In a related sense, if you aren’t shooting at long range enough, you don’t know what you don’t know.If the cost of ten to twenty rounds is a limiting factor, how do you afford to practice with the rifle enough to be competent at long range with it?
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In a related sense, if you aren’t shooting at long range enough, you don’t know what you don’t know.If the cost of ten to twenty rounds is a limiting factor, how do you afford to practice with the rifle enough to be competent at long range with it?
Based on your idea of adjusting bullet exit time to find more precision, do you not adjust seating depth to modify barrel time as well?My load dev process after all this is as follows
I haven't found it to have a noticeable effect. Not nearly as much as powder charge. That being said, I think it can have an effect if you are shooting a secant ogive bullet with excessive jump, but the problem you are solving is one of inconsistent engraving into lands. Also may be more noticeable in chambers with alot of freebore clearance, or really sharp leade angles.Based on your idea of adjusting bullet exit time to find more precision, do you not adjust seating depth to modify barrel time as well?
Love the added info and more in depth look at these things. And your graphs and charts were awesome to look at! I only recently started looking at mean radius, but am honestly not really sure how to read it, and relate it to what an acceptable long range load would be via mean radius.Not to revive a dead horse just to beat it to death again, but here I go...
I have read through the entire thread, and I think I have something to offer. Like many others I was very disturbed by Bryan Litz's chapters (Modern Advancements Vol 3) on rifle accuracy and small sample testing (which by the way came out well before Hornady's podcast). I was just about to begin development on my new barrel, a 26" Benchmark chambered in 284 win (Tikka platform), and this rocked my world.
I used to consider my load dev method a 5x5 on powder in 1% increments, then pick best powder based on group and poi trend, do a 5x5 on seating depth, pick best combo based on group/poi trend, then load up 25 for verification and MV.
Once I read the book, I was thrown into a world of doubt. So I decided to do some testing myself. I grabbed my T1x and went to 50yds and shot 19 10 shot groups over the course of a couple days, and began crunching numbers. This activity resulted in the video below, an interview with Keith of Winning in the Wind, who is a local F class champ and fellow aerospace engineer.
Now I understand not everyone wants to sit through over an hour of two engineers rambling (though I think it's worth your time, obviously biased). So I'll put some cliff notes here of the relevant findings from my testing and how it influenced my load development method.
Actually before I do that, let me say a little bit about load development. I am a structural dynamicist by education and profession, meaning I model and predict structural dynamic loads, deflections, and accelerations. ALL elastic structures have modes of vibration which are determined by their stiffness and mass characteristics. Elasticity means that the material stretches under load. Most materials we interact with on a daily basis are elastic, including the metal of your barrel. The material and contour of your barrel determine it's stiffness and mass distribution, and therefore it's vibrational frequencies and shapes (modes). For a free floated barrel, this can be considered a cantilevered beam in engineering terms, and the stiffness or rigidity of the barrel attachment to the action/stock/shooter/ground system also influence its modes. This page explains the math https://endaq.com/pages/bernoulli-euler-beams, see animations of modes here https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory.
So when I talk about load dev, I'm talking about adjusting bullet time such that the bullet leaves at an extreme of barrel motion, where velocity is close to zero (at least for the largest amplitude modes), and small variations in bullet time don't produce large variations in bullet exit angle. I DO NOT believe that certain powder charges posses magical better MV properties - MV is linear with powder for the useful charge range. MV ES and SD are a function of your components and your reloading consistency.
OK now on to the critical findings:
- Impact radius is far more useful and meaningful than group size. You get more data for the same set of shots, converge to the "correct" answer faster, and characterize the system more accurately. Learning to work in terms of mean and SD radius is game changing.
- Using radius, you can continuously "overlay" more and more shots, so as you go and practice and shoot your baseline load, you can end up with a database of 100s of shots informing your mean/SD radius stats. This is like having a group size of 100s of shots, only much easier and more informing.
- Small samples (3-5 shots) CAN be useful for assessing differences between populations, provided the differences are large (50-100%). As the differences become smaller you need more samples to tell them apart. Due to the large samples required to fine tune a load, it's probably not worth doing. Assessing major deltas across component combinations and broad sweeps of powder is most worthwhile, and once you get below your required accuracy threshold, characterization is more valuable.
