Required precision video and using WEZ

[aschuler]

I didn’t derive it, it’s a concept in statistics for adding random variables

Why Variances Add—And Why It Matters – AP Central | College Board

The Pythagorean Theorem of Statistics Quick. What's the most important theorem in statistics? That's easy. It's the central limit theorem (CLT), hands down. Okay, how about the second most important theorem? I say it's the fact that for the sum or difference of independent random variables...

apcentral.collegeboard.org

Cool, thanks for sharing

 

[hereinaz]

+1 I switched to pretty much only shooting from a tripod. I always have it with me hunting here in AZ (see what I did there) and most of the time I'm in rocky, uneven terrain where it just makes sense. Coues hunters if you know, you know.

Love my tripod. I think hunting coues gives an experience and point of view about precision long range hunting that is unique. Especially when you go practice it.

 

[Tom-D]

Using a standard 6.5 CM load with 147gr ELD-M at 2,700fps MV, 5,000ft DA, 6” square target, and 1.5mia, 1 MOA, and .5 MOA for all. Again, keep in mind these are 1st first hit probability in an unshot/novel environment and target.


4 mph wind caller.

1.5 MOA is 37.4%-
View attachment 685362



1 MOA is 43.9%-
View attachment 685363


.5 MOA is 47.7%-
View attachment 685366


For a 10% increase in hit rate from realistic mechanical precision of 1.5 MOA to a completely unrealistic .5 MOA.



Now, the same but with a 2 mph wind caller:

1.5 MOA is 57.6% (already 10% higher than the 4mph wind caller with .5 MOA rifle)
View attachment 685368



1 MOA is 71%
View attachment 685369


.5 MOA is 79%View attachment 685370


For a difference of 21% from 1.5 MOA to .5 MOA.

You do see more of a difference when the target is at mid ranges- 300 to 500 yards and smaller than the base cone.

Here’s why. With a 4 mph average wind caller- which you (the colloquial “you”) aren’t in broken terrain unless you are shooting in novel broken terrain a lot- the wind is the largest source of error- not precision.

1.5 MOA causes of horizontal error. The vast majority of error is wind-
View attachment 685376


.5 MOA the vast majority of error is wind-
View attachment 685377




If you want to hit things more often, find what is producing the larger source of error in reality, in the field- and reduce that source.

Thats a great report and unreal data. Definitley brings it more align with my personal situation and its good to see what really matters. Thank you for taking the time to write this up

 

[Formidilosus]

Thats a great report and unreal data. Definitley brings it more align with my personal situation and its good to see what really matters. Thank you for taking the time to write this up

No problem.

 

[chindits]

Excellent information right before BLM locks up all the access roads for mud season. Definitely makes me question why I’ve been shooting my rifle so much with such low probability first hit rates in novel environments. Perfect excuse to just shoot the bow now instead of burning up all these components.

 

[MEdude]

Seems alot easier for me to just say “I don’t understand the basis of statistics.” than to… aah forget it.
I know little, and enjoy learning more. I’ll just stuff a bunt cake in my pie hole, and follow the thread.
Good listen, good read, Tnx

 

[aschuler]

So I got really sick this week and was sitting around not being able to do much. After I got caught up on reloading my thoughts turned back to this thread and the idea behind WEZ. I figured I might learn something by experimenting with my own simulations and a ballistics solver.

A few hours later and I have proof of concept hacked together. It's just doing horizontal dispersion due to wind and rifle precision, but all the foundational stuff is there. It's starting to correlate pretty well with results Form posted in his screenshots, but it's not going to the same as WEZ because I'm using a different solver, probably a different way of sampling the distributions yada yada.

Doing this raised a question. In the WEZ screenshots it *looks* like the wind input is calling for the SD of wind in MPH. From the conversations I was thinking the input was +-MPH as the upper an lower bounds of the wind call. As in "I'll always be within +- 4mph of the actual wind". That's very different from the SD of the wind call being 4mph. In that case the 96% wind call would be 2 SDs or 8mph right? I'm curious if @Formidilosus or one of the WEZ users can educate me on this. Thank you in advance.


I'm not a mathematician, statistician, ballistician or "anything-cian"....I'm just a computer geek that likes to hunt and shoot. But here's a screenshot of my little hacked together simulation. It's an interesting learning experience!

