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How many shots in a group?

by B.B. Pelletier

SavageSam prompted this report, but many of you have indicated an interest. The number of shots that should be in a group is determined by how confident you want to be that the group represents what the gun can do. Some people will argue that if the gun shot a particular group they don’t need anything more because obviously that IS EXACTLY what that gun can do. Today, I’m going to try to explain why that is not the case.

It all comes down to statistics, specifically inferential statistics, which is the science of using a small number of data to represent a very large number. But don’t worry, today’s report isn’t going to be about statistics.

“Here’s a partial score – Cleveland 3.”

Doesn’t tell you very much, does it? You don’t know who the other team is, or even what they’re playing. If it’s basketball, it’s most likely very early in the game. If it’s hockey, the game could be over. So, partial data isn’t very helpful.

I can over-simplify this entire report in one statement. A sample size of 30 provides enough data to predict the outcome of a large number of cases to a very high degree of confidence. It doesn’t matter how big your data set is; a sample size of 30 will give a very accurate picture of the entire population.

However, there are many problems–all dealing with the randomness of the sample. If, for example, you want to know the average height of adult men in the world and your sample is taken from just one tribe of Watusi, your results will be skewed toward the high end and utterly worthless. The Watusi are known to be the tallest people on earth, so the average height of 30 adult males might be 6 feet, 7 inches. That’s probably taller than most of the readers of this blog. How the sample is taken plays a huge part in the reliability of the outcome.

Can we set that aside now? I just wanted to demonstrate that I know how samples can be skewed. Let’s get on with the main discussion. How many shots should be in a group to give good confidence that the group represents the accuracy of a given gun?

Well, one shot is worthless for group size prediction. Do we all agree on that? One shot tells you very little about where the next shot is going. If that’s true, why do many people adjust their scopes after firing a single shot? Because they do not understand how a gun works and how randomness plays into the problem.

Three-shot groups
Three shots is the next size group, and, as unbelievable as it seems – at least to me – there are gun writers getting away with publishing three-shot groups in their articles. There’s even one gunmaker who provides three-shot groups to sell all his guns! They’re beautiful groups, too. Very tight. When you see them you really believe the gun could shoot that well. But it can’t. Not all the time, which is what a group is supposed to be telling us.

A three-shot group has just one application. When you’re sighting in, shoot a three-shot group after every change to the sights. Then, adjust the sights from the center of that group. As far as I’m concerned, that’s the one and only use for a three-shot group. Why? Because statistically it does a very poor job of representing how the gun shoots.

Five-shot groups
The next group size commonly used is a five-shot group. While it’s just two shots more than a three-shot group, the probability that it represents how well the gun can shoot increases enormously. Is a five-shot group representative of how good the rifle can shoot? That depends on what YOU mean by how well it can shoot. I can shoot five five-shot groups that will average one size and another single 25-shot group that will be a different size. The 25-shot group is going to be larger than the average of five five-shot groups. Even though the number of shots is the same–25 in both cases–the way the groups are measured will enter into things and give two different answers. Also, because I averaged the five-shot groups, I skewed the results in a favorable direction.

So, is a five-shot group representative? Not if what you’re trying to determine the gun’s accuracy. If you’re trying to show what size five-shot groups it can shoot, then it is representative.


Larger groups
Here’s the deal. Five shots are only a fair predictor of accuracy. Ten shots are much better, but even then the prediction they give is not entirely reliable. Statistically, it takes 30 shots to approximate to a high degree of confidence the group size you will get if you shoot the gun 1,000 times. Twenty-five shots will group very close to the same size as 1,000 shots and ten shots will give a group that’s close enough for most practical uses. Five shots will not.

With five shots, you get in the right neighborhood, but you cannot take your results to court. In real terms, that means a rifle that gives a five-shot group of one inch might give a ten-shot group of 1.4 inches and a 25-shot group of 1.54 inches. A 30-shot group from the same gun might be 1.61 inches and so might 1,000 shots. Do you see how it works? A three-shot group from the same gun might be as small as half an inch.

Who are you and what do you need to know?
There are people who absolutely must know the ultimate truth about everything, and then there are the majority of people who can tolerate a little slop for the sake of expediency. Statistics support the first group by telling them that there will be no measurable difference between 30 shots and 1,000 shots, so they don’t waste a lot of ammunition trying to find out what just 30 shots will show. But even that much shooting is way too involved for anyone who publishes their results.

But sometimes there are very compelling reasons for knowing the absolute truth. Developers, for example, should want to know exactly how their product performs under normal conditions.

Five-shot groups are often used in print, realizing that they do not represent the absolute final word on a gun’s accuracy, but they do put us into the right neighborhood. Just like the EPA average mileages for a given model automobile may not represent the mileage for your car, a five-shot group might only be a rough guesstimate for accuracy. If you buy a gun that shoots half-inch five-shot groups at 50 yards you should get concerned when your gun shoots only 1.5-inch groups at the same distance, just like you should get concerned if your Toyota Prius gets only 15 mpg.

