# Probability - 1 MOA Precision



## goatchze (Aug 1, 2006)

So the saying (and truth) goes, when grouping your rifle, the group will never be smaller than it is after the 2nd shot.

So my question is, if you are shooting a "1 MOA" gun, what are the odds that the second shot falls within 1" of the first one at 100 yards? A 99% chance for a "1 MOA gun"? 85%? Less?

Or another way to look at it, out of 100 shots in ideal, constant conditions, how many shots would fall within a 1" circle, drawn around the center of the group, at 100 yards if shooting a "1 MOA gun"? 99 shots? 85? Less?

The point is, what percentage would you find "acceptable" to fall outside of a 1" group and still say that it is a "1 MOA gun"?

(I'm talking about measuring the center of each shot, I don't want to get into an argument on how best to measure the shots using a ruler...this is all hypothetical)

I know that there isn't really a "correct" answer since it's a matter of opinion. I'm just curious what everyone's opinions are!


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## CoastalOutfitters (Aug 20, 2004)

If you are saying the rifle consistently shoots 1 moa at 100 yds then any fliers outside that are not acceptable. It's either shooter, ammo, mechanics or weather or a combo. Are you counting a 3 or 5 shot group? more shots, more room for error and heat


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## coogerpop (Sep 3, 2009)

I would think that a 1in MOA rifle would be able to shoot a 3 shot,1 in group,using the correct ammo,from a machine rest ,at any time the weather conditions permitting.......There ,did I put enough "QUALIFIERS" in there?????....Really tho,there are a lot of conditions that have to be met rather than just the rifle going "BANG" off the shooters shoulder....And are we talking about 1 moa at 50 yds...100yds...200 yds????or longer....more and more factors come into play....3 shots,100 yards,group size around 1 in...great shooting,rifle and rifleman........


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## Ernest (May 21, 2004)

For me, a 1 MOA weapon shoots five shot groups in a 1 inch cicle at 100 yards, or 2 inches at 200 yards. 

Bigger the sample size per group - 3 shots vs. 5 vs. 7 vs. 10 - merely increases the predictive quality of the conclusions. No reason to run all the way to 100 as group size. 

But, absent a definition of 1 MOA gun, there is not enough data to answer. 

According to the Interwebzs, if a weapon has ever, at any point in its life, shot a group of more than 2 shots that are closer than 1 inch, irrespective of the distance from the shooter to the target, it shoots .5 MOA all day long. All day long, baby. If it merely discharges when the trigger is pulled, it shoots 1 MOA. If anyone in your family has ever been affiliated with the military, including the Salvation Army and the KISS Army, and they have touched your weapon, your weapon is hand built and custom tuned by Navy Seals (according to the Interwebzs).


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## Salty Dog (Jan 29, 2005)

All depends. Are we talking internet forum talk MOA or real life MOA?:rotfl:

With a witness or on my word?:rotfl:

I ain't saying anyone would stretch the truth but about 90% of the folks I talk to will swear their rifle is sub MOA yet of the folks I actually have shot with I see about 10% of the rifles that are, if that. I can't tell you how many "cover it with a dime" guns have bad days shooting 1 1/2" groups just because I showed up. It is uncanny.


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## CHARLIE (Jun 2, 2004)

Salty Dog

Ya know, that happens more times than not. But I have seen some sub MOA's not many but a few.

Charlie


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## Jungle_Jim (Nov 16, 2007)




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## CoastalOutfitters (Aug 20, 2004)

I worked at a rifle range for a bit, 

this boiled down to stupid rifle/scope combo's, poor choice of cals. , poor choice of ammo, range conditions weren't right, wind temps, etc. poor shooter performance. the weapon could do the job , but the shooter couldn't.

I have been thru the Hornady plant a few times, their test barrels are mounted on stands and shoot down a 100yd culvert. their ammo can perform , have seen it in person.


as I said before remmy rep. told me they only go for a 2" group in their entry level ammo and yet you get some guy on the bench whining because his rifle won't group sub moa at 100 yds ?

safe to say that most folks going for one holers are handloaders


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## muddyfuzzy (Jan 2, 2011)

the thing to keep in mind here is that most shooters never outshoot their rig if they have a half way decent set-up. most modern turnbolt rifles are capable of shooting sub-moa out to at least 100 yds. with the correct ammo.