 

[Macht]

Yes, the WEZ inputs are SDs. So if your 95% (roughly 4 sigma) confidence is that you call the wind within +/-4mph, the number that goes into WEZ is 2mph.

 

[solarshooter]

I also don't have WEZ and was also curious about taking my own stab at estimating hit rates. I did this in excel and using Berger's online ballistic calculator for the base trajectory inputs. Basically I have a mean and SD quantified for some of the most common and significant sources of error. Note - this is using my same 284 ballistics and data I have quoted in other threads on this topic.


These are user inputs, and should be done to reflect real data gathered on your rifle. I use the mean and sd of shot radius method (again as described in other threads), so I have pretty solid numbers on those, as well as MV. Wind calling is less solid, since it is hard to measure wind, but I arrived at those numbers by saying, on average I call within 2mph, and my worst case call will be within 5mph.

I run two trajectories through Berger's solver, one with baseline inputs and 1mph wind, the other with +1SD of MV. Then I calculate mean, 1sd, 2sd, 3sd, errors in inches for each of the effects above, as a function of range. Wind error per mph is a simple scaling of the Berger outputs for 1mph. Range error per yd is determined by calculating dElevation/dYardage from the baseline trajectory, and scaling that result. Shot radius is a direct angular calculation as a function of range. Same with 0 error and aiming error. MV induced error in inches is calculated using the second trajectory, first by finding dElevation/dVelocity, and then scaling that by MV sd. Here's an example of what it looks like:


I calculate the mean, 1SD, 2SD, 3SD contributions of error for each component. Then for totals, I directly sum the means, but RSS the dispersions (aka the 1SD, 2SD, 3SD columns). For example, the 1SD column is mean + RSS(all 1SD dispersions). The answer looks like this:


Because I know the mean represents a 50% hit probability, 1SD 66%, 2SD 95%, 3SD 99.7%, I can do some interpolating to figure out what is my needed target size to give a certain hit probability at a certain range. Or said differently, given a certain target size and range, I can estimate my hit probability:


Looking at this result, I can compare against some WEZ values @Formidilosus ran for my gun in a different thread. Now a quick tangent on WEZ vs. my calculator. WEZ doesn't have mean inputs, only SD aka dispersions. I think this is valid for most things, but not for rifle precision or wind calling. The center of the wind calling distribution is not necessarily 0. Said differently, on AVERAGE, most people will have some amount of wind calling error. So to do an apples to apples comparison, I run the following:


Form's WEZ output:

WEZ calculates 58.6% hit probability. I calculate that I have slightly less than 60% chance. Pretty good!

This data is also super informative. Some takeaways:

• If I want ~100% chance of shooting a deer (12" circle), my max range should be 360yds. On elk (18" circle) this goes to 470yds. This ignores shooter induced errors other than aiming.
• Hitting at 600yds is twice as hard as hitting at 400. Hitting at 1000yds is 2.5x as hard as 600. Nonlinear error folks!
• Assuming my system is at least average, MOST people have a <50% chance of hitting a 10" circle at 600yds. This jives with the Cold Bore Challenge results from last year, ~35-40% success rate at 600 if I recall correctly.

I've also been able to mess with various inputs to determine sensitivities to hit rates. Conclusions in this thread are mostly correct, but rifle accuracy sure doesn't hurt! As I've said in other threads, given a "0 sum game" of time, where I have to choose between practicing and developing my rifle system, practicing wind calling and positional shooting is probably the most beneficial use of time. But in my particular situation, I cannot shoot in the mountains at long ranges easily, but I can go to the range and test some different ammo, measure MV, or run the Kraft drill. So my "practice" time is not 1:1 with my development time - I'm going to spend a fixed number of days shooting in the field regardless of if I do some development at the range or not. So I see no harm in it. That being said, "development" has gotten a lot simpler for me as a result of Form's and other's input, and some other studies I've run. See other posts for that.

 

[solarshooter]

Yes, the WEZ inputs are SDs. So if your 95% (roughly 4 sigma) confidence is that you call the wind within +/-4mph, the number that goes into WEZ is 2mph.

