Calculating group size

[Billnpatti]

When we are shooting in traditional matches, the way group size is measured is the distanced between the two most distant POIs. For most matches, this is the accepted way of doing it. True, there are some matches such as chunk matches where the way a group is measured is the total string length of all of the holes from a reference point such as an X. However, when we are working up a load, we want the best representation of the group for that specific ball, powder, patch and lube combination. Using the traditional way of measuring a group size gives way too much weight to any fliers. What is a better way for measuring a group that truly represents what a particular ball, powder, patch and lube combination produces is one that minimizes the effect of fliers. I have found two ways to do that and have found them to be very effective in telling me exactly how my load combination is doing. These two methods both require more figuring than the traditional way of measuring a group but yields far better results. Method one is the Maximum Mean Radius (MMR) and the other is the Circular Error of Probability (CEP). Both yield very similar results but of the two, the MMR is the simpler to calculate. In both cases, the target needs to be marked off in a Cartesian coordinate grid. That is simply a checkerboard pattern. In both methods, each POI will be given its X and Y coordinates. From this will be determined the mean diameter of the group. By so doing, the value of fliers will be minimized as opposed to the traditional method where the value of fliers is maximized.

Anyone interested in trying either of these methods, can find them online by simply Googling them. If you have any problem finding them, just contact me with PM and I will tell you how to calculate your group using either or both methods.

For those who would argue that this ain't the way grandpappy or Ol' Davy or Dan'l did it or it is just too much work....okay, just don't do it. I use it and find it to be the best way for me for me to calculate my group sizes for comparison when developing a load. I'm a scientist by education and I like figures and accuracy in measurements. But that's just old me, 'tain't for everyone.

 

[Elkeater]

You make perfect sense for measuring the accuracy of rifle and load; in pursuit of it's best performance. When satisfied with that, total group size measures the shooters ability to humanly make meat.
Both are important.

 

[bender20]

I think some of it has to do with what is important to you. Me personally who uses firearms primarily for hunting and plinking the issue of group size is overshadowed by the issue of a flyer. I will take a load that shoots a consistent 4in group over a load that shoots a 2in group but will occasionally throw a shot to 6in once every couple shots. I must confess I didn't run these examples through any of the calculations but I think you understand my point.

 

[hanshi]

Sounds like something I should try. Always have used the "traditional" method. With some flintlocks, such as the 20ga smoothbore, only three shots are fired which makes fliers less likely. Sort of the same for some rifles that would be taken into the bush for deer. I don't feel this is a good way for my squirrel rifles; sometimes lots of shooting happens. I'm going to check out the MMR method. I've actually heard of it being done before but it's been decades.

 

[Idaho Ron]

I have always just measured outside to outside of the farthest holes. Then I subtract the diameter of the bullet. If I want to get a better idea I take several measurements and average them.

 

[coloradoclyde]

only three shots are fired which makes fliers less likely.

A 3 shot group gives you an inaccurate sample, only about 60% accurate....
A 5 shot group is about 90% accurate...
A 10 shot group is about 98% accurate....

 

[Idaho Ron]

only three shots are fired which makes fliers less likely.

A 3 shot group gives you an inaccurate sample, only about 60% accurate....
A 5 shot group is about 90% accurate...
A 10 shot group is about 98% accurate....

I disagree if your taking about hunting accuracy or target accuracy. For hunting 3 shot groups are MORE than a guy should have chances at a single animal. If the rifle can put 3 shots under 2" it is more than fine for deer or elk.
If your target shooting for X's then I could see the need for more but for hunting shooting 10 groups of 10 is pointless.

 

[coloradoclyde]

I disagree if your taking about hunting accuracy

True!.....One shot is all that you need to take an animal.....And one shot is not a group.
I've seen lots of guys who couldn't shoot straight be very efficient at killing animals....Accuracy and group size are not requirements for hunting....

However!.....I thought we were talking about group size....Not hunting... :hmm:

 

[kansas_volunteer]

I like CEP. That's the way the accuracy of guided missiles is established.

