. Or, for example, I hit the spot behind the shoulder and it shudders and moves. And then stops, I could aim at the same spot and get within in inch.
But a bigger sample would give a more usable mean radius. That was my next question. Which sample size for which job. 5 for game hunting? 40 for competition?
18:35 - A perfect donut shaped group would produce a mean radius exactly half of the group size. It would not be 1 and 1.
A podcast or podcasts dedicated to load development would be awesome. After listening to episodes 99, 50, & 52, I would like to hear Miles and Jayden's process on load development. How do we pick powders? (the Hornady load data lists about 10 per projectile), Seating Depth? (before finding charge weight/after/unimportant?). Miles said if a combo doesn't work, make big changes. Does that mean try out different projectiles with the same powder to determine the best combo. The combinations of powder & projectiles with 20 round groups would wear out the barrel of some calibers. Anyway, you get the idea. Thanks for all the thoughtful topics, I really look forward to listening to the new topics every week.
Pick a single base high consistency powder with low temperature sensitivity. That's it. Generally they're not the fastest powder for a given case, that's where double base comes in with the trade off of higher sensitivity and lower consistency.
3rd time through these videos as well as the small groups. Love the information.
Glad you like them!
@@hornady it has made me rethink all my load development strategies. I am going back to the drawing board.
Mean radius is somewhat limiting compared to a complete distance probability distribution curve.
With the 4 DOF app.. can you differentiate or calculate mean radius relative to “point of aim” vs “ group center”
This is a nice way to have a brag-worthy figure and more confidence in guessing follow up shot POA, but I still mostly care about group size since it’s really what determines if you can even hit a target with a correct distance and wind call. That probability better be 100% or I’m working up a new load. Both are important. 🎉
the problem with taking 20-35 shots for a single group:
if you've got a tight groups, you'll get one or more big holes where you can't ID individual shots. not needed for measuring group size but hard to get individual radii.
I've got target with a single ragged hole representing 2 boxes of ammo, and there's no way I could ID individual shots.
Is there a way to combine multiple targets electronically/mathematically within the Hornady app to get a mean radius from, e.g., 6 5-shot groups or 10 3-shot groups?
If you put 40 in one big hole I'd say your good 👍 your mean would be around 1/4 the group size. Shoot multiple groups, average the averages
Love the group analysis part of the app but it would be nice if mean radius was also output in moa. The range I go to, the closest target is 130 yards. I can do the math but it would be nice if I didn't have to.
I think I kinda understand when Jayden said max radius…. It kinda clicked
Is there a similar process for finding velocity. Mean average velocity seems to suffer from the same problem as traditional group size. I shot a string that had five shots all within 25 FPS but then I also had one that was 100 FPS high and another that was 100 FPS low. I don't think those two flyers are indicative of the ammo. Do I include them in my average, do I just throw them out or better answer is there a equation that will give me a better velocity probability output.
Awesome podcast. Not much of a stats guy, but could you provide a "suggested"/recommended Mean Radius appropriate for different game size. For example, I'm primarily a moose hunter - what Mean Radius (assuming perfect shooting conditions and sniper-level ability") should I aim for when developing a load for moose. If relevant, my personal distance limit would be 450 yards. Currently, I use 18" as the diameter of the moose I hunt (Eastern Canadian moose).
Yep. Using extreme spread as a metric of precision is like doing 10 runs to figure out how fast you run 100 yards and then only keeping the data from your fastest and slowest runs. Not only is that obviously extremely wasteful, but it also only keeps the data from the two runs most likely to be outliers. Mean radius on the other hand is like taking your average run time.
Does 4dof give you a standard deviation? Without SD I don’t see how mean radius helps calculate hit probabilities.
Once you’ve established a reliable mean radius; could you then create a high confidence interval such as 90-95% about what your group size might be or how likely you’d be to impact a target that’s “X” size?
That would just be group size at those % since mean is figured from the center of the group
@@zachstrassburg3729 ah that makes sense. Thank you. Seems like a dumb question now 😅 outside input helps sometimes haha
This sounds similar to what I use. I look for and measure where my group lands from center across my powder charges and select the most consistent powder charge.
Question, if I shoot a group size at 1" at 100 yards on 20 shots how do I do make sure the shots I can't track on paper are accurate the the mean radius measure ment because I will for sure not be able to judge a number of shots and where they hit?