I think you're both correct, and I've mentioned this to @Formidilosus in the past. I think his take is that the 4mph SD input is representative of the actual misses people have in the field. Now, I think it's pretty hard to accurately measure misses in the field into dirt, but I get the sentiment that the 4SD number has sort of been "calibrated" to realistic scenario hit rates. That being said, a 4mph SD means that in 20 calls, you will be 8mph off. This is excessive for wind at the shooter IMO. But, maybe it's also incorporating wind changes due to terrain that experienced shooters "bake in" to their overall wind call for the shot. But again, I'm just inferring info from Form here. Personally, I think my worst case wind call at the shooter will be within 5mph, and on average I'm within 2mph. Therefore, mean = 2, sd = 1, mean + 3sigma case aka 99.7% likelihood = 5mph.

 

[aschuler]

Yes, the WEZ inputs are SDs. So if your 95% (roughly 4 sigma) confidence is that you call the wind within +/-4mph, the number that goes into WEZ is 2mph.

That's what it looked like to me as well, thanks.

 

[Macht]

I think you're both correct, and I've mentioned this to @Formidilosus in the past. I think his take is that the 4mph SD input is representative of the actual misses people have in the field. Now, I think it's pretty hard to accurately measure misses in the field into dirt, but I get the sentiment that the 4SD number has sort of been "calibrated" to realistic scenario hit rates. That being said, a 4mph SD means that in 20 calls, you will be 8mph off. This is excessive for wind at the shooter IMO. But, maybe it's also incorporating wind changes due to terrain that experienced shooters "bake in" to their overall wind call for the shot. But again, I'm just inferring info from Form here. Personally, I think my worst case wind call at the shooter will be within 5mph, and on average I'm within 2mph. Therefore, mean = 2, sd = 1, mean + 3sigma case aka 99.7% likelihood = 5mph.

At the most basic level, the math is the math. We don't get to make up a separate definition of what SD is.

In some sense I'm just restating what you said, but my takeaway from what form has written about it is that people are just even worse at judging wind than they think.

Even without taking that into consideration it's a very hard thing to put a number to. Probably the single hardest WEZ input to get even close to right.

 

[aschuler]

I also don't have WEZ and was also curious about taking my own stab at estimating hit rates. I did this in excel and using Berger's online ballistic calculator for the base trajectory inputs.

Solid work sir! Really nice way to visualize some possible scenarios for your setup.

Now a quick tangent on WEZ vs. my calculator. WEZ doesn't have mean inputs, only SD aka dispersions. I think this is valid for most things, but not for rifle precision or wind calling. The center of the wind calling distribution is not necessarily 0. Said differently, on AVERAGE, most people will have some amount of wind calling error.

I was wondering about this myself. I've kind of gone back and forth with it. I think I've come around to the idea that a normal distribution is still the best fit for this. But I have nothing concrete to back that up.

So to do an apples to apples comparison, I run the following:
View attachment 696958

This is a really good use of this type of exercise. Either to reach a conclusion about what a reasonable distance would be for a target or a reasonable target for the distance.

This data is also super informative. Some takeaways:

• If I want ~100% chance of shooting a deer (12" circle), my max range should be 360yds. On elk (18" circle) this goes to 470yds. This ignores shooter induced errors other than aiming.
• Hitting at 600yds is twice as hard as hitting at 400. Hitting at 1000yds is 2.5x as hard as 600. Nonlinear error folks!
• Assuming my system is at least average, MOST people have a <50% chance of hitting a 10" circle at 600yds. This jives with the Cold Bore Challenge results from last year, ~35-40% success rate at 600 if I recall correctly.

Again, really nice job pulling some concrete conclusions. This is the type of stuff we're going for here. I have to admit at least part of my motivation is to show some of my "less skilled" shooter friends how risky their shots might be and that they might not want to take them

I've also been able to mess with various inputs to determine sensitivities to hit rates. Conclusions in this thread are mostly correct, but rifle accuracy sure doesn't hurt! As I've said in other threads, given a "0 sum game" of time, where I have to choose between practicing and developing my rifle system, practicing wind calling and positional shooting is probably the most beneficial use of time. But in my particular situation, I cannot shoot in the mountains at long ranges easily, but I can go to the range and test some different ammo, measure MV, or run the Kraft drill. So my "practice" time is not 1:1 with my development time - I'm going to spend a fixed number of days shooting in the field regardless of if I do some development at the range or not. So I see no harm in it. That being said, "development" has gotten a lot simpler for me as a result of Form's and other's input, and some other studies I've run. See other posts for that.

I'm pretty much in exactly the same boat!