 

[Artificer]

A documented quote Spence originally brought up from a well known Hunter in Kentucky in 182O offered to shoot at a Dollar (almost certainly the Coin) at 100 yards with the understanding that every time he hit the coin, the other person owed the Hunter a Dollar and every time the Hunter missed, the Hunter owed the other person the dollar. The other person declined the bet and was later informed that the Hunter almost never missed the Dollar at that distance. Since the Dollar Coin was right at 2 ½” in diameter, that meant the Hunter normally fired into that diameter group at 100 yards and the rifle was almost certainly capable of at least that accuracy when held and fired correctly.

What I love about that quote is it is perhaps the most quantifiable account of the accuracy of a flintlock long rifle in the hands of a Hunter and not a target shooter with a special target rifle. The account does not mention the shooting position the Hunter used, but most probably it was shooting from some kind of rest as was so often mentioned in the previous century as well.

I very much agree that not all groups that fit into say a three inch circle show the same amount of accuracy. A three inch group where the bullets all are just inside the outer edge of the circle is not as good as the same number of rounds fired in a 3 inch group where most hit in the center of the group and only one or two are near the edge of the circle. For example, the latter group would be much more likely to hit the Dollar size coin when the element of human error in shooting is also added in.

What is often not mentioned is how valuable it is to shoot a fresh target when changing something in load development and saving that target for later scrutiny. The information should include the ball diameter, the powder charge, the type and thickness of patch material, the lube, etc. HOWEVER, it should also include numbering the shots as to when they were fired in the group. It is quite possible that groups will open up as more shots are fired due to fouling left over in the barrel, the barrel heating up and other things. Let’s say for example the fourth round fired consistently shoots a little high and to the right of the other shots in a group. That kind of information is more valuable to a target shooter, than a hunter, though.

I see value in the MMR for two things. The first is if you have two groups that are so similar it would be difficult to see which one is tighter by eyeball measurement alone. This is perhaps more valuable to a target shooter. However, the second important thing about the MMR is figuring out the actual center of a group. This is extremely important to both a target shooter and a hunter because once you get the tightest group possible, you can adjust your sights to center the group for aiming purposes.

Gus

 

[BrownBear]

The only real value to me in firing groups is for sighting in a gun, the repeated shots supposedly "cancelling out" sighting errors.

When I'm testing loads for deer and larger once the gun is sighted in, I'm frankly not interested in shots #2 through #10.

I fire one shot from a clean bore, then clean the bore thoroughly before firing another. I do it several times at separate targets, only measuring distance from center.

That's cuzz for hunting larger game I'm only interested in the first shot from a clean bore, the only shot I'm likely to get.

With light loads for small game where I'll fire multiple shots from a dirty bore in the field, then I'll shoot groups because that's more reflective of the shooting I'll get.

Doesn't have to make sense to anyone else. It's for me and my guns.

 

[fleener]

"For those who would argue that this ain't the way grandpappy or Ol' Davy or Dan'l did it or it is just too much work....okay, just don't do it".

I think some folks might of missed this part of the OP.

Thanks for bringing up and showing the method that you use and why. Always open to learning something.

I think that there is a benefit for shooting small and a large number of shots for a group, all depends on what you are looking for and trying to do.

Fleener

 

[Loyalist Dave]

colorado clyde Said:

hanshi Said:

only three shots are fired which makes fliers less likely.

A 3 shot group gives you an inaccurate sample, only about 60% accurate....
A 5 shot group is about 90% accurate...
A 10 shot group is about 98% accurate....

I disagree if your taking about hunting accuracy or target accuracy. For hunting 3 shot groups are MORE than a guy should have chances at a single animal. If the rifle can put 3 shots under 2" it is more than fine for deer or elk.
If your target shooting for X's then I could see the need for more but for hunting shooting 10 groups of 10 is pointless.

Brown Bear hit upon a point, and I think you guys might be missing an important part of "groups". I'm not sure that adding two additional shots necessarily gives you 38% better testing on barrel + load accuracy...., It Might..., but it might not. I think there are other variables.