Not sure why y'all are saying MR is a "new" thing, it's been a thing for at least 175 years that I know of, and used to be the main method of evaluation shooting stuff for anyone who took it seriously. It used to be known by a couple of other names, one of the most popular being Figure of Merit.
so, assuming youre talking about a precision gun, .3 MR at 100 is great, what about for a hunting rifle? thanks
A lot of it depends on what you are doing with it. How far, size of game, etc. We strive to have the same precision out of gamers and hunting rifles.
Does it automatically plug in your Zero Angle as well if you tie it to your favorites?? That would be a great feature!!!
Yep, it will figure your zero angle
@@hornady i just purchased the feature and can’t wait to try it!!! Thanks!
What do you think of the Circular Error Probability measurements?
What if you're not zeroed to your test load and your shots land a half inch off point of aim? Does this affect your radius negatively? But you're shooting a bug hole?
It strikes me that as we talk about optimizing tiny variables in rifle systems, we expend almost no effort in analyzing the effect of wind, which may have much larger effects. Do we test how much drift comes from a 5, 10, or 20 mph wind? Do we measure wind speeds and develop a good feel for how windy it is? I suspect that most shooters do not. How many shooters have and use an anemometer?
Most shooters enjoy buying and playing with equipment but have less interest in going out in varying wind conditions and testing. If you're about hitting targets you need to spend more time on wind and less on load development.
Hornady: If I shoot (6) separate five shot groups (all at the same style target) in order to gain 30 relevant shots, thus I have 6 M.R. Measurements, do I just have to average those 6 M.R. Measurements to get the M.R. Relevant to my 30 shots?
I think there’s one element that could throw that off. That is, the “average center” might change from one group to the next, which could give you a more precise estimate than the actual estimate would be. Technically you would need to overlay the groups so that a proper group “center” could be estimated. Realistically, you probably wouldn’t be far off by just averaging the averages, but you are definitely introducing error via your calculation method.
@@phild9813i deleted my previous response because i see what you are saying.
A true average center would be calculated off of the full 30 shots.
Vs having 5 average centers.
I bet the results would be close either way with that many data points. I was getting betwen .2 and .3 MR at 100 yards.
@@phild9813 Makes zero sense.. If you shoot a 5 shot group your spread is going to be smaller than shooting a 6+ shot group because the barrel is going to be hotter regardless point of aim. Say you aren’t hitting your point of aim your sights/scope is off…
The group analysis function crashes the app when choosing a photo from your photos library. Any updates coming?
Same here
Very Interesting '' Great Stuff 💯💥💥💥💥💥💥💥
Instead of the mathematical center of the group, wouldn’t be more useful to use POA as the center for the calculations???
It would be nice to change Mean Radius from inches to MOA on 4DOF
Agreed!
Can the 4DOF app export the group data to an excel format?
Wouldn’t group size give enough info to approximate mean radius with a Gaussian distribution algorithm? …and vice versa? I’ve never seen a tiny group with only 1 “flyer” that wasn’t shooter induced.
13:20 - looks like the Hornady group analysis doesn’t calculate mean radius based on the point of impact relative to the point of aim. It looks like it’s based on the point of impacts relative to the center of the group. So you’d first need to calculate the center of the group as a whole before you could calculate the mean radius based on that center point
Yes, the mean radius is centred around the calculated centre of the group & not the point of aim however, the POA is input into the group analysis picture & we can simply use the vertical & horizontal offsets listed in the stats to see where our true group centre is vs the mean POI. The POA could be used but this would skew the MR around the POA giving an erroneous result unless the POA matched the POI. The calculated mean centre of POI is used to measure the pure dispersion of that group without the bias of the POA if POI is different to the POA.
@@rotasaustralis I was pointing out how you’d actually need more data to calculate the mean radius that what they described at this point in the video. As I mentioned in my comment, and as you eluded to in your comment, you’d need to calculate the center of the group before you could actually calculate the mean radius.
The app calculates the centre of POI.
The Hornady app is quite good IMHO compared to others like Range Buddy or Ballistic X.
The seamless integration of the Hornady app into their 4DOF app is a gamechanger in my opinion.@@TheParkingLotGarage
Does Group Analysis in the app have export data feature?
5:10: Dang Seth. Shots fired!
I measure a Mean Radius 0.62 Centimeters at 100 Meters ~ 1/4“ at 110 yards for a 10 shot group out of my RPR in 6,5 PRC pushing a 130 gn CX with 58 Grains Vihtavuori 565 at 948 Meters or 3100 ft. I’ ll leave it like that. Thank you for 4 Dof 👍🏻
Love the Hornady app...BUT the darn Group Analysis section crashes a BUNCH. Let's get that tightened up boys
I Need a link to the app you're referencing to analyze shot groups. I can't get the name from your speaking it. Ford Off?