 

[Toomuchon]

Thanks to the contributors of this thread! I know from previous reading that time spent at the reloading bench fussing over advanced reloading operations was a waster of time, but this thread provides the ‘why’. Buy more ammo, and get out in the wind more (which I have in abundance here…)

The question I gave for the experts - @Formidilosus will probably be able to comment here…. Where is the cross-over between gains in probability due to cartridge performance vs probability losses due to recoil? Looking at a specific example:

6.5cm with 140gr ELD-M @ 600yds gives me a probability of 89%

7mmRM with 175gr ELD-X at 600yds (and same atmospheric assumptions (wind velocity and angle variability) gives a hit probability of 98%.

Granted, these probabilities are optimistic (based of a 1.2 MOA mechanical accuracy but it shows the difference that velocity and BC make. However my gut feel is that in practical terms, the hit rate of the 7mmRM would be lower than the creedmoor based on recoil effects. Would my assumption be correct? I don’t have a RM at my disposal to prove or disprove for myself. The RM is very popular here due to the low wind drift, and supposed ‘killing power’, but the mystique is probably just that

 

[solarshooter]

I think the answer depends on how much wind you apply to the problem, and how much loss of group size you attribute to increase in recoil, and/or less ideal positions. I have also been thinking a lot about how to characterize this, and the answer is it's difficult. For instance, I can shoot just as good of a group prone as I can from the bench, with rifles from 6CM to 28 Nos (with a brake). So for prone, I would argue there is no real loss in precision. From freehand, I also see no loss in precision (though the groups are much larger), likely because the error due to the wobble dominates the problem. Seated supported and unsupported may show a slight difference, but I haven't tested enough to prove if it's real or not.

So in short, like I said, I haven't found a good way to characterize this. Bryan Litz has a formula to estimate rifle precision in his latest book, called the TOP Gun theory, which basically is a conservation of momentum solution that says a heavier rifle will a lighter/slower projectile will move less under recoil and will therefore be more precise. He anchors this with some extensive testing of a lot of types of rifles, and it seems to correlate well. However, I have firm data on a couple rifles (that 28 Nos in particular) that falls totally off this trendline, so I don't know how valid it really is.

I think excessive recoil can be really bad in situations where you are shooting a lot of volume, like competitions or in practice. For those reasons, I personally don't like big magnums. However, that IS NOT what we're doing when we're hunting. So the idea of a very fast high BC cartridge for hunting applications is not a bad one, in my opinion. What @Formidilosus does for a job is a mystery, but he seems to be shooting a ton of volume, so I can see why he tends towards lighter recoiling cartridges. But if you have say a practice gun and hunting gun with similar ergonomics and controls, the practice gun in a light recoiling cartridge (the .223 rokslide special for instance) and the hunting gun in a heavier recoiling one (a 7RM, for example), I think you could get the best of both worlds.

Going from a 4mph gun to an 8mph gun means your error due to windage will be cut IN HALF, and since that is the biggest source of error, your hit rates will go up dramatically, especially in heavier winds. To me, that has to outweigh the gains of a lighter recoiling rifle. There is obviously an upper limit to this, which I would say is being able to spot your hits. Muzzle brakes and some suppressors can offer a way to "cheat" this tradeoff, and it does work.

 

[Formidilosus]

I think the answer depends on how much wind you apply to the problem, and how much loss of group size you attribute to increase in recoil, and/or less ideal positions. I have also been thinking a lot about how to characterize this, and the answer is it's difficult. For instance, I can shoot just as good of a group prone as I can from the bench, with rifles from 6CM to 28 Nos (with a brake). So for prone, I would argue there is no real loss in precision. From freehand, I also see no loss in precision (though the groups are much larger), likely because the error due to the wobble dominates the problem. Seated supported and unsupported may show a slight difference, but I haven't tested enough to prove if it's real or not.

So in short, like I said, I haven't found a good way to characterize this. Bryan Litz has a formula to estimate rifle precision in his latest book, called the TOP Gun theory, which basically is a conservation of momentum solution that says a heavier rifle will a lighter/slower projectile will move less under recoil and will therefore be more precise. He anchors this with some extensive testing of a lot of types of rifles, and it seems to correlate well. However, I have firm data on a couple rifles (that 28 Nos in particular) that falls totally off this trendline, so I don't know how valid it really is.

