I've been reading a 1936 book on woodchuck hunting. The author warns against using 5-shot groups for handload development. He says they will give you a misleading idea of the load's accuracy. He recommends averaging two 10-shot groups and comments that a 1.5 inch average is good.

The 3-shot group seems to be the common standard now. There are sometimes comments about how much accuracy is improved with modern barrels and components.

What would some of these modern 0.5 inch 3-shot group rifles do if the shooter averaged two 10-shot groups?

The comment on load testing got me to remembering an old article that had an approximate conversion factor for estimating group size for more or fewer shots. For example, a 3-shot group of 0.75 inches would be multiplied by 2.3 (I made up that number) for the expected size of a 10-shot group.

Anyone remember that article?

Thanks,

Bruce

Bruce: Must be Charles Landis's book.I have a vague memory of the article;there may have been more than one.I happen to agree that 5-10 shot groups do tell you more than 3 shot groups.

That said,I don't believe in shooting 10 shot groups everytime you go to the range.Group shooting is interesting but I prefer to practice MY shooting from field positions instead.

But when I'm learning my way around a rifle,or it's new,or the load is new,I've found that shooting 8-10 shots will disclose accuracy issues more reliably than 3 shot groups;and they will frequently disclose mechanical issues with the rifle itself.

After you do it a couple times,though,you can resort back to the 3 shot routine for zero checks,etc.

Within the last year,I was working with a rifle that held 3 shot groups at about 3.5" at 300 yards;but two shots were always close,and the third was "low",which always opened the group.

I did not think anything of it until I took the rifle to 500 yards and shot a 5 shot group and two shots were about 12" below the other 3(?!)The rifle was double grouping;but it is so accurate that 3 shot groups looked "OK" at 300 and under.I traced the problem to a loose dovetail scope mount.

I have two thoughts on the question: (1) a 3 shot group is too small. You can easily have two shots touch, and a third off, and draw an incorrect conclusion that the load is inaccurate. You can also have a 3 shot group in one hole, and draw the wrong conclusion that the load is more accurate than it is. I think of throwing 500 darts: somewhere along the way 3 consecutive tosses will touch, and another 3 will hit wildly apart. Neither is a true measure of your accuracy. Statistically, three shots is really too small to rely on. I've seen too many shooters chase something that isn't there with small groups. (2) for hunting rifles, 3 shots is really all you need to be concerned about under most circumstances. IF, and only IF the flyers always come from something beyond the third shot, then I wouldn't worry very much. If you put four shots in one hole, and the fifth is wild, for example, that would be OK for me in a hunting rifle.

For hunting rifles, I want to shoot multiple groups at the same target. It really doesn't matter too much to me if the groups are three or five shots, as long as I end up with multiple groups of a minimum of 10 to 15 shots. Really, when you think about it, one of the best measures of a hunting gun's potential might be to shoot ten 1-shot groups, from hunting positions, on entirely different days, at the same target. Where the bullet goes from a cold barrel, the first time, is very important.

I suppose a 3 shot group is very adequate for changing the scope when zeroing a rifle, but it is lacking in giving a clear idea of load consistency.

The bottom line is many 5 or 10 shot groups will have flyers, while some good loads will not. Until you actually shoot the groups you can't have a clue. I would rather have a good load without flyers than an exceptional load with flyers.

If I can get a cold bore shot (fouled OR unfouled; but I don't demand both fouled AND unfouled) to always land at the same exact spot I don't really care what happens after that.

I've seen too many lucky 3 shot groups to have much faith in them. A rifle that will shoot good 5 shot groups is consistent.

I'll bet if you had the author flip through a 2008 Midway catalog he'd re-think his stance on ten shot groups.

Travis

While that article makes a point on a rifle that may be used for multiple shots I find that for some rifles whats most important is where the first shot goes!

That means, in a way, a one shot group!

A rifle that is stable and stays sighted in is most important for many uses.

Not every rifle has such demands. A target rifle might have its impact tested at every match. Thats what we do.

