Groups, Accuracy, and Statistics

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HowieG

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I constantly read things on this forum pertaining to the accuracy of rifles, whatever your definition of accuracy is. Most are referring to their rifles as being accurate because they can shoot an X size group. Rarely in such posts is the X size group actually defined. Is the X size group 1 shot, or 20? At what range? Is this group size consistent over a number of groups shot, or was it one group?

The overriding idea of these posts seems to be that the rifle discussed is better than the mythical ONE MOA rifle. I think we all like to believe that all of our pet rifles ARE actually ONE MOA rifles, or better, and that we, as shooters, are actually good enough to make use of such a fine instrument.

I am going to jump right out and say that I probably do have a couple of rifles that are ONE MOA rifles. Can I prove that statistically? Maybe, or maybe not. I will also say right out front that I am not always capable of wielding them in a manner they deserve. I have good days and bad. I may have had too much coffee. I may be pissed off at the bug flying in my ear. I may just be jumpy. I am pretty sure that my rifles would outperform me if they were strapped down to some kind of machine rest.

Anyway, enough of the prelims. I would like to read your thoughts on the subject. Now a warning. Science Spoken Here. Attached is a .pdf entitled GROUP SIZE STATISTICAL ANALYSIS, courtesy of Chris Long at this website: Techshooters Shooting Pages (the-long-family.com)
 
After narrowing things down a bit, I utilize 10 shot strings for evaluation. Doing so seems to help me identify loads with good consistency. I use three or five shot strings for rough evaluations only.
 
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My immediate takeaways from the .pdf attached above are that 1) Rifles that actually shoot small groups have good repeatability, not accuracy. Accuracy is actually the capability of the rifle/shooter to put a group on target.

2) Based on the author's own conclusions in doing his analysis, he proofs his loads with 4 groups of five shots.

3) Also based on his statistics, he has created a Group Size Correction factor to help interpolate groups of varying shot sizes. I think that is handy.
 
I personally am a fan of 5-shot groups. Statistically 7-10 shots probably results in better math but from the shooters perspective 5-shots is better due to shooter focus and consistency. It also divides nicely into standard boxes of ammo for those with OCD :p. I also do not judge a rifle on one group but several groups, three to five, 5-shot groups assuming they are relatively similar in performance is usually sufficient to give me a good idea of what that combination of rifle and ammo is capable of. I try my best to not over analyze it too.

For this reason I love the "Range Buddy" app on my phone. I can snap a picture of my target use the app to quickly and easily measure my group size and position relative to point of aim. It also has the ability to log these pictures/data for each gun I like to track. I can then later look back at this data as desired.

index.php

Example of what Range Buddy does for me.
 
If I went out and shot twenty groups of one shot each, I could get on here and state that my rifle shoots 1/4 MOA based on 20 groups at 100 yards. I don't think that would be viable statistically though.
 
mcb said:
I personally am a fan of 5-shot groups. Statistically 7-10 shots probably results in better math but from the shooters perspective 5-shots is better due to shooter focus and consistency. It also divides nicely into standard boxes of ammo for those with OCD :p. I also do not judge a rifle on one group but several groups, three to five, 5-shot groups assuming they are relatively similar in performance is usually sufficient to give me a good idea of what that combination of rifle and ammo is capable of. I try my best to not over analyze it too.

For this reason I love the "Range Buddy" app on my phone. I can snap a picture of my target use the app to quickly and easily measure my group size and position relative to point of aim. It also has the ability to log these pictures/data for each gun I like to track. I can then later look back at this data as desired.

How about that? I am going to have to get that on my phone. Never heard of it before.
Click to expand...
 
BBarn said:
After narrowing things down a bit, I utilize 10 shot strings for evaluation. Doing so seems to help me identify loads with good consistency. I use three or five shot strings for rough evaluations only.
Click to expand...

I agree. As many shots a possible. The proviso for me though is I just can't sit there and fire off 10 rounds of 300 WSM and do myself any good. Also, it can be tough to do 10 or 20 in a row and not have a oops moment on the trigger.
 
I just found out that Range Buddy takes Android 7.0. I guess I need to upgrade my phone again.
 
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I shoot 5 shot groups. Just what I do.

Best group ever doesn't dictate what I call the rig.

Its what it does repeatably.

Why I like synth stocks.

Emailed Pendelton about a set for Ruger #1.

Blasphemous some would say LOL
 
As mentioned by another above, shooter fatigue is real and comes on way faster after age 50
Eyes, mental, body.........sometimes though you can get beat into a decent groove ;)

I also don't run to the range to shoot for an hr. Will spend however long it takes to do what I need.
Eat before I go, relax and get heart rate down..........and go for groups. My club proly 40 min drive one way........
helps mellow me out actually.
 
Accuracy is placing all shots in or very near the bullseye.

Precision is placing all shots in a small group.

A firearm may shoot 4" high and 6" left, but 10 shots are 1 ragged hole. That rifle is NOT accurate. Depending on how adjustable the sights are, that accuracy may be difficult correct.

A firearm may shoot 10 shots, all within the 7 ring. That rifle is accurate, but not precise.

Working up loads, I shoot 5 round ladder at 100 yards. Promising load, I will shoot 10 round group at 100 yards. Often, the load .2 gr above and or below. The best noted and shoots 10 rounds at 200 yards.
Have had loads shoot 1" or less at 100, be 3" or more at 200. But, some loads shoot 1 1/2" at 100 and shoots 1 1/2" at 200.