I think excessive recoil can be really bad in situations where you are shooting a lot of volume, like competitions or in practice. For those reasons, I personally don't like big magnums. However, that IS NOT what we're doing when we're hunting. So the idea of a very fast high BC cartridge for hunting applications is not a bad one, in my opinion. What @Formidilosus does for a job is a mystery, but he seems to be shooting a ton of volume, so I can see why he tends towards lighter recoiling cartridges. But if you have say a practice gun and hunting gun with similar ergonomics and controls, the practice gun in a light recoiling cartridge (the .223 rokslide special for instance) and the hunting gun in a heavier recoiling one (a 7RM, for example), I think you could get the best of both worlds.

Going from a 4mph gun to an 8mph gun means your error due to windage will be cut IN HALF, and since that is the biggest source of error, your hit rates will go up dramatically, especially in heavier winds. To me, that has to outweigh the gains of a lighter recoi. There obviously an upper limit to this, which I would say is being able to spot your hits. Muzzle brakes and some suppressors can offer a way to "cheat" this tradeoff, and it does work.

No, or mostly no. Shooting untimed from a bench does not translate to groups size/accuracy in the field in stressed or timed shots on animals. From 6.5cm to 7mm RM is generally around 1.5x to 2x to worst shot in a 10 round group on average. For example: if a shooter using a 6.5cm did standing to prone for 1 shot with a 10sec par time; ten times in a row and his worst shot hit a 1.4 MOA circle, with a 7mm RM his worst shot would only hit a 2moa to 2.8 MOA.

That’s not accounting for not spotting hits/misses, animal reaction, etc.


Recoil has a very large effect while hunting.

 

[solarshooter]

No, or mostly no. Shooting untimed from a bench does not translate to groups size/accuracy in the field in stressed or timed shots on animals. From 6.5cm to 7mm RM is generally around 1.5x to 2x to worst shot in a 10 round group on average. For example: if a shooter using a 6.5cm did standing to prone for 1 shot with a 10sec par time; ten times in a row and his worst shot hit a 1.4 MOA circle, with a 7mm RM his worst shot would only hit a 2moa to 2.8 MOA.

That’s not accounting for not spotting hits/misses, animal reaction, etc.


Recoil has a very large effect while hunting.

So if you ran WEZ with those numbers for rifle precision, but then also accounting for differences in ballistic performance, which one gives an overall higher hit rate?

Spoiler: I'm willing to bet 6.5CM wins because it's got great ballistics, and 7RM doesn't have as big of an edge on it as say 308 or 223. But I would really like to see the WEZ results for 7RM, 6.5CM, and 223, assuming high performance hand loads in a 24" barrel and a 4mph wind SD, if you have time and interest!

 

[Macintosh]

Why dont you actually measure the difference in precision for yourself? Ie cook up your own test based on the Kraft drill but using your own most commonly used field positions, and do this a couple times over a couple range sessions and find your actual average precision for each. Assuming anyone interested in this stuff practices somewhat regularly, this is easily done on a 100 yard range and would be pretty easy to compare two rifles under the same “test”. Then youd be able to see if there is a recoil effect and even quantify it to a large degree.

 

[Formidilosus]

So if you ran WEZ with those numbers for rifle precision, but then also accounting for differences in ballistic performance, which one gives an overall higher hit rate?

Spoiler: I'm willing to bet 6.5CM wins because it's got great ballistics, and 7RM doesn't have as big of an edge on it as say 308 or 223. But I would really like to see the WEZ results for 7RM, 6.5CM, and 223, assuming high performance hand loads in a 24" barrel and a 4mph wind SD, if you have time and interest!

I’ll run it. But it will be next week, remind me if you will.

In that specific scenario, at 600 yards first round hit probability will be 6.5cm, 7 RM, 223 from best to worst. The second round hit rates is/will be 223, 6.5cm, 7mm RM from highest to lowest. At 400-500, in real life is where the cross over from 223/77gr TMK being better, to 6.5cm with high BC. It’s way out there when 7mm mags take over.

 

[solarshooter]

Why dont you actually measure the difference in precision for yourself? Ie cook up your own test based on the Kraft drill but using your own most commonly used field positions, and do this a couple times over a couple range sessions and find your actual average precision for each. Assuming anyone interested in this stuff practices somewhat regularly, this is easily done on a 100 yard range and would be pretty easy to compare two rifles under the same “test”. Then youd be able to see if there is a recoil effect and even quantify it to a large degree.

This is basically what I've done, with Tikkas set up identically in .22lr and 284 Win, and I've seen basically no difference in score.