- The "T-Test" can be used to statistically assess whether populations of data are actually different. You need a mean and standard deviation of each population to do this.
My load dev process after all this is as follows, and keep in mind I'm always working in radius and logging every shot as I go:
It's worth noting this is about the same number of shots as before, but I am using different metrics and looking for different information. I'm also making much more significant changes in each set of testing.
- Load up 5 shots for each bullet/powder combo I want to test (I don't mess with primers until I look at MV stats). Shoot and look for best combo by a large margin. If all similar pick my preferred and move on.
- Load up a 5x5 broad powder sweep, 1-2% powder increments. Shoot and look for best combo by a large margin. If all similar pick my preferred and move on.
- Validate - load up 20-30 and shoot for groups and MV. Note that these groups will later be overlaid via radius methodology, but you get 4-6 5 shot group agg for comparison to that metric and other rifles. At the end of validation you will have between 20 and 40 shots informing your mean and SD radius stats, and your mean and SD MV stats.
- If at the end of this process (~80rds) you don't have a load you like, start over with new components. If you do like it, start shooting and practicing with it and log all your data as you go to increase your statistical basis.




Thank you for the in depth reply! How did you find the radius SD?In order to inform the likelihood of hitting a certain size target, you need to look at mean and standard deviation radius. In your example, shooting at 1k yards, group size only will not tell you overall hit percentage since other errors dominate the equation. But lets say just for example we want to know the likelihood of a 1MOA target at any range just due to rifle error. Mean + 2SD radius will cover 95% of shots, meaning 19/20. Mean + 3SD radius will cover 99.7% of shots, meaning 997/1000. If you want the everyday likelihood, use mean+2SD. If you want the absolute worst case you will likely ever see, use mean+3SD. It's worth noting that the quality of your mean and SD radius grows as you add more shots to the database. For example I'll use data for my 284 which has 51 shots recorded for radius.
Mean = 0.27moa
SD = 0.16moa
2 sigma (SD = sigma) group = 2*(0.27 + 2*0.16) = 1.18moa. This is the group I'd expect if I shot about 20 shots.
3 sigma group = 2*(0.27 + 3*0.16) = 1.5moa. This is the group I'd expect if I shot 50+ shots.
As a further example of how this relates to reality, here are 3 5 shot groups I shot from the bench last weekend. Note the zero shift from prone, which is how I zeroed my gun. This shift caused me to clean miss a big old muley this year.
View attachment 658768
I haven't tried to overlay the groups to measure, but visually I bet the combined 15 shot group is at or just below 1.18moa, aka my predicted 20 shot group.
Going further, if you average the 3 groups, you get 0.74moa, which is close to what you get if you do mean + 1 sigma radius, 2*(0.27 + 1*0.16) = 0.86moa, aka predicted group size for 5 shots. This also shows a little bit of why groups on their own are a poor way to characterize the rifle. The average of multiple groups is a better way to do it, which is what BR aggs are doing. Mean and SD radius is the best, because you'll converge to the correct answer in fewer shots.


for a single group is very easy to claculate the standard deviation. just throw the radius of each shot in excel and calculate standard deviation using the stddev formula. To keep a running totally of MR(mean radius) and SD (standard deviation on your radii) your going to need to log X and Y locations of every shot. Then each day or each time you change your zero you will need to calculate the effective center for the day and convert the x/y locations in to radius measurements aka distance from center. So if you shoot 5x5 groups with out changing any variables, you want to calculate the cumulative center of all 25 shots and then calculate radius, don't just calculate radius from each each groups center.Thank you for the in depth reply! How did you find the radius SD

Just out of curiosity, how far was the shot on the muley that a .5 moa zero shift caused a clean miss?In order to inform the likelihood of hitting a certain size target, you need to look at mean and standard deviation radius. In your example, shooting at 1k yards, group size only will not tell you overall hit percentage since other errors dominate the equation. But lets say just for example we want to know the likelihood of a 1MOA target at any range just due to rifle error. Mean + 2SD radius will cover 95% of shots, meaning 19/20. Mean + 3SD radius will cover 99.7% of shots, meaning 997/1000. If you want the everyday likelihood, use mean+2SD. If you want the absolute worst case you will likely ever see, use mean+3SD. It's worth noting that the quality of your mean and SD radius grows as you add more shots to the database. For example I'll use data for my 284 which has 51 shots recorded for radius.