When I tested my USFT rifle, the best group of JSBs at 50 yards measured 0.335″ c-t-c.

The ultimate in reliable data
Ten-shot groups are used whenever the goal is to publish defensible results. And 25- to 30-shot groups are used by developers, testers and anyone who wants their results to stand up to peer review. Three-shot groups should be reserved for scope adjustment, only, and never used as a predictor of a gun’s accuracy.

Test target sent with the rifle shows 25 shots at 51 yards passed through a 0.663″ group.

At this point in our discussion I could show you numerous ways of manipulating the data to represent anything you want to show. But I think most of you are aware of that possibility, so I’m not going there.

You can do something about these different group sizes when you see them in print. If you see a three-shot group, double the size to get the probable 5-shot group from the same gun. To convert a five-shot group to ten shots, multiply by 1.4. To convert a ten-shot group to 30 shots multiply by 1.15.

Please don’t do the math on the two groups shown above and then write me to say that what I said about the difference between five shots and 25 shots did not play out that way. You will only confuse yourself. I know it didn’t work out exactly as I described. What’s missing is the CONFIDENCE you can have that the five-shot group is telling you anything worthwhile.

I will continue to show five-shot groups in my reports because of time constraints, which is the big reason most writers use them.

author avatar
Tom Gaylord (B.B. Pelletier)
Tom Gaylord, also known as B.B. Pelletier, provides expert insights to airgunners all over the world on behalf of Pyramyd AIR. He has earned the title The Godfather of Airguns™ for his contributions to the industry, spending many years with AirForce Airguns and starting magazines dedicated to the sport such as Airgun Illustrated.

58 thoughts on “How many shots in a group?”

  1. Morning B.B. a nameless writer for one of the major gun mags said that he was told by the tec guy at a major bullet maker that 7 shot groups are enough shots to be statistically significant. Your thoughts please. Did your USFT gun go from 1600psi to 1300psi shooting those 25 shots and is it regulated or am I misinterperting the 1300-1600psi? TGIF Mr B.

  2. B.B.,

    Very informative as usual. If anyone aspires to be as accurate as their gun is capable of, this should be required reading. It’s always seemed delusional that a three-five shot “test” was representative of anything significant. The missing piece in this equation, that I can’t help think about whenever someone is having accuracy problems, is the shooter.

    I thought Watusi was a dance. Wow, I learn something from you everyday. Thanks.


  3. Very nice article. What really got me thinking was: “One shot tells you very little about where the next shot is going. If that’s true, why do many people adjust their scopes after firing a single shot?”

    How true. It makes plenty of sense, but sometimes you need to hear it from someone else before you realize what you’re doing wrong, and are slapping your forehead, saying “Of course!”.

    I’ve spent a lot of time in the backyard, ‘POW, click click, POW, click click click’, and eventually giving up in frustration because the shots were moving this way and that with each scope adjustment. So, next time, it’ll be three or so ‘POW’s followed by some ‘clicks’, if needed.

  4. B.B.,

    I've used statistics extensively in my career as a scientist. You miss two very important points. First there is a difference between accuracy and precision in statistics. Second the group size is a measure of of the statistical parameter called range.

    Accuracy is a measure of how close the average of the POI for the shots would be to the aim point.

    Precision would be a measure of the spread of the impact points about the average POI.

    Range is measure of high to low, or total spread. However also as the sample size gets bigger, the range increases slowly, but indefinitely. Thus the group size for 10 < 100 < 1000 < 10,000 and so on forever.

    What should be measured for dispersion is the standard deviation of the spread. Probably both horizontal and vertical components. But that is really overkill since game won't stand still and allow you to take 30 shots to be sure and hit the kill zone. Thus shooting is forever stuck in small sample statistics. Once you start chewing up the target so that there is a single hole, you also obviously can't measure the placement of each shot.

    There is another component to all of this as well. With pellets there are no doubt "flyers." Thus there is some variation which is due to the pellets themselves. The flyers are not an average variation in pellets but an abnormal variation (e.g. a deformed pellet, or large weight difference from average). If you truly measured the standard deviation of the POI, then you could compare the standard deviation with and without the "flyer." If the flyer can in fact decided to be abnormal, based on some chosen confidence interval, then it could be rejected.


  5. Hi BB,
    I also appreciate your article. One thing I wonder about is that as the number of shots goes up in a group, I feel that there is an increased chance of the shooter loosing concentration. In other words, I think there is less of a chance of a shooting error in a 5 shot group than a 10 or 30 shot group. I don’t have any idea how this can be accounted for. If the gun was machine rested, that is not a problem.

    David Enoch

  6. Should have pointed out that adjusting the scope changes the statistical accuracy and not the precision.

    Thus if I am zeroing a new scope, it is reasonably to adjust after only one shot if the shot indicates that the scope is aligned significantly different from expectation. At this point all I’m trying to do is make sure that (as I back up the the distance from which I really want to zero the scope) I’m going to stay on the paper.