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## BIG PAPPA (Apr 1, 2008)

*1"MOA RIFLE?*

Goatchze, Very interesting post/Question. Being you are asking I will Assume you are a Great Shooter. with Great Shooter said: I feel a gun that can shoot with a Great Shooter behind it should be able to consistantly perform at a 1" group(with quality ammo) of course. I have several rifles, and if i cannot shoot a 5/8 inch group (measured Your way) I don't want it. I've only gotten rid on 1 rifle in my life. It was a 338 Mag weatherby. After shooting paper and all over the place 2-3" groups, I sent it to MagnaPort in Detroit MI. when i got the gun back it shot a 3/4" consistant group. Problem was, i already HATED that gun and traded it off. Truth also was, it was me and not the gun. I've shot about every Big Bore Caliber money can buy, but the 338mag was by far the Thumpinest Gun i ever shot at paper. I mean 416rigby, 460 weatherby, 375 H&H, 300 weatherby mag, and on and on. The 338 was Horrible in the weatherby Accumark. setup?? I dunno, but the gun is gone and all my others are what i call Shooters.

Great Post by the way. Greenie commin at ya


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## Capt Scott Reeh (Jan 21, 2006)

goatchze said:


> So my question is, if you are shooting a "1 MOA" gun, what are the odds that the second shot falls within 1" of the first one at 100 yards? A 99% chance for a "1 MOA gun"? 85%? Less?
> 
> If it's a 1" MOA @ 100yds.....100% or you can't call it a 100yd 1" MOA gun.
> 
> ...


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## 27contender (Dec 22, 2008)

Many factors involved. My BEST rifle will touch the first two IF I do my job. I suspect that a mechanical rest would eliminate human error and make it near 100%. The third shot through 5 shot seem to hurt me the most. IF I let the gun cool it will hang less than one. If I just keep jamming them in there after a minute or two she opens up to an inch or more. Everyone has a one holer group. My best ever was two 5 shot groups with DIFFERENT loads and bullets. I put a mark on the target where each load would land (they shot different elevations due to different velocity) and marched it out to 100 yards. The first group was all 5 touching, the next round and first three were a clover. Number 4 (9th bullet though gun in a 18 minute period) was 4" to the left. Number 5 was about an inch to the right. I suspect the error was all mine and I suspect I have some stock work to do. BUT what drawing an "X" on a target and hitting it dead on does for you is amazing. I am not sure I am the best shot or the gun I have is special, but I THINK IT IS! And what a difference it makes to "know" where it is going when you start to squeeze.

R


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## CHARLIE (Jun 2, 2004)

Capn Reeh

Two shots consistantly in the same hole at 200 yards . Now thats some shootin. But being from the old school all my groups would be 5 shots.. Seems a few years back it went to 3 shot groups, now I hear 2 shot groups. Next thing it will be where the first shot prints. Ha 

Charlie


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## goatchze (Aug 1, 2006)

Interesting results so far!

For me, when I talk about precision, I always talk about "me + gun". After all, the two of us work as a unit. Sure, the gun may hold me back, or I may hold the gun back, but anytime I hear someone say, "this gun shoots MOA" I assume they mean "I can shoot this gun MOA". I don't think you'll ever be able to seperate the man from the gun.

Here's something to chew on for those of you who voted 100%. For _*100%*_ of shots to fall within a 1" circle (OK, 99.9999999999%), _you must shoot an average 3 shot group of about 0.25"._

That is typed correctly. Statisticly speaking if you go out and shoot 30 rounds, 10 groups of 3, if you don't average 0.25" in group size, you don't shoot MOA. That is, if your definition of MOA is 100% of all shots must fall within 1" at 100 yards.

Anyone want to change their vote?


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## Baja Dreamer (May 10, 2010)

Salty Dog said:


> I ain't saying anyone would stretch the truth but about 90% of the folks I talk to will swear their rifle is sub MOA yet of the folks I actually have shot with I see about 10% of the rifles that are, if that. I can't tell you how many "cover it with a dime" guns have bad days shooting 1 1/2" groups just because I showed up. It is uncanny.


I don't stretch the truth at all about my guns, and will let others not only see me do it, but I'll let them give the rifle(s) a whirl too.

Then there's a lever gun I own that has trouble shooting minute of paper plate at 100 yards no matter what load you try. I like watching others try that one too. 

FISH HARD!

Chris


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## CHARLIE (Jun 2, 2004)

goatchze

I just caint follow what you are trying to say. Guess I am too dumb.. I think my gun (and me)would shoot the first two shots inside an inch. That doesent mean my gun shoots .25 MOA 

Charlie


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## Ernest (May 21, 2004)

He is making a point about statistics. The sample size is the number of shots in your group. With a sample size/group of only two or three, the predictive value of those two or three shots (in predicting the accuracy of future shots) is very, very low. 

Basically, in order for anyone in their right mind to conclude, with a reasonable level of confidence, that 100 shots would be within an inch, they would have to shoot those three shots into .25 MOA. 