The chase never ends. Find what you believe is the ultimate and a new bullet is released, a new powder, powder lot changes, different primer, different brass, etc.
 
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Seedy Character said:
Accuracy is placing all shots in or very near the bullseye.

Precision is placing all shots in a small group.

A firearm may shoot 4" high and 6" left, but 10 shots are 1 ragged hole. That rifle is NOT accurate. Depending on how adjustable the sights are, that accuracy may be difficult correct.

A firearm may shoot 10 shots, all within the 7 ring. That rifle is accurate, but not precise.
Click to expand...

A precise rifle is only only a sight adjustment (easy in nearly all cases) away from also being an accurate rifle too. A rifle that is not precise can never reliably be an accurate rifle especially as group size approaches one.
 
mcb said:
A precise rifle is only only a sight adjustment (easy in nearly all cases) away from also being an accurate rifle too. A rifle that is not precise can never reliably be an accurate rifle especially as group size approaches one.
Click to expand...


Accuracy has been improved greatly, at times, with ONLY minor changes. Tightening or loosening a stock screw. Glass bedding. Free floating. Ammo change.

I had a Ruger Vaquero that shot 3" right and 4" high. Fixed sights. Shot precise groups, but not accurate. ONLY a sight adjustment is not easy. Front sight is attached, Rear sight is groove milled into top strap.
 
Hookeye said:
I shoot 5 shot groups. Just what I do.

Best group ever doesn't dictate what I call the rig.

Its what it does repeatably.

Why I like synth stocks.

Emailed Pendelton about a set for Ruger #1.

Blasphemous some would say LOL
Click to expand...

Yeah, absolutely blasphemous. And probably wouldn't do any good anyway.
 
Hookeye said:
As mentioned by another above, shooter fatigue is real and comes on way faster after age 50
Eyes, mental, body.........sometimes though you can get beat into a decent groove ;)

I also don't run to the range to shoot for an hr. Will spend however long it takes to do what I need.
Eat before I go, relax and get heart rate down..........and go for groups. My club proly 40 min drive one way........
helps mellow me out actually.
Click to expand...

I am as good once as I ever was. I just haven't figured out whether that means one group or one shot.
 
mcb said:
A precise rifle is only only a sight adjustment (easy in nearly all cases) away from also being an accurate rifle too. A rifle that is not precise can never reliably be an accurate rifle especially as group size approaches one.
Click to expand...

Precise, of course, varies with the gun. A precise 1894 30-30 with buckhorns isn't the same as a precise varmint rifle with a telescopic sight. If your lever shoots 3 inch groups at 100 yards and clusters each group nicely centered on your desired POI, I would say it's accurate for that rifle. Actually a 1.5" radius from the desired POI isn't bad at all. Many rifles would do better on the bench, but how many would actually do that off hand in the field?
 
I think an excellent gauge of precision and accuracy is the Cooper One Shot. If you don't have a Cooper, that's a contest they run up in Montana where you get one shot at a 1/4" dot at 150 yards. Any Cooper rifle is eligible to compete. Try that one out on the next breezy day at the range.
 
Seedy Character said:
Accuracy has been improved greatly, at times, with ONLY minor changes. Tightening or loosening a stock screw. Glass bedding. Free floating. Ammo change.

I had a Ruger Vaquero that shot 3" right and 4" high. Fixed sights. Shot precise groups, but not accurate. ONLY a sight adjustment is not easy. Front sight is attached, Rear sight is groove milled into top strap.
Click to expand...

I was speaking in generalities. It is typical easier to adjust sights to make a precise firearm also accurate on an overwhelming number of firearms, especially rifles. It is typical harder and more time consuming to do the work required to tighten groups on a imprecise firearm. There are exception to both.

And if the gun is precise but not accurate you can still be accurate with it.

My woods revolvers is often a S&W model 10, it shoots slightly left, it has fixed sights. I know it shoots this way and use a sight picture to compensate for this and put the bullets were I needed them.

I got to my first 3-gun match after a cross country move where my scope had been unmounted and remounted the QD mounts did not return to zero as expected and I did not get a chance to check zero. The rifle was shooting ~8-inches to the right at about 80 yards. I figure that out on the clock on the first stage (that poor tree beside that first target) shot the rest of the match holding left and still managed a top five finish since the precision was there and I knew (the hard way) how far off the sights were and compensated for it. Had the rifle suddenly started shooting 4 MOA even if that group was centered on my point of aim I would not have done as well as I did. It also would have been much harder, in the middle of the stage, to try things to tighten up the groups than it was to compensate for sights that were off.

In my experience precision almost always take more effort/money than accuracy.

index.php
 
Depends on the application. My hunting guns the most important shot is the 1st one. Light guns with pencil barrels heat up fast, after 2-3 shots they start opening up. For my hunting rifle I want cold bore 1 shot accuracy. Very seldom do you get a second shot or need one.

For bench guns, like said repeatability over a broad range, and tightest grouping possible. I shrive for sub moa on the vertical axis, when working up loads. Knowing the wind can greatly effect bullet flight. I also know the person behind the trigger has a greater input than most realize.
 
I shoot 5 and 10 shot groups. Tons of load development done with 5 shots but all verifications are done with 10. I probably could do 2 or 3 shot work ups but I like to shoot and a dialed load at 1 or 300 gets pretty boring fast.
 
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