Mean = 0.27moa
SD = 0.16moa
2 sigma (SD = sigma) group = 2*(0.27 + 2*0.16) = 1.18moa. This is the group I'd expect if I shot about 20 shots.
3 sigma group = 2*(0.27 + 3*0.16) = 1.5moa. This is the group I'd expect if I shot 50+ shots.
As a further example of how this relates to reality, here are 3 5 shot groups I shot from the bench last weekend. Note the zero shift from prone, which is how I zeroed my gun. This shift caused me to clean miss a big old muley this year.
View attachment 658768
I haven't tried to overlay the groups to measure, but visually I bet the combined 15 shot group is at or just below 1.18moa, aka my predicted 20 shot group.
Going further, if you average the 3 groups, you get 0.74moa, which is close to what you get if you do mean + 1 sigma radius, 2*(0.27 + 1*0.16) = 0.86moa, aka predicted group size for 5 shots. This also shows a little bit of why groups on their own are a poor way to characterize the rifle. The average of multiple groups is a better way to do it, which is what BR aggs are doing. Mean and SD radius is the best, because you'll converge to the correct answer in fewer shots.
644yds cross canyon. It was that plus likely an updraft that wasn't accounted for, maybe a poor rear rest causing the rifle to recoil nose high, nerves, and I suck. Roughly 2moa miss, deer was bedded broadside, aimed in the armpit, bullet went about 1-2" above the head between the ears and the antlers.Just out of curiosity, how far was the shot on the muley that a .5 moa zero shift caused a clean miss?
Ryan
Not to revive a dead horse just to beat it to death again, but here I go...
I have read through the entire thread, and I think I have something to offer. Like many others I was very disturbed by Bryan Litz's chapters (Modern Advancements Vol 3) on rifle accuracy and small sample testing (which by the way came out well before Hornady's podcast). I was just about to begin development on my new barrel, a 26" Benchmark chambered in 284 win (Tikka platform), and this rocked my world.
I used to consider my load dev method a 5x5 on powder in 1% increments, then pick best powder based on group and poi trend, do a 5x5 on seating depth, pick best combo based on group/poi trend, then load up 25 for verification and MV.
Once I read the book, I was thrown into a world of doubt. So I decided to do some testing myself. I grabbed my T1x and went to 50yds and shot 19 10 shot groups over the course of a couple days, and began crunching numbers. This activity resulted in the video below, an interview with Keith of Winning in the Wind, who is a local F class champ and fellow aerospace engineer.
Now I understand not everyone wants to sit through over an hour of two engineers rambling (though I think it's worth your time, obviously biased). So I'll put some cliff notes here of the relevant findings from my testing and how it influenced my load development method.
Actually before I do that, let me say a little bit about load development. I am a structural dynamicist by education and profession, meaning I model and predict structural dynamic loads, deflections, and accelerations. ALL elastic structures have modes of vibration which are determined by their stiffness and mass characteristics. Elasticity means that the material stretches under load. Most materials we interact with on a daily basis are elastic, including the metal of your barrel. The material and contour of your barrel determine it's stiffness and mass distribution, and therefore it's vibrational frequencies and shapes (modes). For a free floated barrel, this can be considered a cantilevered beam in engineering terms, and the stiffness or rigidity of the barrel attachment to the action/stock/shooter/ground system also influence its modes. This page explains the math https://endaq.com/pages/bernoulli-euler-beams, see animations of modes here https://en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory.
So when I talk about load dev, I'm talking about adjusting bullet time such that the bullet leaves at an extreme of barrel motion, where velocity is close to zero (at least for the largest amplitude modes), and small variations in bullet time don't produce large variations in bullet exit angle. I DO NOT believe that certain powder charges posses magical better MV properties - MV is linear with powder for the useful charge range. MV ES and SD are a function of your components and your reloading consistency.
OK now on to the critical findings:
- Impact radius is far more useful and meaningful than group size. You get more data for the same set of shots, converge to the "correct" answer faster, and characterize the system more accurately. Learning to work in terms of mean and SD radius is game changing.
