Help: Need Statistical Geniuses - Rifle Precision

[dross]

I could throw it into Minitab and spit out the difference in standard deviation for a 1moa rifle versus a 2moa rifle, but what you really have is an integrated bell curve of normal distribution, centered on the exact center of the bull. Which means that if you drew a line of 1" length evenly bisecting the bull, at any angle you wish to draw, you would the heaviest distribution of holes in the exact center, tailing out to less frequent strikes at the ends of the 1 inch line. If you are being pedantic, you would say that the process of you would ask "how many of 1 million shots are going to have the outside edge of the hole outside a 1" circle, centered on the bull. A "6 sigma" shooting process, with proper limits ( and for the purposes of this exercise, exactly centered) would have less than 4 shots outside that circle. So, to answer your question, I would want to know how you wish to define accuracy. A rifle that keeps a group of 10 shots at 100 yrd distance is 1moa, even if every shot touches, but stays within the circle. A rifle that (assuming your perfect conditions) puts 9 shots of a 10 shot string through the same hole, but strings the 10th shot outside the circle is not a 1moa rifle, but the standard deviation of the shots in the second case will be smaller, and you could make the case that it is more "accurate". So, if you define what accuracy means to you in this case, I could mock up a set of sample data and run it through the computer and give you the results!

This sounds correct to me, is this based on what you know to be true? Is it a standard bell curve from the center?

If it isn't too much trouble I think a chart showing the actual differences between a 1/2 MOA, and 1MOA through 4MOA would be very, very interesting.

BTW, I understand chasing accuracy as a hobby. I like owning rifles I know are very accurate. Honestly, though, I'm a little weird about it. I have a 2MOA rifle that I really like and I can't get it out of my head that it's inaccurate. I have to keep reminding myself that I'm being silly and that it's plenty accurate and I love everything about it.

I just got to thinking that a 3MOA rifle is really a 1MOA rifle most of the time. Also, I'm a bigger factor in the accuracy equation than the difference between a 1MOA rifle and a 3MOA rifle, unless I'm at the range on a bench on a calm day with a nice rest. In all other situations, the biggest factor will be the execution of my skills or the lack thereof.

 

[Double T]

Accuracy and precision are NOT the same thing. It's been about 10 years since I've done any stats and prob, but...

Precision is how close together your "group" is. A 100% precise weapon would put all rounds in the same hole if fired under the same conditions.

Accuracy is the average distance of all shots in relation to the center point of a target.

You can be highly precise, and inaccurate.
You can be highly accurate and lowly precise.

 

[dross]

Accuracy and precision are NOT the same thing. It's been about 10 years since I've done any stats and prob, but...

Precision is how close together your "group" is. A 100% precise weapon would put all rounds in the same hole if fired under the same conditions.

Accuracy is the average distance of all shots in relation to the center point of a target.

You can be highly precise, and inaccurate.
You can be highly accurate and lowly precise.

This is true, but "accuracy" is often substituted for "precision."

If a rifle has precision, accuracy is only a sight adjustment away. If the rifle does not have precision, however, it cannot have accuracy as it relates to rifles, only as it relates to statistics.

How does this reminder enlighten the discussion?

 

[rockhopper46038]

Well, without real data I cannot 100% guarantee that your theoretical rifle will deliver a shot pattern that is a normal distribution, but non-normal distributions are very rare in nature, and generally have a known term in the equation that describes them which addresses why they are not normal. Since we've stipulated that we are not considering variables like barrel temperature, etc, then I would say that yes, the distribution of shots is almost certainly normal, so long as enough shots are taken to provide an adequate sample size. So, if the distribution is normal, and not shifted (like you would expect with a stiff, steady crosswind) then if you drew a circle 1/3 of an inch in diameter, centered on the bull, you would expect roughly 68% of the shots to fall in that circle. About 95% of all shots would fall in a circle with diameter 2/3rds of an inch, and 99.8% of shots would fall within the full 1inch bull.

Standard deviation - Wikipedia, the free encyclopedia

There are some suppositions in this, but I think it covers what you are asking. Where it gets tricky is when you want compare a rifle that groups really well, but throws a flyer (which we all know is almost certainly not the gun) vs a rifle that opens up the group some, but is always predictable shot after shot.

 

[Double T]

True they are often referred to as interchangeable, they are similar but not the same.

You need to eliminate or have reproducible external factors to determine precision...which also needs a large test run to get a very precise mean of your groups...and have a set way to eliminate operator error (flinching...jerking...etc)

I'm sure you know all this though.

Accuracy is dependent on the shooters understanding of the projectiles flight path, and possible external forces effects on it. You can sight I'n a gun on a calm day...and go to shoot on a day with a very steady breeze...and well...you may not have thebest results.

In order to truly know, you need tocontrol all external variables.

 

[kludge]

Dross, I'm amused a the premise of taking the largest variable out of the equation, regardless, I'll play along... Another interesting read:

Secrets of the Houston Warehouse

In the spirit of this thread, I just ran a ballistic caculator and a spreadsheet to shed light on why I think the chronograph is the most important reloading tool when it comes to long range precision.