For instance I have a 40X used for free rifle matches. Thats a three position 120 shot match. What matters in that match is every shot. You might say a 120 shot group! Now there is time to clean the bore after each 40 shot string but I have shot the entire match without cleaning.

The details of the demand on the rifle set the testing parameters.

I do both.

I start with 3 shot groups across a broad range. The gun isn't going to shoot any tighter with 5 shots than 3, so I can reject a lot of options with less components with 3 shot groups. Once I've got something that looks promising I go back and reshoot with 5 shots, sometimes more, with more closely spaced increments of powder. If it's something I want to shoot really well, then I'll pick the best load from the 5 (or more) shot groups and vary seating depth to see if that improves accuracy even further.

A friend of mine does something else. He shoots one shot groups. He loads across a broad range of charge weights, 0.2 grain increments, and fires 1 shot per increment tracking where the bullet hits paper. He's looking for areas where the load is stable, where successive shots hit the paper in the same area, staying away from loads that "move" increment to increment. It seems a little funny to me but it works, he's gotten loads to shoot sub inch at 300 yards within 20-25 shots this way, but generally only with trued actions / aftermarket barrels / custom chambers, not quirk-collection factory rifles.

Whatever works for you. Just make sure you compare apples to apples so the results mean something to you.

Tom

I would probably agree that 3 shot groups completely alone do not tell a complete story. But 3 shot groups shot consistently day after day would, for my purposes, tell the complete story of that load and that rifle if it were a hunting rifle. If it was a benchrest or target rifle or even a varmint rifle it would be an entirely different story. I have rarely if ever taken more than 3 shots at any game other than birds during one small period of time. ALL rifles are purpose built and you first have to define the purpose before you can go about measuring the accuracy. That is of course only MY opinion.

That's right. If you're shooting a hard-kicking big game rifle, 5 shot groups are not going to be necessary or desirable. For a varmint rifle, 5 shots is probably a minimum. For a sniper rifle, ?

I've seen way too many rifles shoot a 3/4" three shot group, and then a 4" three shot group.

A load I hunted last year was tested with two shot groups, as it was pretty hot that day. I'd already ran a few over the chronograph on a previous range trip where I was looking for pressure and velocity. When I got to my "range", I set up a paper target at 100yds, another at 250, and a gong at 425. My JBM printout told me that I needed to be 2.5" high at 100 to be zeroed at 250. As the rifle was already pretty close, I shot two touching shots that were right at 2.5" high at 100. After I let it cool down a few minutes, I shot two at 250, with one landing on either side of the 1" bull. After a few more minutes, I clicked out to 425 per my printout and fired two more. They landed right on point of aim, about 2.5" apart. Done deal and I went hunting. I likely wouldn't do that with a varmint gun, but it worked just fine to get me going with this light barreled sporter.

+1, and well stated!

I've been fooled by 3-shot groups, but not by 10-shot groups.

It would make more sense to shoot 10 two-shot groups and then calculate the average.

The problem with the average of two 10-shot groups is that you are really just using four out of 20 shots.

By using multiple groups of fewer shots, you get a better statistical (numerical) picture. On the other hand, viewing a couple of ten shot groups on paper would give a better "real" picture.

I had a very wise statistics prof who told his students to always make a graph along with calculating the numerical statistics. You can think of a group on paper as a kind of graph. Both the numbers and the picture are useful in understanding what is happening.

Paul

I love the statistical mind.

"Well, okay, it's accurate in practice, but is it accurate in theory?"

Read an article some years ago where the author contended that a 7 shot group is the minimum needed to be statistically significant. I forget what confidence level he was going for, IIRC it was 95%.

Am pretty sure the article was in an old "Handloader" - maybe one of you guys that hasn't sold or tossed out your collection could find it?

I think one of the Speer manuals (#13?) may have had a similar statement about a seven shot group.

FWIW, once a few three shot groups have seemed to indicate a possible accurate load, I'll shoot a ten shot group made up of 2 and 3 shot groups all on top of each other. It doesn't make for the pretty bragging groups posted on the internet but it definitely tells you if the combination of you and your rifle is capable of laying'em in the same place shot after shot.