For example, for how you shoot at the range, yes a five shot string might give you a much better indication of the accuracy of one's barrel and load, BUT if one does not shoot that way in the field, it might not translate the same from the range to the hunting environment.

Brown Bear completely cleans his barrel between shots, so he's much closer to a "hunting barrel" condition at the range. However, does the heat from the round fired effect his barrel, and does he wait until the barrel is cool before he fires another shot? (True, the thickness of most black powder rifle barrels tends to eliminate the problem of the barrel heating and perhaps changing the point of impact, so perhaps this is not a factor.)

Also, can the shooter see the previous impacts between shots? Either with the naked eye or using a spotting scope? A group is the objective but it also must be in-the-bull, no? Could the shooter subconsciously be slightly adjusting the hold on the target to get better hits in the black when shooting a "grouping" to check accuracy? OR does the person doing the testing fire three shots or five and then looks at the target through the spotting scope?

The previous question is only a slight possibility..., but cleaning does change things. At the range when I'm shooting I often swab the bore after every third shot, not every shot. It depends on if I'm plinking, or working on practice for timed firing event, or doing something else. I've not found a problem with either of the two rifles that I normally shoot when only swabbing every third shot, BUT are my 3rd and 5th shots actually a good sample of either of my rifles' accuracy when it comes to hunting?

After sighting in a hunting rifle, leading up to opening day of hunting season, I take the rifles down to the range two more times. I note where each shoots its first shot with a cold barrel that I've just wiped dry of rust preventative. I worry about where that first shot hits on each of those days from each rifle. That's what I consider a good indication of where the rifles are shooting. I submit that for hunting, it would be a better test to shoot each morning, one shot, for three consecutive days, than for shooting five shots on one day, unless one does as Brown Bear suggested. However, many of us don't have the means to do what I suggest.

LD

 

[Artificer]

First, I could not agree more strongly with your “one shot” hunting philosophy/procedures. :thumbsup: :hatsoff:

As a 22 yr old Sergeant, a very famous Marine Sniper taught me the same way and maybe a bit more. He had me show up at the range with a clean/dry bore and fire a single “cold barrel” shot at each distance. I would return the next day with the scope adjusted and again fire another round from a “cold barrel.” This continued until I hit dead center from a single shot and repeated it the next day, then we began the procedure over at different ranges and finally different shooting positions. THEN we began in different environments of bright sun, dark days, rain, and finally freezing rain and snow. Wind direction and speed were recorded each day, brightness, temperature, humidity and anything else possibly contributing as positive or negative factors were recorded.

Now of course it was extremely important I was able to “call my shot” after I fired and I got much better from all that practice.

It took about five weeks to do that to get a “cold barrel zero” for each distance and position, because we could not do it every day in a row. When we finished the basic zero for each range and position, the Sniper almost delighted to call me out of the blue over the next 8 months or so, to shoot in different weather conditions and especially the bad ones. He was almost gleeful about the day we went out when there was over 4 inches of snow on the ground (very unusual for most of Virginia, except the mountains) AND freezing rain was coming down hard. I balked a little at that, but when he asked me, “Are you going to HUNT in these conditions?” I agreed and went out for the shot that day.

Now, we were extremely fortunate to work at a Rifle Range, so we had no problems doing that during lunch time. When we finished, I could go out on almost any day of the year and in any environmental condition and could look in my log book to put the exact windage and elevation on my rifle for a dead center shot from a cold barrel.

Brown Bear, where I may disagree with you is on the value of shooting groups for finding the best/most accurate load for hunting and then shooting 3 shot groups with that load at different ranges to learn where the ball is going to hit. This is a test of both the shooter and the rifle. Now, if someone is really a good shot and can call their shots well, he/she may only need a second shot at each range to verify how the rifle will shoot at that range. However, many people are not that good at calling their shots or being consistent marksmen, so a 3 shot group at ifferent ranges may tell them more on where the bullet will hit at different ranges, positions and environmental conditions.