I'll use the standard ".308 Match" ammo as the reference. Group size at long range is all about the "Extreme Spread" (ES) of the load, the shooter, and the rifle. The groups can be no smaller than the ES. The muzzle velocity (MV) is but one factor in ES in which to key - the one where a chronograph is useful.

.308 Match ammo runs ~2650fps with a 168gr SMK. I don't know how to make charts come out on a web forum, so, just the results...

With and ES(MV) of 200 fps (I know, how can ammo be that bad, right? - bear with me...)

Assuming a perfect rifle, no wind and a shooter on his game, the group size will be (all in the vertical, presumably)...

0.42" @ 100 yd.
4.16" @ 300
20.71" @ 600
78.23" @ 1000

Notice that 1MOA @ 100 yards does not mean 1MOA anywhere else, and this is just the variance of the ammo. And as long as the rifle doesn't care (a really stiff barrel), you can shoot 1/2 MOA @ 100 yards with really crappy ammo. But only at 100 yards. Case in point -- I can shoot 7.62 NATO ammo into to 1" groups at 100 yards out of my 110FP. I figure I'm at least half of the other 0.68"

Now, with an ES(MV) of 50fps (just OK, not great -- you could expect most factory hunting ammo to do that) things get to looking much, much better.

0.10" @ 100yd
1.03" @ 300yd
5.16" @ 600yd
19.53" @ 1000yd

The best 1000 yard shooters are 3x better than that. How good are they, right? Notice again that 0.1" @ 100 yards still doesn't mean 1" @ 1000 yards. Not even close.

Just a note though that an inch at 300 yards can be done with a mediocre load. Not many shooters can go out and put 10 shots in an inch at 300 yards. It's hard to blame the ammo though at typical hunting distances.

OK, so what about the wind? I also factored in a 10mph cross wind into my spreadsheet...

At 300 yards a 10 mph wind can open up the group to 8.05" (by adding 7.99" or horizontal variance). At 1000 yards it can blow the 168 SMK up to 110" off target.

How good are those shooters now? (Honestly I can't say whether they attempt to run matches with 10mph wind.)

 

[Litlratt]

For arguments sake, consider barrel vibration and the point at which the bullet leaves the barrel.

 

[Yeah]

The linear distance from POA will be normally distributed.

I used to shoot with some obsessive BR competitors and we measured it with dozens of barrels, always getting high p values. This includes ammo variation and a normal environment. Gusty wind can push things around, as a shooters natural tendency is to try to time it with bimodality the result. Still a minor transform away from normality from everything I recall. If I could remember they are I'd put up some Originlab files.

I don't know that this applies to some theoretical system where variables external to the rifle are removed, as I am not an academic.

 

[dross]

Here's what it comes down to, as best as I can figure.

If a rifle shoots 1 inch at 100 yards and another rifle shoots 2 inches at 100 yards, out of 100 shots, the one inch rifle will hit within one inch approximately 97.5% of the time.

The two inche rifle will shoot inside one inch 75% of the time.

In practical field terms, there is very little difference between a 1MOA rifle and a 2MOA rifle.

To reintroduce the shooter back into the equation, the shooter is a much, much bigger variable than the rifle. Which of course we knew, and several people mentioned.

 

[forthehousew]

Good conclusion and I have to say a very interesting topic with impressive technical comments from the ingo group, glad to be a part of this forum.

 

[MarkRW]

The linear distance from POA will be normally distributed.

I used to shoot with some obsessive BR competitors and we measured it with dozens of barrels, always getting high p values. This includes ammo variation and a normal environment. Gusty wind can push things around, as a shooters natural tendency is to try to time it with bimodality the result. Still a minor transform away from normality from everything I recall. If I could remember they are I'd put up some Originlab files.

I don't know that this applies to some theoretical system where variables external to the rifle are removed, as I am not an academic.

The idea is precisely contained in "The Central Limit Theorem."

What this means (you can Wiki it) is:
If you have a system with several variables, each with its own statistical distribution, the variation in output will approach a Normal Curve (Bell Curve). So, everything is perfect = you hit center. Then you have wind gust, or variation in muzzle velocity, or variation in drag coefficient of bullet, or barrel flex at different position as bullet exits barrel, or you jerk the trigger, or your heart beats or doesn't... all these variables will "smear" out when they are of similar size, but one overidding "mistake" will throw you way off in a given direction (outlier/flyer).

So, in the case of shooting a gun, the distance from center will not be uniformly distributed but "normally = bell shape" distributed. You won't fill in the circle uniformly - because - you are not randomly shooting at the target. You are shooting at the center, and the variations you get are around the center, and being close (some errors go one way, some go the other) is much more likely than being far away (all errors go the same way).

Imagine you have a box with a circle in the middle, and you throw a coin in. The coin will land randomly in the box because you no longer have any control over it and it bounces around in there until it stops. This is uniformly distributed and random. The bullet at the target is bell shaped and random.

PLUS - read what DROSS wrote 2 posts up.