That could very well be it. I'm good at remembering that I remember reading something but not so good at remembering where.

There are a lot more factors then just the technical that play into how many you shoot to 'test'.

To start off there is purpose as others have stated. A big game rifle the 1st cold barrel shot it the one that counts, and sometimes the 2nd, and almost never the 3rd. The Ol' hunter saying, "0ne shot, dead deer; two shots, maybe deer; three shots, no deer." So for a big game rifle I see no problem with three shot groups as long as you can do them from field positions.

Varmint and target rifles have different demands on them and should be developed and treated as such.

Now the real factor is for any group you have to know what you are measuring. Are you measuring the rifle / load combo or the shooters ability. I have shot a fair number of sub one inch groups in my life with five shoots, but never been able to do it with ten shoots. This is not the rifle or loads fault but mine as a shooter. I have my rifles for hunting and fun (plinking) and I am not a target shooter.

To give a real world example I have a Marlin 1895GS 45-70 lever action. Now no lever action is 'easy' to test from the bench. If I start out try to test new 'hunting' loads the first few targets are all over the place regardless. Now if I warm up shooting with some mild plinking loads and get myself settled in with the rifle first, then those hunting loads targets start to mean something.

Remember the shooter is a 'BIG' part of the test here. Now if you have heavy recoiling rifle, how well will you be shooting on shot number 10 to 12 lets say.

The bottom line is that it all depends. Not that what you read was wrong, but rather that it just is not an absolute in all cases.

This is the long way of saying what is important is .... Can you hit what you want when you want with the rifle / load combo ???

If the answer is yes you are fine. If the answer is no then you need to work on it.

Let us stay focused on the purpose and use only the details that get us to where we want to be.

What's important to keep in mind in these discussions is the total number of shots, as well as how many per each group.

If you're talking about a single target, then more shots obviously give a better picture. That may be the context of the "seven shot theory", I don't know.

The question of how to best use a given number of shots, as in two 10s vs. 10 twos, is somewhat different.

Paul

The book I'm reading is "The Woodchuck Hunter" by Paul C. Estey.

His recommendation of two 10-shot groups was specifically aimed at load development for a varmint rifle, not zero checking, shooting practice, or high recoil rifles. Make 20 loads of each combination, fire 2 10-shot groups, then average them.

The trouble I see with ten 2-shot groups on separate targets is that the two holes may be close but shifting. The pairs move in relation to the aiming point but are still close together.

I have a problem with people who shoot a <1 inch group 6 inches from point of aim, then brag about their accurate rifle. I think it is a consistent or precise rifle, not an accurate one, until they can hit the aiming point.

Bruce

Three shot groups will give one a general idea of how well his rifle performs. If one wants some serious statistical evidence, then series of 20 shot groups would offer about the most economic and best sample size if one wants to quantify their dispersion around some point in space. T values, used to calculate confidence intervals in our statistics tables, decline very slowly once one exceeds a sample size of 20 or 21.

BCP: Good point that might be elaborated slightly. Accuracy relates to ones ability to hit a desired point. A rifle/shooter putting a 3" group around the bull is more accurate than a rifle/shooter who can do 1/4 inch groups 6 inches from the bull. The second shooter, however, is much more prcise than the first. If the second shooter can get his sights adjusted properly, then he will dominate in both (precision/accuracy) categories.

If you're an active shooter, you're gonna shoot them all.....one shot to test cold barrel POI;3 shots at all ranges to check zero;10 shots to test load consistency,etc etc. Is the accumulated knowledge from all kinds of shooting that gives you faith and confidence in your rifle,scope,load,etc

I personally want a precise rifle, I can always adjust the scope and get an accurate rifle.

It mostly depends on your mindset in such matters..Missing a woodchuck or Rockchuck to me is not very stressing...

I mostly use 3 shot groups for working up loads then when I get a 1/2 inch group (varmint rifle) I will fire some 5 shot groups and even a 10 shot at some point if I get the notions which I may or may not..I can't recall a rifle that shot 1/2 inch for 3 shots every going heywire on a 5 shot group and 99% of them shot within an inch or inch and a half with 10 shots..