Another :thumbsup: to LD for mentioning going out to verify where the rifle shoots as close to possible to hunting season. A rifle is not going to hit in the same place it was sighted in the heat of summer and when it is colder in winter. The colder it is the day you hunt compared to the day you sight in, the more variance one will see in where the first round goes on the colder days.

Gus

 

[Col. Batguano]

That's a great way t o do it. I like it.

Another even simpler way would be to simply overlay a clear bulls eye grid (I would use ISSF 50 meter smallbore when shooting rested at 100 yards) and add up the score as it scores best, disregarding where the rounds actually land relative to your intended point of aim. Count the X's as 11's. That way a 4" group (using the traditional method emphasizing flyers) with one flyer out of an otherwise 1" group wouldn't score as badly as a more consistently but randomly placed 3" group.

It really gets down to what your intended shooting is. If a single flyer could be the one shot you get (such as in hunting) then that's important to pay attention to. If you're shooting in a 60 shot bulls eye match, the single flyer won't kill your total score the way the other 59 shots would if they hit more randomly.

 

[hanshi]

In a very real sense, accuracy is in the eye of the beholder. Maybe to shooter "A", accuracy is a one hole group at 50 or 100 yards; but to shooter "B", accuracy could be a consistent 4" at the maximum range he would feel comfortable shooting at game.

Think about it; one never truly shoots a "string" of shots with a muzzleloader. Each shot is a single, non-repeatable event; unlike modern rifles where each round of ammo is identical the the previous round. Each time someone loads and shoots, they are creating a separate event. That such shooting can be so very consistent is a testament to the skill of the gun maker and the shooter.

A well known world class hunter/competitor said a statistician once told him to forget shooting 5 and 10 round groups; that a 7 shot group gave all the relevant accuracy information. According to the math guy 10 shots muddied the picture and 5 shots weren't telling the whole story. This, of course, was not with muzzleloaders but rather with modern rifles.

My story, and I'm sticking to it, is that each time a muzzleloader is loaded and fired; a brand new event is being produced. If that one shot - as was mentioned previously - hits well then it tells the complete story. I hope this post won't be misinterpreted as it goes along with what some of the others were suggesting. Now, I could be wrong and have been wrong before; I just can't remember when. :idunno:

 

[bender20]

I agree completely to many variables go into it to possibly be able to control everything so it will be slightly different each time. However my question to the last couple posters is how much variation are we talking. I will agree what poi will change with weather but how much are we talking. I'm not a good enough shooter (unless from a bench) to be able to notice a change of 1 Moa or so. Even from a bench I don't know that I would even both trying to adjust anything if I'm within 1 Moa of my desired poi for that range.

 

[Idaho Ron]

colorado clyde Said:

hanshi Said:

only three shots are fired which makes fliers less likely.

A 3 shot group gives you an inaccurate sample, only about 60% accurate....
A 5 shot group is about 90% accurate...
A 10 shot group is about 98% accurate....

I disagree if your taking about hunting accuracy or target accuracy. For hunting 3 shot groups are MORE than a guy should have chances at a single animal. If the rifle can put 3 shots under 2" it is more than fine for deer or elk.
If your target shooting for X's then I could see the need for more but for hunting shooting 10 groups of 10 is pointless.

Brown Bear hit upon a point, and I think you guys might be missing an important part of "groups". I'm not sure that adding two additional shots necessarily gives you 38% better testing on barrel + load accuracy...., It Might..., but it might not. I think there are other variables.

For example, for how you shoot at the range, yes a five shot string might give you a much better indication of the accuracy of one's barrel and load, BUT if one does not shoot that way in the field, it might not translate the same from the range to the hunting environment.

Brown Bear completely cleans his barrel between shots, so he's much closer to a "hunting barrel" condition at the range. However, does the heat from the round fired effect his barrel, and does he wait until the barrel is cool before he fires another shot? (True, the thickness of most black powder rifle barrels tends to eliminate the problem of the barrel heating and perhaps changing the point of impact, so perhaps this is not a factor.)