So, those that define a "1 MOA" weapon as all 100 shots within an inch either have very, very accurate weapons OR they fail to appreciate the predictive qualities of their data sample. 

I think a related point he is potentially making is that 3 shot groups really don't mean jack.


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## CHARLIE (Jun 2, 2004)

Thanks and I agree they dont mean "Jack". Just because my gun (and me) would shoot the first 2 inside an inch certainly doesent mean the next three (5) total would. Certainly 2 shots really mean absoloutely nothing.. 

Charlie


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## Screeminreel (Jun 2, 2004)

I voted for 100%, but I figure I am a bit more anal than most about my rifles and loads. Reason being when I work up a load for a rifle, I require that it shoot under 1" at least to 100yards and preferably to 200yds or more, from a bench on sand bags. I freely admit that some of my rifles were a bit more inclined to not participate in the exercise, but that is what makes handloading fun for me. I can throw factory into some of them, and not have them shoot under an inch at 50yds, but others will day in and day out. Heck most have never even shot factory loads. 

I work loads up for accuracy with a predetermined velocity in mind. If I get to that velocity with the accuracy I am looking for great, if not I will try something else or keep the best load. Accuracy with a load having a velocity of 2800 - 3000fps in most cases will do anything and everything I need done out to around 400yds, if I am so inclined to shoot that far. In some rifles this velocity spread is between 3000 and 3400fps, but I expect the same groups sizes none the less. These rifles are not off the shelf rifles and not meant for shooting rapid fire groups, in fact if I shoot more than 10 rounds at a setting it is due to a component change, simply to reverify the load out to 500yds. With these I do not even consider a 100yd group for anything other than checking the drop table against, as the long bullets have shown me a tendency to group better at 250 - 300yds, over the shorter ranges. 

Bottom line for me is, I know for a fact that when I reach into the safe and grab which ever rifle for the weekend hunt, that where I settle the cross hair will be where I hit. I don't have to try and remember which rifle does what, with what bullet and load, as I only use one for each at a time. If the rifle has a mil-dot scope I know that the initial zero is set for 200yds and everything else has been worked up to fall along the rest of the dots. If it has a standard duplex, the zero is at 100yds for anything off a .308 case or smaller and 200yd for anything off a '06 case. Either way the rifle and load will deliver, and the rest is on me. With so many variables in the field that can and do influence one shot from another, coupled with being excited or out of breath, I don't want to have the thought in the back of my mind, is this the shot that is going to hit high left or low right when I squeeze the trigger. All I want to be concerned with, is settling the + on the spot I want to place the bullet, and controlling my breathing as I gently squeeze the shot off. 

This all might seem a bit much, but I have been hunting now for 40 years and handloading my own rounds for over 30. I have learned a LOT through it all, and I might be a bit more demanding than some. I am however confident, that when I break the shot, I know I don't have to worry about what part of the intended target I am going hit, or if an animal runs, where it was hit.


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## goatchze (Aug 1, 2006)

Ernest said:


> He is making a point about statistics. The sample size is the number of shots in your group. With a sample size/group of only two or three, the predictive value of those two or three shots (in predicting the accuracy of future shots) is very, very low.
> 
> *Basically, in order for anyone in their right mind to conclude, with a reasonable level of confidence, that 100 shots would be within an inch, they would have to shoot those three shots into .25 MOA. *
> 
> ...


Couldn't have said it better. The real point is that to say 100% means *A LOT.* In fact, just claiming MOA means a lot more than we realize!

For example, if I said MOA was "95% of shots land in a 1" circle at 100yards", then I would need to _average_ 3 shot groups around 0.45" in diameter, instead of 0.25". In otherwords, by just letting go of that last 5%, the requirements are half as strict.

To achieve 85%, I would need to _average_ groups of around 0.55".

This is why I chose 95% as my answer to the poll. Besides, for all intents and purposes, 95% means I'm pretty dar n certain of what the gun and me will do. That's two sigma!

On a side note, the following average group sizes are required for a 95% certain MOA gun (approximately, based on the Excel model I built which uses the average of 100 groups of each size, 100,000 shots in total):

3 shots - 0.45"
5 shots - 0.48"
10 shots - 0.53"
1000 shots - 0.55"

So for all intents and purposes, if you don't average 0.5" groups, even by the 95% definition, you don't shoot MOA.

A 95% certainty MOA is a very, very strict requirement and difficult to obtain. Not impossible, but very difficult. I for one haven't achieved it yet with my rifles. If your "average" group size is 1" (as mine normally are)...it means you're really shooting closer to 2MOA.

_But it's not just the group size; it's also the number of groups._ I'll post later with some "simulated targets" to explain.