I have shot several 10 shot groupd with my 6x45 5 pound walk about varminter and it shoots one hole every time and center to center is alway right at .300 and 3 shot groups are just a tad smaller at .270 average of 5 different 3 shot groups..It is my most accurate rifle in my life time..It is a miniture African big bore in design..kinda cute...

Don't know about the article in question, but here's a link to a pretty good discussion on 3 vs. 5 shot groups:

3 vs. 5 shot groups.

For a while, I used to stack two three and one four shot group on top of each other. It does seem to visually provide a much better feel for what a rifle is doing than just looking at the same groups separately.

John

When my DMPS put ten rounds into .85" at 100, I knew it was a shooter... when it did it again, I was like... yeah baby!

Then I sold the sucker. Sad ending.

Not surprising. Expected no less

I start with three shot groups. If they do will, then I retest with five rounds groups. I will test the five round group a total of two times.
This works for me.

Jim - There may have been an article that included the confidence level for the seven-shot group, but I did find what I referenced earlier. See Speer #13, p. 81, right column.

Excerpt:
"A single five-shot group is seldom adequate to give you an accurate picture of the quality of your ammunition. ... For best statistical confidence, five groups of five shots each is considered minimum. However, the cost of components mounts up quickly. A statistical analysis performed by the CCI-Speer Quality Assurance Section showed that a seven-shot group gave the highest degree of confidence with the fewest shots."

I think the reason I remembered the source for that quotation is that the Speer #13 was my first reloading manual, and the only reloading manual that I owned for a few years.

I aim for 0.5 inch three shot groups in all my rifles. Don't have one that doesn't.
What's important to me is that the gun consistently shoots 0.5 inch three shot groups and most importantly that first shot from a cold barrel is on the mark.

I check my rifles before every hunt at the range, I've been know to pick up an old favorite fire 1 or 2 shots, if it's 2 inches high and dead in line at a 100 yards; I'm just as likely to put it away, confident that if I miss it ain't the gun.

How about this? It tests POI, accuracy, and shooter. When I made a one click left adjustment (third row from top, third dot from left) the POI became perfect and they really started falling in there.

I shoot 5 "one shot" groups!

Dan

I like the way Ranch Dog does it on his levergun Postal Match. Fire 5 shots at one target. The score is determined by the one hole that is farthest from center. The closer to center, the better the score. Accuracy, precision, and shooter ability all rolled into one score. bxroads target shows the same things.

Having said that, I measure my deer rifle's ability with three shot groups.

-

3x3 shot groups that I call the shot as being good. If they are consistently around an inch or better I save them. Next time at the range I try the same load, again three or four 3 shot groups. If after I have 10 to 15 groups and they are mostly good with nothing strange going on I call it good to go and start shooting gongs and such from field positions.

I believe statistically a 10 shot group would be better, but this also gets into the "FOULED BORE" issue for some rifles. I believe the 10 shot group, even the 5 shot group that I prefer, has a considerable amount of "fatigue, eye drift and other shooter conditions that muddy the results if you are really developing a load for the the gun, and don't realize your 10 shot group is a combination of ammo quality, gun condition, and shooter ability....

A compromise may be to look at the 10 holes and determine which may be shooter influenced and weed them out. Group stringing, roundness and other conditions where you may have 2 good clusters can tell a lot , or baffle you....

I believe good record keeping, shoot many groups over a few months or many range trips, then lay all the targets out and decide from there which load is best. I have several pages of targets that prove one day a load did .75", and another target has a spread-out 1.5" group... either a fouled gun, poor marksmanship, poor weather conditions, guy next bench shooting a 300 Wby...... All add up to what drives some of us batty...lol

A friend told me a story that makes sense. When he did load development range day, he initially got out his 222 rem that shot .5" groups. He would determine if he would do load development, or have a play day by how well he shot the "GOOD GUN". Makes sense. If the overall conditions were not "right" he would know by the gun's group size....