Hornady Ballistics with 4DOF
.24“ / 0,62cm @ 100Meters. Thanks for the new way of looking at my results.
The group size should be around 4x the mean radius, like Jayden said, because a normal curve is approximately +/- 2 SD. Hey Hornady, I need a job! 😅
It would have been great to actually show with a group size to demonstrate and explain how to figure it. Some of us are visual learners.
It saves me money and time. Been doing it for years, but 4dof is quicker and easier.
why not calculate a centroid and then the normal distribution around it?
Please make it so we can overlay multiple targets (combine targets based on the selected POI).
This feature would set the 4 DOF app above the rest and make the paid feature valuable.
Without the ability to combine targets… I’ll stick with excel 😅
Using a mean radius has been actually been around for a long time. The British referred to it as 'Figure of Merit'. This video discusses more and has a method with excel spreadsheet to calculate:
th-cam.com/video/zAntq2M0o30/w-d-xo.html
In the U.S. back in the muzzleloading days the 'string measure' was used. After several shots were fired on a target a string measured the distance from the center to each bullet hole. The sum of all strings was the 'string measure'. So it's mean radius times the number of shots. J.R. Chapman's (1841) The Improved American Rifle and Ned Roberts (1940) Muzzleloading Caplock Rifle books talk about this method and how many competitions between gunsmiths to see who's rifle as more accurate used this method.
Wouldn't the mean radius be from the aim point though? Why does it go from the group's center?
Mean radius from the group center tells you how good the ammo/gun/shooter is. Distance between the mean point of impact to the aim point tells you how far to move the crosshairs.
The 4DOF group analysis function needs work fellas. It still produces erroneous expression of angular group size in MOA when inputting target distance in meters instead of yards… this is dead simple to fix.
I am mildly annoyed that it is taking a long time between 4DOF software updates. I would actually prefer to pay money for 4DOF if it meant you could hire an extra geek to white glove that app and turn around bug fixes and updates weekly.
I now use the 4DOF group analysis function bloody every time I go to the range… it has become an essential tool for me… it is TREMENDOUSLY USEFUL!
One thing that would be very nice would be the ability to delete individual impacts when building a group in group analysis… when I make an oopsie during input… I have to delete the group and start over instead of just editing the errors.
I have way more positive and constructive feedback to share but not sure of the best way to communicate to the 4DOF team at Hornady.
Shoot us an email at podcast@hornady.com
👍🏻👍🏻
6mm arc gas gun w/ a 24" barrel and 108 ELDM projectiles would work best with reloader 15.5. Varget is less than ideal for that application.
Thank you!
Welcome!
@@hornadyQuestion.. How many shots are you intending to take with a particular rifle consecutively? You never once mentioned barrel heating up by taking 10 to 35 shots you are talking about. Each round you shoot is going to cause the barrel to get hotter which is going to effect where the bullet impacts.
Like hypothetically say you buy a new rifle and you find a round it likes that shoots 5 .50 groups consistently and you draw a circle around the group with an X in the center and sight the rifle in on that X. If you go and shoot 35 rounds at the same size target I bet you will have a lot of rounds outside of it because the barrel is hot. I mean it can be useful if you are shooting a lot of rounds consecutively, but as far as hunting goes I don’t see how it’s useful. I’m not a match shooter so I won’t pretend to know how many rounds are shot consecutively in a match.
4DOF Group Annalisis still does not work on my Samsung S22 Ultra
Shoot us an email. tech@hornady.com
So .7 @350 yards is decent?
Yep
It’s science Cedric. Numbers don’t lie.
Science also says the more shots you fire in a string the hotter the barrel gets. Science also says the hotter the barrel the less accurate..
The Army does mean radius with 10 shot group at 200 meters.
So it's SD (mean radius)and ES (group size) for groups...
0.67 SD radius - so your real world (3 SD radius) group is ~4.5 times bigger.
50% group size is basically what NATO ammo qualification used for half a century. They are all switching to SD, because of their real world application.
I get it, for most ammo/rifles it will give you a sub-MOA sounding 'number', for your no where near 'sub-MOA' "precision" ammo/rifle... "guaranteed".
