Ep. 099 - Let's Talk Mean Radius 

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 👍

Glad you enjoyed!

Glad you like them!

@@hornady it has made me rethink all my load development strategies. I am going back to the drawing board.

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

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.

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.

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.

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.

Same here

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

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…

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

Yep, it will figure your zero angle

@@hornady i just purchased the feature and can’t wait to try it!!! Thanks!

Agreed!

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.

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.

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

Yep

Shoot us an email. tech@hornady.com

Shoot us an email at podcast@hornady.com

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..

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!👍

You can adjust the aim point to the center of the group...

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

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.