Allen

3 shots is enough to zero the sights.
3 shots is enough to indicate where the rifle is shooting
3 shots is enough to indicate how good a particular load might be.
3 shot group can be smaller than the rifle actually shoots.
You move, and get lucky.

3 three-shot groups, averaged, gives a much better indication of rifle accuracy.

Group size at 100 yards does not extrapolate linearly to 200, 300 and 400 yards. Just because your rifle shoots 1 MOA at 100 yards, does not mean it will shoot 1 MOA at 200 or 300 yards. More likely, it will shoot 2 MOA.

If you expect to take a 300 yard shot, you need to shoot for groups at 300 yards from a bench. 10 shots from a cold barrel will indicate how good your rifle and ammunition are.

In the real world, you have no bench. So you have to shoot 10 shots from various positions at various ranges, to see what your limits are.

If you can't do better than 10 shots into 3 inches offhand at 100 yards, then 100 yards is your limit for offhand on big game.

If you can shoot 10 shots into 3 inches at 300 yards from sitting or prone, then you are good for that 300 yard shot hunting. If you can't put all 10 into 6 inches at 300 yards, then you have no business shooting at live game at 300 yards.

If you can shoot 20 shots into 1 MOA at 500 or 600 yards from prone, you can bet your rifle is shooting 1/4 MOA at 100 yards.

Remember that the question was "to test a load's accuracy". Shoot a target similiar to mine above and I'll guarantee you that it tells the tale.

When I start needing to shoot 5 to 10 shots at critters, then I'll consider 5 to 10 shot groups

Thats why I like the target above. It exposes the tendencies of POI going from a cold barrel to a hot barrel. You can see POI was center on a cold barrel and then begin to shift ever so slightly to the right. It gives you an idea of where to set the POI for a happy medium.

How small do you think the "kill zone" is on a deer?

Who needs to put 10 shots into a game animal?

A 6" group means that no shot hit farther than 3" from your point of aim and that shot is under 1 MOA from your aim point at 300 yards. One MOA is 3.1416" at 300 yards.

If that makes you feel good about your rifles then by all means, carry on. For me, I require more. No problem with that either.

I didn't say that made me feel good. I comitted on Lee's post and nothing more.
I have some very accurate rifles and that has nothing toi do with the ability to reliable take game at 300 yards







I am more interested in what my rifle does with the first shot from a cold barrel, if that shot is dead on then no need for more when in the game fields

3 shots on 3 different days

We agree. Nothing drives me more crazy than shifting POI. Give me a consistent 1.25" rifle any day over a smaller grouping rifle that shifts. Drives me nuts!

Anybody who can shoot like that could win just about any high power silhouette championship, as that is approximately the proportionate size of the center body mass of the steel silhouette animals.

Paul

I always check the cold barrel consistency of my rifles by shooting one shot onto a target when I first get to the range.
I use the same target, which I keep in a 3-ring binder, and I date each bullet hole and the temperature.

A friend of mine bought a Ruger 77 .308 target rifle for his deer rifle. He has a range on his farm, 250 yards from the dirt road to the berm across a field, with a shooting bench. Every morning for a month, on the way to work, he stopped and shot one time on the target, a 6-inch circle on plywood. By deer season, he knew how well his rifle shot.

But a warm barrel 5 shot group is worthwhile, too.
A battle rifle like an M-16 or M-14 need to shoot well with a warm or even hot barrel. After a session of tuning an M-14, running 25 or 30 rounds through it, pulling it from the stock every 5 rounds or so, if it fires a .625 group with iron sights and ball ammo at 100 yards, I have confidence in it.

If you think 10 shots into 3 inches offhand is too tough for deer or other big game hunting, let's say 100% of your shots into 6 inches offhand being the definition of your maximum range. That might be 50 yards for some people and their rifles, and 300 yards for others.

Aw, geez, time for the old man and the .30-30 story. Seems I have to drag it out every year.

Rifle range off of US 89, south of Logan, UT, circa 1977 just prior to hunting season. Bunch of us were sighting in our scoped rifles, I had a #1 .25-06. We would fire our groups, then make those 1/2 MOA adjustments, fire another 3 shots, maybe move the settings one click and so forth.