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## Ernest (May 21, 2004)

But what if I shoot 9 consecutive 5 shot groups that average .520 MOA at 200 yards? All in the same day, same weapon, same ammo, same shooter. None larger than .70 MOA. Is it a 1 MOA weapon? 

How about if I shoot 9 consecutive 5 shot groups that average .520 MOA at 200 yards on five separate occassions? Can the weapon be fairly described as 1 MOA? 

Statistics are fun. 

And, its 9 consecutive five shot groups only because I shoot five foulers at the start of each session, and my ammo boxes hold 50 rounds.


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## RJustice (May 28, 2008)

*1 MOA???*

Does this count as a 1 MOA gun. It is the first 5 shots out of her after having her bedded. Its a XR 100 in 22-250 with a Jewell trigger. I gave the target to my Dad with the rifle. That is why I had to take a picture of the picture on my phone.


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## RJustice (May 28, 2008)

It was 100 yards on a windy day.


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## Screeminreel (Jun 2, 2004)

Well this is what I strive for from my rifles....









Whether or not it meets your criteria or spreadsheet model I can't say. I can say that most if not all of my rifle will get darn close to that.

But what would this be at 500yds? I realize it is only two shots but it is pretty repeatable in good conditions. (the white spot is 2.5")


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## goatchze (Aug 1, 2006)

First off, I'm not saying that is is impossible to shoot MOA. I have little doubt that some of you (and others) can do so. By saying that I haven't managed to do it is not saying it's impossible.

But back to the numbers.

Here are 5 targets fired from the same "Gun #1". Would you be satisfied with these groups? The scale is in inches, the markers represent the center of each bullet.

Which would make you happy? Which would make you unhappy?


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## RB II (Feb 26, 2009)

Goat, in my book, only one of those targets would be acceptable, even for a hunting gun. The one that is good is the last one which groups the pattern together, the others spread out the pattern too far across the target. IME, a rifle that patterns in the same general vicinity, even if it is MOA or a little more, it is an acceptable hunting rifle/load, but when it scatters that shots to all four quadrants it is too inconsistent.


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## CHARLIE (Jun 2, 2004)

Looks like they all are less than an inch to me.

Screeminreel

How many shots are there in that target ??

Charlie


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## Screeminreel (Jun 2, 2004)

CHARLIE said:


> Looks like they all are less than an inch to me.
> 
> Screeminreel
> 
> ...


The one with the calipers is 5 shots @ 100yds. The rifle is a used Sako .243 I picked up at Carters. The ammo was the cheapest box of Winchester 100gr that I could find at Academy. Since then, I have changed the stock out with another piece of factory wood, swapped the scope and played with working up one load for it. With nothing more than that here is the work up,









The bottom two left groups were the final load using two different primers, all else the same. Both groups were 5 consecutive shots in around 2 minutes max. Since then I have relieved the barrel channel where it was making contact, swapped the scope again and the grandson used it on a hog around New Years weekend.









Still need to tweak it a bit, but I think I got a good handle on it so far.


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## CHARLIE (Jun 2, 2004)

Nice target with the calipers. I would say that one is "good enough" Cool bottom picture. The lil guy looks happy.. Speaking of the Winchester ammo the best any factory ammo ever shot in my little gun was the cheap 45 gr Winchester brick that you used to be able to buy cheap. Havent seen any in a while. Claimed 3600fps with that 45 gr varmit round. Worked on ear shots with pigs.

Charlie


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## goatchze (Aug 1, 2006)

CHARLIE said:


> Looks like they all are less than an inch to me.


Yep. All of those groups were taken at random from a "1 MOA" gun. The average of those 5 groups is around 0.5". But even a "2 MOA" would make a group just like the last one (it took 10 random samples for me to find one). But it won't do it as often, so when you averaged the group sizes from that "2 MOA" gun they would come up closer to 1".

So the point is this, be careful taking a single 3, 5, or even 10 shot group and reading too much into it. You might end up like me, getting discouraged. Or, you might come to the conclusion that your groups are really better than they are. It never hurts to sit down with a Big Chief tablet and calculate the average over, say, 10 groups, because this number will tell you *much* more about what your gun is really doing! The more groups you can average, the better it will get.

For example, with Screeminreel's target, if we were shooting the same round everytime, averaging each of those groups would tell us a lot about how we're shooting. Taking each individual group unfortunately doesn't. Of course, the downside is that you have to do a lot more shooting!

Anyway, this is what I've learned from my own struggles working up loads.

And just for fun, here is 1,000 shots from a 95% certain "1 MOA" gun. Remember that the "average" three shot group size for these shots is a mere 0.5".


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