- Using radius, you can continuously "overlay" more and more shots, so as you go and practice and shoot your baseline load, you can end up with a database of 100s of shots informing your mean/SD radius stats. This is like having a group size of 100s of shots, only much easier and more informing.
- Small samples (3-5 shots) CAN be useful for assessing differences between populations, provided the differences are large (50-100%). As the differences become smaller you need more samples to tell them apart. Due to the large samples required to fine tune a load, it's probably not worth doing. Assessing major deltas across component combinations and broad sweeps of powder is most worthwhile, and once you get below your required accuracy threshold, characterization is more valuable.
- The "T-Test" can be used to statistically assess whether populations of data are actually different. You need a mean and standard deviation of each population to do this.
My load dev process after all this is as follows, and keep in mind I'm always working in radius and logging every shot as I go:
It's worth noting this is about the same number of shots as before, but I am using different metrics and looking for different information. I'm also making much more significant changes in each set of testing.
- Load up 5 shots for each bullet/powder combo I want to test (I don't mess with primers until I look at MV stats). Shoot and look for best combo by a large margin. If all similar pick my preferred and move on.
- Load up a 5x5 broad powder sweep, 1-2% powder increments. Shoot and look for best combo by a large margin. If all similar pick my preferred and move on.
- Validate - load up 20-30 and shoot for groups and MV. Note that these groups will later be overlaid via radius methodology, but you get 4-6 5 shot group agg for comparison to that metric and other rifles. At the end of validation you will have between 20 and 40 shots informing your mean and SD radius stats, and your mean and SD MV stats.
- If at the end of this process (~80rds) you don't have a load you like, start over with new components. If you do like it, start shooting and practicing with it and log all your data as you go to increase your statistical basis.
Yes, and I think it's adequate performance. I could've tried to go further, but I chose to focus on validation and practice once I reached this level. I think we agree that if you assessed most rifles more rigorously you would find this is pretty good performance. Also, relative to other combos I tried, it was a significant improvement. I don't have WEZ available, but it does increase hit rate at shorter ranges based on trajectory error analysis I've done. At longer ranges wind dominates.So after all this, you ended up at just over 1 MOA for a 15 round group?
And, with doing all that, how much has your hit rate in the field improved?
Yes, and I think it's adequate performance.
I don't have WEZ available, but it does increase hit rate at shorter ranges based on trajectory error analysis I've done.
Would it have been better spending all that time practicing at long range, yes, but it's not an either or for me since my local range is only 200yds. Plus shooting under ideal conditions is the best way to practice a lot of fundamental mechanics. Load dev is also shooting practice.
Positional shooting work is also valuable, but at short ranges if the rifle precision is poor, it's hard to know if you are doing well or not. Let's say my ideal 3 sigma group is 2-3moa, and when I have to build a position and shoot under pressure, that group increases by 1 moa. This is only a 30-50% signal, whereas if my ideal group was 1 moa it would be a 100% signal, and would take fewer shots to see.
And finally, if I had just bought box ammo and shot, I would know so much less about how a rifle system works, down to the detailed inner anatomy. That is worth a lot to me, and will benefit all future shooting and rifle building that I do.
Yes, and I think it's adequate performance. I could've tried to go further, but I chose to focus on validation and practice once I reached this level. I think we agree that if you assessed most rifles more rigorously you would find this is pretty good performance. Also, relative to other combos I tried, it was a significant improvement. I don't have WEZ available, but it does increase hit rate at shorter ranges based on trajectory error analysis I've done. At longer ranges wind dominates.
Would it have been better spending all that time practicing at long range, yes, but it's not an either or for me since my local range is only 200yds. Plus shooting under ideal conditions is the best way to practice a lot of fundamental mechanics. Load dev is also shooting practice.
Positional shooting work is also valuable, but at short ranges if the rifle precision is poor, it's hard to know if you are doing well or not. Let's say my ideal 3 sigma group is 2-3moa, and when I have to build a position and shoot under pressure, that group increases by 1 moa. This is only a 30-50% signal, whereas if my ideal group was 1 moa it would be a 100% signal, and would take fewer shots to see.
And finally, if I had just bought box ammo and shot, I would know so much less about how a rifle system works, down to the detailed inner anatomy. That is worth a lot to me, and will benefit all future shooting and rifle building that I do.