Up pulls a beat up old green pickup, probably from the 50's. An old guy straight out of cowboy central casting steps out. Could have been a hard lived 50 or fit 80, sweat stained cowboy hat, grey stubble beard. He goes downrange to 100 yards and sets up a cardboard box big enough to hold a stove, no target, no aiming point. Gets back to the line and fires three shots offhand from an open sighted M94 .30-30 about as beat up as he was.

When we went downrange, he had a three shot triangle about 12" across in the middle of the box. Walking back to his wife waiting in the pickup, he says proudly, "Lookee there, Martha, it shoots to the same place as last year." With that he gets in the truck and drives off.

Driving back to Logan, I passed a farm/ranch house with that same green pickup parked in front. Nailed to the weathered barn were more deer and elk antlers than I could count in the time it took to drive past at 55 mph. The barn was literally covered with them.

Circumstantial evidence for sure, but I'm guessing that old Hunter wasn't too concerned with the statistical differences between three or five or seventeen shots.

I just had an article on this topic published in Varmint Hunter, along with the conversion factors for various numbers of shots per group. Judging from the email I've received, it's a popular topic.

The question is not how many shots you might take at a critter. The question is how well the number of shots you shoot in a test represents the long term performance of the firearm.

A single three-shot group is a poor indicator.

Groups get bigger as you do more shots.

If you shoot one five-shot group, you know the long term performance of your firearm within plus or minus 50%. If you average two five-shot groups, you know the performance of your firearm with plus or minus 25%. That's about the best tradeoff between difficulty and precision.

Yes this is true, the reason we have to actually test the loads at distance.
So many times I have seen the frustrated puzzled expressions when people shoot the 300 yard targets for the first time. Often, their 1"@100 grouping loads shoot 7" or 8" @ 300 and they are in shock!

I understand what you are saying from a mathematical point of view, but don't see the correlation in the field.


Here are 2 5 shot groups with my 300 win and the 180 TSX at 300 yards






Purely a from a hunting perspective how does this tell more any more than I would have gathered from a 3 shot group. At 3 shots I knew that I had a rifle, load combination that would not let me down. I am never going to fire 5 or more shots at an animal in the field, unless he is the dumbest one in the forest.

I've seen that many times when I've invited other folks at the range to go ahead and shoot one of my 300 yard targets.

However I have several good loads for my rifles that do better MOA wise at 200 and 300 yards than they do at 100. I've checked this on essentially windless days using parallax adjustable scopes.

In my opinion, for load development purposes, with good shooting conditions:

A large 3-shot group will identify a bad load, but a small 3-shot group doesn't indicate a good load. It may be just a lucky arrangement from a much larger group. Probably every 2 inch 5-shot group has 3 holes under an inch.

Bruce

I am quite happy with an avarage for several 3 shot groups.
All my currant rifles are hunting rifles.
I usualy show up at the range with 16 rounds of up to or 3 loads.
I shoot 5 3 shot groups as there are 5 individual bullseyes on my targets.
I clean beetween targets. the 16th round is usualy used as a fowler over the chrony.
I avarage the 5 3 shot groups. Most of my rifles have relitiovly light barrels so I give 1 minite to cool beetween rounds.
One of my best rifles is my Kimber .308 It will most often avarage about .75 to .85. Worst group is ususlly about 1.25 and best about .50.
For the purpose this rifle is intended for , that is excelent.
I have been contemplating a heavy barreld .308.
I may use 10 shot groups with that rifle just cause it should not heat up as fast.
...tj3006

If I don't shoot a one holed group with one shot, I figure something is seriously wrong.

If I am truly looking to know the accuracy potential of a load or rifle I use the average of four five shot groups. I believe this standard provides a statistically reliable measurement for load/rifle accuracy evaluation. A shooter can often get a lucky three shot group that shows nothing of the loads/rifle true potential. And it can happen with a single five shot group. Using this somewhat arbitary standard very few hunting weight rifles will be MOA shooters. That's the bad news. The good news is they don't need to be.