Also, can the shooter see the previous impacts between shots? Either with the naked eye or using a spotting scope? A group is the objective but it also must be in-the-bull, no? Could the shooter subconsciously be slightly adjusting the hold on the target to get better hits in the black when shooting a "grouping" to check accuracy? OR does the person doing the testing fire three shots or five and then looks at the target through the spotting scope?

The previous question is only a slight possibility..., but cleaning does change things. At the range when I'm shooting I often swab the bore after every third shot, not every shot. It depends on if I'm plinking, or working on practice for timed firing event, or doing something else. I've not found a problem with either of the two rifles that I normally shoot when only swabbing every third shot, BUT are my 3rd and 5th shots actually a good sample of either of my rifles' accuracy when it comes to hunting?

After sighting in a hunting rifle, leading up to opening day of hunting season, I take the rifles down to the range two more times. I note where each shoots its first shot with a cold barrel that I've just wiped dry of rust preventative. I worry about where that first shot hits on each of those days from each rifle. That's what I consider a good indication of where the rifles are shooting. I submit that for hunting, it would be a better test to shoot each morning, one shot, for three consecutive days, than for shooting five shots on one day, unless one does as Brown Bear suggested. However, many of us don't have the means to do what I suggest.

LD

Actually most of my shooting is exactly how BB does it. Back when I was doing load development I shot a lot of groups on paper. After I got that work done all I do now is a one shot group. But I throw in various yardages. So I will shoot 137 yards, then 88 yards, then 163 yards. I also do all of that shooting from Shooting sticks.
I use a range finder get the yardage set the sight and shoot. Then I clean the barrel and do it all again. My target is steel. This is a video I made a while back on how I practice.

https://youtu.be/39arn7qj3JQ

 

[Col. Batguano]

You made very good points. Everybody has here. I also submit that the expected application and position technique has a lot to do with things too. I'll use smallbore 3-P position shooting as an anecdote. A lot of new shooters in our competitions get really obsessed about getting the best ammo / gun combinations out there, and I see them shooting Tenex, Lapua Midas PLus, and RWS R-50 ammo. The $20 a box stuff. Well, in prone position, and they are able to shoot 99's and 100's all the time, I would say it makes a difference. The only outcome from inferior ammo is lost points. But these guys are shooting mid 90's in prone, and 60's-70's in standing. Statistically speaking, an ammo that deviates from the aim point at the shot break for these guys might be as likely to GAIN them points as cost them points.

So what I'm saying with all of this is that the position and technique typically have FAR more impact on where a shot is going to land than any small variations in a perfected load / ammo / gun combination. I would say that most people will get far more benefit out of working on their technique and physical conditioning than fiddling with their loads for hours and weeks on end.

With ML'ers, there is also the issue of lock time to think about. Due to Pletch's generous contributions here, we know that the time from sear break to ball exit is around .032 seconds for a cap gun, and about 3x that for a flinter. I think the time for a cartridge gun is around .008 seconds (but I'm not entirely sure of that number). Shooting from a very stable benched position can't really reflect that. the muzzle just doesn't wobble or difference very much. However, shooting from an UNSTABLE position can and WILL reflect it much more. A (standing position) shot break that would produce a 10 in standing from a cartridge gun might give you an 8 with a capper, and a 6 with a flinter. All with the same sight picture at the time of the break!

So what I'm saying is, as soon as you decide on your load, get OFF the bench and practice shooting in a way that reflects the actual intended use of the gun as best you can.

 

[meanmike8665]

Traditional matches include Bench Matches, any one try to shoot a heavy bench gun off hand? The original post talked about Traditional matches, we have people talking about their bullets guns and fast twist barrels and shooting varied distances. While I find it all interesting, can someone explain what matches are shot for group size besides Chunk and Table matches? I shoot lots on matches and only care about the 10 ring and my screw ups. So, I don't really know if my rifle a mom or not, but if I keep them all in the black when all is said and done, I will place in more matches than not. BTW, it is not that easy.

Michael