Single digit E.S. dont mean squat.

An old timer methodically shoots six 5 shots groups that average to .3 moa can say with 90% confidence that he has a 1/3 moa rifle and load. This can be done without a chronograph and no knowledge of elementary statistics and all the misinformation going around about how to use them.
It can also be meaningless to misleading.

This guy is sitting at a bar to my right. He's pretty sure he has a 1/3moa rifle, as his last 6 groups suggest.
I want to box this into meaning, so I ask: WHAT RANGES, WHAT ACCURACY, FIELD REST, OR BENCH
He provides 100yds, Farley rest,, didn't measure accuracy.

A guy on my left says he killed 30 groundhogs last week, 100% kill rate.
WHAT RANGES: all kinds
WHAT ACCURACY: good enough
FIELD REST, OR BENCH: Harris bipod

Groundhog killer is way more more interesting than 1/3moa of 100yd BR precision dude.
He would get a spot on my Minutemen Sniper Team.
 
Did everbody forget what the original title was SINGLE digit E.S don't mean squat?
As usual thread gets off in the weeds just like most anymore, the point was I have read many times were reloeaders get obsessed with single digit E.S. and was just trying to prove a point that repeatedly and what the target says is the most important thing instead of what numbers say. Then we get to well it matters past 1,000 well that might be true but is it 1200, 1500, or 2000 only way you will know is TEST which I do alot!
Yep
 
1/3moa of 100yd BR precision dude.
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If he changed to a 30BR he'd be in the .0s. Might have an ES of 120FPS, but he'd be there 🤣
 
I've had too much going on at work to really contribute here much lately, but this seems a topic where I can without too much brainpower expended.

@QuietTexan is right about sample size and I can see where @Culpeper was going, but I don't think the details are quite right.

If we assume that bullet speed per a fixed charge is normally distributed (and I have no idea whether it is or not), then the relationship between extreme spread (which is called the range in statistics), standard deviation, and the mean is as follows. The mean is a measure of central tendency: the value around which the data (our bullet speed) is centered. The range (or ES) is the set of values that define the lower and upper bounds of possible value for bullet speed (0 and infinity, we'll get to why later), and the standard deviation tells us how the data are distributed around our measure of central tendency.

Let's talk about standard deviation. A small SD indicates most values are close to the mean and a larger one means they become more disperse around the mean. If we assume a normal distribution, roughly 68% of the data will be within +/- 1 SD of the mean, 95% 2SD, and 99% 3SD. Once we get to around 5 SD we have pretty much captured all of the possible values with high certainty (but still not the range).

In statistics there are two versions of most summary statistics (mean, SD, range, median, etc.): the population version and the sample version. The population version is the universe of all data for that measurement. If you could record all bullet speeds for that charge then you would know the population. The sample is what you actually observe. If you are doing three shots and then calculating your statistics, then your sample is of size three. As you can imagine, if your sample size increases, your certainty of the veracity of the statistics increases and eventually becomes indistinguishable from the population versions. Think of creating a histogram (a bar chart with the y axis being the number of times a value is observed and the x axis being the values in increasing order from left to right). If you only take three measurements, then that histogram is not likely to be very accurate. In the same vein, taking 1000 measurements is likely more than you need to characterize the shape of the histogram. What is the right number depends on the range and the standard deviation (which we do not know ahead of time, unfortunately). So taking a reasonable guess for the sample size seems like an appropriate course of action.

Let's say we shoot 30 rounds and measure the speed of each one. We could create a histogram and inspect its shape. Assuming speed is normally distributed, does your histogram look like that normal bell shape curve? If not, maybe shoot 20-30 more times and then check. I would guess that you would need 50-100 rounds to really capture something that looks like a bell shaped curve. Take your mean and standard deviation of those 50-100 rounds and I think you could be confident of the performance of that particular recipe. 3x the SD will tell you what speeds you should expect 99% of the time (actually 99.7% of the time). I would not worry about range (or ES as it's know here) as long as 3x the SD gives you upper and lower bound numbers you can live with.

The important thing is that we have an appropriate sample size to have values we can trust. I would not trust a SD calculated from 3 values. Who knows what adding a fourth would do to the calculated SD. As you get into larger numbers, that adding a new number matters less and less. Hence trusting values from larger sample sizes more.

I don't know if this helps anyone or not, but I feel better now.

You're correct but I think you are going further than the average reloader is able to do.

I was only limiting to the variables that a Chrono calculates. But based on my experience it takes 30+ shots to get into the 90% confidence level. We are not working with a sufficient population to pull a reasonable sample from to begin with so we are not really sampling. You're getting into Statistics 101.

A 10 shot string shot with a Chrono is a way to predict the population size that has yet to be reloaded. But to simplify we can calculate confidence and the higher the better.

You obviously know what you are doing. I worked auditing with random and then later statistical sampling. The latter required special software. But in every case we always had a large population to start with. If we had 5000 rounds of factory match ammo and randomly selected the required sample size for confidence then we would compare that to the factory specifications, which was calculated using sampling to begin with. With a Chrono we are trying to achieve this without a population for reloading. Example, with 30 shots on the Chrono we are only hoping with some level of confidence that the next 1000 reloads will give similar results, statically speaking only. It's a prediction.
 
Yup. If ES isn't ~5x of SD all it means is that there aren't enough samples in the population. Anyone can post up a 3-shot 0SD, 1ES is they shoot enough 3-shot groups. But when you add them all together ES will approach 5x SD, it's a mathematical certainty.