Here is an interesting article.
http://www.shootingtimes.com/ammunition/st_statistics_200810/

"While I was on vacation one year, an outdoor writer called for me at Speer and ended up transferred to our quality department. His question was a great one: "What is the least number of shots fired in one group that gives me high confidence that the whole batch is accurate?"

A PhD statistician went to work, applying all the classic statistical methods to the questions. Even if I could, I won't attempt to document his work here, but the number he derived was seven. "Doc" was able to demonstrate a jump in statistical confidence level between a five- and a seven-shot group that was remarkable."

It is best that we do not shoot any paper so as to leave no evidence to support the contention that we are exagerating.

.

Three shot groups for the really hard kickers, very expensive or hard to find ammunition. Five shots for everything else.

I usually use 5, but 7 sounds like the ticket actually.

The question of how many groups, and how many shots per group is a tradeoff between the precision you need and how difficult it is to collect data. More data gives more precision, but also more cost. So you design your test to give as much precision as you want to pay for.

One of the governing ideas is the Central Limit Theorem. In very broad terms, one thing it says is that precision goes up with the square root of the number of observations. So to double the precision of an estimate you have to quadruple the number of observations. (The square root of 4 is 2.) This forbids a large improvement in precision by going from a single five-shot group to a seven-shot group.

Another basic idea is that shooting a group is taking a sample. From the sample, we attempt to estimate long term performance. We do this because the other alternative is to get the real true value by shooting the gun until the barrel wears out. In that latter case, we have the true value, but the information is no longer interesting or useful.

The question is NOT how many times we plan to shoot at a target. The question is how well a sample predicts future accuracy.

For a single five shot group, that prediction is not very precise. For a rifle free from identifiable large issues, such barrel rubs or shooter flinches, a five-shot group predicts long term precision to within only about plus or minus 50%. So for a rifle with a long term ability to produce 1" five-shot groups, you can routinely expect groups as small as about .53" and about 1.54". If you shoot 3 five-shot groups, your estimate pulls in to plus and minus about 25%. If you want plus and minus about 12.5% precision for your estimate, than you need to average 12 five-shot groups. So if you shoot 12 five-shot groups and they average 1", the true long term average of many five-shot groups will be between about .88" and 1.12".

Three-shot groups have less predictive power. A gun that has a long term average of 1" three-shot groups will routinely print groups as small as .43" and as large as 1.65".

If you want to convert a long term average from groups with one number of shots to groups with another number of shots, here are the conversion factors:

To convert from 3 to 5, multiply by 1.27.

To convert from 3 to 4, multiply by 1.16.

To convert from 4 to 5, multiply by 1.1.

To convert from 5 to 3, multiply by .79.

To convert from 4 to 3, multiply by .86.

Here is an image of the distribution of group sizes you can reasonably expect from a gun that has a long-term average group size of 1" with three shots per group. If you shoot enough groups, even the worst sewer pipe bullet hose will occasionally produce a fine group. Note that with three shot groups, the distribution is very broad. The horizontal axis is group size in inches. The vertical axis is number of cases.

/

Forget conjecture and theory. Check it out for yourself.

� Tack three targets to the board (three targets "stacked," with two behind the one in front).

� Fire three rounds. Remove the face target.

� Fire two more rounds. Remove the face target.

� Fire five more rounds.

� Compare the targets.

You have one target with a three-shot group, one target with a five-shot group, and one target with a ten-shot group. Has your group grown, or has it remained the same size, as you've fired more rounds?

Mr.Howell, I have actually done this and groups always in my limited expirence grow with the number of shots fired, which should not be a suprise. In my files I have several one hole three shot groups fired at 100yds. I have no five shot one hole groups. Please note I am not talking about bench rest rifles here.

Denton: interesting histogram. How many cases is this based on? For example, the graph indicates you can expect approximately 375 groups of .4 inches: 375 groups out of how many total?

If I remember correctly, that's for 20,000 groups.

Here's a few illustrations that might help the discussion. Note that one of the graphs is the 5-shot version of Denton's 3-shot group size distribution graph.