Will be a lot of upset customers when they measure their mathematically correct accuracy in SD and go toward ~99% group size.
not really, mean radius describes the group mathematically. "Group size" could be viewed as an ES, but to be accurate, you always have to take the largest size you shoot, and update it every time you shoot a larger size group with that load and gun combo. Doing this allows you to say that ALL of your shots from this load/gun combo fall into a 4 MOA circle at 100 yrds for example. Mean radius lets you say 50% of my shots from this combo are inside of a radius of 1.5 MOA, that means 50% of your shots are inside of a 3 MOA diameter circle. So using both better describes the group. In this example, 100% of your shots are in a 4 MOA diameter circle at 100 yrs and 50% of those shots are inside of a 3 MOA diameter circle, and by default, the other 50% fall outside of the 3 MOA circle but inside of the 4 MOA circle. MR also helps identify TRUE "fliers" if you calculate the SD of the MR. Most scientists consider anything beyond +/- 1.5 to 2 standard deviations of the mean to be a "true outlier". By applying this shot groups, true outlier = true flier. So back to our example. You work up a load, and over a few months shoot 200 rounds of it. The widest it ever shoots is a 4 MOA diameter circle, you know this because you have tracked every shot with extreme OCD. This seems odd to you, because the groups "looked" better in development. You look at the MR and see that it is 0.75 MOA, so 50% of your shots are inside of a 1.5MOA diameter circle, the other 50% are outside of the 1.5MOA diameter circle, but inside of the 4 MOA diameter circle. You calculate the SD of the MR, and see that it is 0.25 MOA. You decide that anything beyond 2 SD of the MR is a true outlier. So, 0.75 MOA + 0.25 MOA + 0.25MOA=1.25 MOA radius, X2 = 2.5 MOA diameter circle. So based on a normal distribution, 97.7% of your shots fall in a 2.5 MOA diameter circle, 2.3% are true fliers and fall outside of the 2.5 MOA diameter circle, but inside of the 4 MOA diameter circle, and 50% of all shots are in the 1.5 MOA diameter circle, while 47.7% of all shots are outside of the 1.5 MOA diameter circle, but inside of the 2.5MOA diameter circle.
So
100% of all shots = 4 MOA diameter circle
97.7% of all shots = 2.5 MOA diameter circle
2.3% of all shots are true fliers and will land outside of 2.5 MOA but inside of 4 MOA
47.7% of all shots will fall outside of a 1.5 MOA diameter circle, but inside of a 2.5 MOA diameter circle
50% of all shots will fall in a 1.5 MOA diameter circle
You can do more with it but that's a general overview of the basics
Standard Error of the Mean (SE) is how you calculate the needed sample size. The more variation you have, the more measurements you need to meet the probability of making a Type 1 or Type 2 error.
@@joearledge that is not correct. ES will only be useful in your example if the sample (number of shots) is high. SD can become useful at 8 shots or more. ES from only one group needs to be way bigger than that, or it is just the ES of that one group, which we call "Group Size", which as established in the Hornady discussions is not a good measurement.
When your cut off is 50% that is 0.67*SD. To get to "100%" ~ 3*SD the size goes up from 50% to 100% by 4,5 times (the say it in the video themselves).
So your 1.5MOA@50% circle is 6.75MOA@100%. 4MOA ES no where near 100% in that case.
For criteria to remove outliers refer to Chauvenet or Grubbs and Student or Graf-Henning respectively, depending on how you want to check for outliers.
Also a big problem with using just the "radius", but not the X and Y direction, is that you cannot see from the mean radius if you have accuracy problems like bad support (X) or high Velocity deviation (Y).
The "mean radius" is way better than "group size", but is like going from rifleman rule to advance rifleman rule for inclination. The result is more precise, but it is still not correct.
@@sheepshooter1424 Yep, that's why I said you have to update the "group size"(ES) over time. It's also in the second part of the example I said "you shoot 200 rounds over a couple months".
Sample size matters... a lot.
I'm not clear on what you're trying to say about SD. Generally in stats, there are 6 or 8 standard deviations under a normal curve. 3 or 4 above the mean and 3 or 4 below it. In shooting, you don't really mess with the SD's below the mean, unless you're playing with stats concerning the absolute tightest shots for whatever reason.
Next, you can't calculate a SD of a mean, if you don't have the numbers in the sample population. Ex: your mean velocity is 2,700 FPS, you can't calculate the SD of that mean without the individual velocities. So you can absolutely have a sample population ES of 4 MOA, with a MR of 0.75 MOA(which is a diameter of 1.5 MOA) and an SD of 0.25 MOA.