Show us. If you had a sufficient population to begin with you would only need to pull one sample. So, you can show us with mathematical certainty, lol. So, show us.
 
This is why the internet is stupid.

ES absolutely matters.
Barrel harmonics/accuracy node also absolutely matter.

If you want the most repeatable and accurate load, you need to find both… simultaneously and at the the same time.

I know what you are trying to get at, but ES is not the measure that will get you there. ES is only the tails of the distribution, the extreme ends. No matter what distribution we look at (normal, Poisson, Negative Binomial, Gamma, etc.) the tails all have extremely low probability of occurring. Close to zero probability. What I care about is where are the bulk of my bullet speeds going to be. There are only two statistics that matter for this and those are the measure of central tendency and the measure of dispersion. Here, we'll use the mean and the standard deviation to measure each.

To make sure that my bullet speeds are under control, I want a small standard deviation around a mean that I find acceptable. Plus or minus 3x the SD will tell me the upper and lower bound where I would expect 99.7% of my bullet speeds to be. No need to go to 5x as that last 0.3% is really likely out of my control anyway. If I find that I have a SD of 10 for a load, that means that my total spread from minus 3 SD to plus 3SD is 60fps., I'm probably OK with that as long as the mean speed meets my expectations. 99.7% of my shots should be within that range with the occasional, very rare at 0.3%, shot outside that range.

I don't care about the ES, I care about the SD as that tells me where the bulk of my shots are going to be and I think that is what you're after in the end. From your last sentence I can tell we're after the same thing, but I want to tell you that SD is the measure that will tell you there, not ES.
 
Did everbody forget what the original title was SINGLE digit E.S don't mean squat?
As usual thread gets off in the weeds just like most anymore, the point was I have read many times were reloeaders get obsessed with single digit E.S. and was just trying to prove a point that repeatedly and what the target says is the most important thing instead of what numbers say. Then we get to well it matters past 1,000 well that might be true but is it 1200, 1500, or 2000 only way you will know is TEST which I do alot!

Don't become like Butterbean. Why can't enjoy how beautiful it is today. Why can't you say something righteous and hopeful for a change. -- Oddball
 
I know what you are trying to get at, but ES is not the measure that will get you there. ES is only the tails of the distribution, the extreme ends. No matter what distribution we look at (normal, Poisson, Negative Binomial, Gamma, etc.) the tails all have extremely low probability of occurring. Close to zero probability. What I care about is where are the bulk of my bullet speeds going to be. There are only two statistics that matter for this and those are the measure of central tendency and the measure of dispersion. Here, we'll use the mean and the standard deviation to measure each.

To make sure that my bullet speeds are under control, I want a small standard deviation around a mean that I find acceptable. Plus or minus 3x the SD will tell me the upper and lower bound where I would expect 99.7% of my bullet speeds to be. No need to go to 5x as that last 0.3% is really likely out of my control anyway. If I find that I have a SD of 10 for a load, that means that my total spread from minus 3 SD to plus 3SD is 60fps., I'm probably OK with that as long as the mean speed meets my expectations. 99.7% of my shots should be within that range with the occasional, very rare at 0.3%, shot outside that range.

I don't care about the ES, I care about the SD as that tells me where the bulk of my shots are going to be and I think that is what you're after in the end. From your last sentence I can tell we're after the same thing, but I want to tell you that SD is the measure that will tell you there, not ES.

I've never had a single digit ES load without an SD that wasn't pretty similar. Multiple loads with single digits in both.

You can think ES doesn't matter that's fine too, but i disagree. To each his own, as long as it shoots right…but I think both ES speaks to your overall consistency and attention to detail in your hand loading…as does SD, admittedly. If you're doing it right, but numbers should be low.
 
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I've never had a single digit ES load without an SD that wasn't pretty similar. Multiple loads with single digits in both.

You can think ES doesn't matter that's fine, but it does…but I think both ES speaks to your overall consistency and attention to detail in your hand loading…as does SD, admittedly. If you're doing it right, but numbers should be low.

Generally, that should be true, but with ES, you could get into a case of chasing your tail. The tails of the distribution are always what we in statistics call long. This means that they extend way off into eternity in both directions. Just by random chance you could get a speed somewhere in this "eternity" area which would lead you to think that this is a poor load when in reality it was just a fluke of random chance. The SD will tell you a different story (assuming a reasonable sample size) in this case. If you had shot say a 30-50 shot string and calculated your SD in this case that SD may be perfectly acceptable but that one shot will put your ES out of acceptance.

In that scenario I just described, the ES and SD are telling you different stories and I would argue that the SD is telling a story closer to the truth.

All of this is also assuming that the distribution of shots is unimodal or single humped. If you have two (or more) modes, two (or more) humps, then that is a different story altogether. If your reloading process is under control you should have a unimodal distribution of speeds. If not, then something happened in your reloading process that you'll have to figure out.

I'm just trying to help you not spend time you shouldn't by getting sidetracked by one random fluke should that happen. If the SD and ES are telling you the same story, then great. If not, I would trust the SD more and I would inspect my distribution to make sure that there wasn't some other influence on my reloading process (so ES isn't entirely useless, it's just nowhere near as useful as the SD).
 
Show us. If you had a sufficient population to begin with you would only need to pull one sample. So, you can show us with mathematical certainty, lol. So, show us.
Learn Something New!

There's the water. Drink it or don't, I really don't care. If you don't know the difference between descriptive and inferential statistics you have more than a little bit of catching up to do.

The 5x ES standard is a shorthand way of telling people they don't have enough data to know if the distribution is normal or not.
 
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