In case you can't make out the watermark, they're from the writings of Creighton Audette some 30 years ago in which he recounted work done much further back in artillery fire which had been adapted to rifle accuracy.


There's some relevant text that goes along with the article, but I'm not in a typing mood so that will have to wait a bit. I'm sure ya'll like pictures better anyways...

Chris, you have no idea how much I enjoyed your post!! To see that Audette presaged my work by about 30 years, and to find such agreement is a great pleasure.

His conversion factors back and forth from 3-shot to 5-shot groups only differs by about 3% from mine.

Audette shows the normal range of 5-shot groups as being .54->1.45 X the average, and my estimate was .53->1.54. And look across his histogram for three 5-shot groups: plus and minus 25%, exactly as I had estimated.

Wow!

I have GOT to get a copy of that book. What's the title, and who is the publisher?

Super neat post! Thanks again!!

When you are shooting expensive bullets remember this:

If three won't shoot, five won't either!


I'll leave the mathmatical arguements to the mathmaticians. But I do know that it's not too smart to waste 2 more bullets into a bad group.

And a question for the Mathmaticians: Which do you learn more from, 3-10 shot groups or 10-3 shot groups? What if they are on different days?..............................DJ

A BIG thank you to both ChrisF and to Jon Green.

By email, Jon has provided me with an article out of the NRA book Handloading, 1981, which teaches many of the same things and which uses the same graphs that Audette published.

Jon, how about posting the article here for all to see?

Now I'm curious as to the root source of those graphs. Audette indicates that they come from a source prior to him.

Excellent points IMHO

I seems like such a waste to shoot five shot groups and not be able to impress your friends. For those that shoot three shot groups just think how much you could impress your friends with one shot group size.

My point was not intended to say that 5, 7, or 10 shot groups aren't more usefull statistically than 3 shot groups. I'll let the expert statisticians such as Denton explain that.

I'm just saying that if your first 3 shots are a lousy group, don't waste the next 2, 4, or 7 bullets! Pull them and try another load in whichever number you are testing..............................DJ

Denton,

I'll ask the NRA for permission, I don't think "fair use" would cover this.

Jon

All I've ever shot is 5 shot groups, more times than I can remember the last two have come back and had a tiny little clover leaf with one above and one below. On my first loads I always load 10ea. I will fire groups a week apart to see if they will repeat, if they look promising I come back the same way loading my next set .2 on either side and repeat a week apart. Somewhere down the line I come up with what I'm looking for. More expensive, you bet, but I'm looking for the most accurate load I can find, not just an accurate load. I let my daughter shoot my 223 for the first time week end before last. She shot 10 rds into about and 1 1/2" group. Seven were all over the place but when I settled her down and watched her, telling her what to do the next 3 went where the 1st one did and she had four rounds inside a 1/2 diamond and all together.

Unless you are taking the standard deviation of each shot from group center, 10 3-shot groups are better than 3 10-shot groups.

You are welcome denton,
It's funny how what's old is new again. I've found Creighton Audette to be a pretty sharp guy for a Highpower Shooter! In his article, he attributes some of the source material to articles in the American Rifleman (as I've watermarked). He also makes mention of eariler works such as the 1929 edition of the British Textbook of Small Arms. Not surprisingly, one of the Rifleman articles he refers to (which is reprinted in the NRA's "Handloading" compilation) was authored by Bill Davis Jr, who is another of my favorite writers.

If any of you find the subject being discussed interesting, you might be well served to hunt down a copy of "Handloading" (sadly last printed in 1986) which have much more of value (and mostly not as math intensive or technical).

Another resource to pursue is Fr Frog's compilation CD's on Ballistics which contain many of these articles in their original form from the Rifleman. The Davis article actually first appeared in AR in 1964. The source beyond that is probably Frankford Arsenal, or Rock Island I'd guess. Bill Davis if you're not familiar was a career Ballistic Engineer working on projects such as SALVO et al. He retired a handful of years back from his own firm, Tioga Engineering. I'm hoping that he's still doing well enough to answer your question about source material, but sadly I no longer have contact with him.