Furthermore, it was just an example, not a full on stats class, Mr. Sheeple. The numbers and concepts were kept fairly simple so that more people could understand it.... without sitting through a stats class...
Yes the criteria for outliers is relatively subjective, and dependent on a lot of stuff.
4DOF does give you XY coordinates... so if you want to use those to analyze accuracy problems, you can. MR is concerned mainly with precision, not so much accuracy.
I'm glad to see you are starting to learn stats Mr. Sheeple, keep at it!👍
Statistics is hard. LOL’s Skewed distribution statistics are even harder! The real math becomes difficult. The issue with just using a generic mean radius versus an aim point radius is the world in my opinion. In other words the mean radius HAS TO BE measured from the aim point and NOT the impact center to mean anything. Maybe that’s what you are trying to say. I took it as the center of the group is the measurement point for radius.
You can adjust the aim point to the center of the group...
Define good mean radius. Does this mean PRS level or 1 MOA factory rifle level? 😂
Please, how do you spell that fordoff app? Haha
Hornady 4dof 😂❤
Hey let’s talk about how when you go to load your first load of 7mm PRC with your red Hornady funnel and end up dumping powder in your lap! Good thing I’ve bought all this Hornady shit that doesn’t work together! Fuck!
27:00 - I think it could be argued that the more conservative approach in terms of deciding whether to take the shot would be to use group size instead of mean radius. Your group size number will always be larger than mean radius, unless you have a magic laser shooting perfect single hole groups.
Using Mean Radius calculation gives the shooter a view of the probability of the imagined outcome vs overall group size. Mean radius is not an alternative measure of extreme spread. Mean Radius calculates the MEAN of the radius of all the shots which, is a statistical representation of the probability of placing a bullet within a certain size target.
If you use extreme spread to analyse a 10 shot group, 9 of which shoot within 1MOA with the tenth shot pulling the group extreme spread out to 3MOA, then, by that measure, you would base the rifles repeatability on 3 MOA. If Mean Radius calculation is employed, you will assess the rifles repeatability by the far more representative probability of placing a shot at or within 1MOA. In the above example, there is a 9/10 chance of meeting the 1MOA criteria of the target. Using extreme spread would cause you to abandon the 1MOA target based on a 1/10 probability of missing the target.
@@rotasaustralis I don’t dispute anything you’ve said, but my point was that your hit probability is ~100% within your group size (assuming you’ve validated your group size with a sufficient number of shots. And of course that’s not considering any other environmental factors). So if you solely relied on group size to determine whether or not you engage an animal, it is a much more conservative approach than using mean radius.
I supose you could look at it that way however, I think you would be limiting yourself unnecessarily. All rifles have dispersion & the point of mean radius is to express a more representative outcome using probability which, mean radius gives us, provided an adequate number of samples are used in the calculations however, sample number applies to every statistical calculation with ES being by far, the least efficient.
Since ES does not give a probability beyond that which any random group could suggest, the limits of ES become particularly apparent. The point is that whatever number of sample shots you use would be far more beneficial if used to calculate mean radius because this gives a probability factor based upon whatever sample number you have rather than the reliance of an ES which could be the result of a 1 in 1000 shot dispersion.
I've been using Mean Radius for many years & I can assure you that it really does work. @@TheParkingLotGarage
Mean radius just "smooths" the data. If i shoot an 1.5" group with one odd ball and a bug hole the odd ball has less weight on the over all group.
Second, I would not extrapolate mean radius for a guaranteed hit at distance if it's only a 50% chance ,in a hunting situation, i would go full group size.
Third, you should be able to see a good mean radius with your eyes, a 20 shot bug hole is awesome, a bug hole with a couple flyers, good, shotgun blast bad.
Just dick swinging to say numbers.
Awesome to see a table of 2nd Amendment supporters can out perform the CDCs work on mRNA analysis with its $9B annual budget
Your (podcast) commercials need to be timed better. Its more than annoying.
🤪 This Sounds To Me Like Just Different Terms For Precision and Accuracy? 🤭
Makes zero sense to me.. They are if I’m understanding correctly saying you need to shoot larger sample sizes. Each round you shoot consecutive the barrel gets hotter, and hotter the barrel gets the less accurate.. I guess it all depends on how many rounds you typically shoot conservatively..
Like say I buy a new hunting rifle.. I find a load the rifle likes by shooting a 3 to 5 round group and then set my sights/scope in the center of where the impact was. Seems to me they are trying to overly complicate things and looking for computers to solve basically a mechanical problem.