    Thus if I know from past experience that I can get one inch groups at 25 yards, and I put three shots that can be covered with a quarter that are four inches left and two inches high, then I can be certain that the scope is misadjusted. But as the POI for the shots get closer to the POA, then adjusting the scope gets trickier and trickier.


  7. David,

    I’ll jump in and say “it depends.”

    As I mentioned before if you measure the standard deviation of the POIs, then you could throw out outliers – for whatever reason.

    No doubt the loss of concentration is a factor. To design such an experiment you’d record POI with the number of each shot, say for 100 shots. Then you’d look at the standard deviation of each ten shot sample (1-10, 11-20, 21 -30, and so on…) to the standard deviation for the whole round of 100 shots. Now if you do this experiment 10 different days with 10 different shooters on each day, then you’d no doubt find that it takes some shooters a few shots to settle down, and some lose concentration faster than others.


  8. Just spent this Sunday putting 25 different pellets through my Benjamin Discovery inorder to determine which pellet the rifle likes best. I shot 5 pellets each and am I glad this is a PCP and not a break barrel. The winner? I need to conduct a shoot-off between 5 different pellets from the JSB’s to Beeman Silverstings to Crossman Premiers (groups ranged from 1/2″ to 3/4″ for those). The other pellets produced some groups as wide as 3″ and started to introduce doubt as to my rather mediocre abilities. The JSB’s were somewhere in the 18th set I shot. Range was outdoors and 25 yards. I didn’t have enough light for my Chrony to function (late afternoon) so I still have to determine the “sweet pressure” spot for this PCP. All of these points were learned or were reinforced from reading this Blog and all you folks commenting.

    This really is a great source of information for “weapons of air destruction”.

  9. Way to go Fred… that’s a lot of pellets. Well, come to think of it, I do have quite a few tins of pellets in .177 cal. and .22 for 6 different airguns. I keep a record of my airgun specs along with performance results.

    For pellets I generally use an average of five 3-round or 5-round groupings. Often, I take a few different pellets for an airgun and check their rankings. The top ones go hunting and the others go plinking.

    I will probably go with an average of five 5-round groupings now. The reason I don’t shoot a lot in one target is just I like to see some action when I’m shooting and to see any patterns in the way they are hitting.

  10. Fred,

    All three of the Discovery in .22 cal I got had the "sweet spot" of pressure from 1,800 down to 1,200.. So start there and see how yours compares.. and JSB Exact turned out to be best in all three, with kodiak & RWS superpoint a tie for a close second.

    Ashland Air Rifle Range

  11. B.B. & All,

    After Matt61's idea about small dot focus, I made up a 25- 1/8" dot page with 3/4" crosshair lines through the center of each dot. I use the back of used 8-1/2×11 copy paper… and just fun off a bunch of them on the copier..

    After adding another layer of that clay stuff to the "silent trap", because the pellets were coming out the back, I found that the paper sticks to the clay.. super easy to just lay it on the front of the sticky clay target trap..

    Like Herb says as you take out the center of the dot with more and more shots, you loose the ability to know where your hitting inside the paper hole… no problem if the hole is 1/4", but if you do a 30 shot group, you can't tell really how your doing on a micro basis…
    So, I shoot 5 shots on each dot and end up with 125 shots per page. Doesn't this method give the best of both worlds? Does it matter if the POA (point of aim) changes from dot to dot? Don't we still get an accurate POI (point of impact) evaluation measurement?

    Ashland Air Rifle Range

  12. I neglected to mention that the RWS Superpoints also produced good results, Wayne. 1800 to 1200 psi is the way to go for you, huh? My next mission is the RWS 52 I just bought this weekend from the local gun store going out of business here. Price was too good to pass up. I asked the salesman if anyone had dry-fired it (it had been in the store long enough that it had some very light surface rust on the compression cylinder loading port portion). The first shot in my basement, that large screw at the rear of the scope rail popped up and landed right on the back of my hand! I then tightened all the screws and used loctite on that little rascal. I don’t think I can put 125 pellets down that barrel in one afternoon.

    Now I have to make sure my wife doesn’t find out about this purchase.

  13. Hello to everyone once again:
    Yesterday I posted a question concerning the AirForce Condor, and as always it was inmediately replied; but Mr. Wayne also mentioned something about putting a BlOOP TUBE to the rifle…….. What did he meant??? Thanks again, Take care everyone!!

  14. Fred,

    I usually fill to 2,000 or so, for more shots per fill. I'm too lazy to go fill again, and I like the personal contest of dealing with the "valve lock", which will give you low shots on the first 10 shots or so, with that 2,000 # fill, then 25 shots on the POA, then 10 or 20 shots with the POI lower and lower.. I like to pretend that I'm stuck on an island and every shot means a meal, so I have to adjust for the valve lock.. It takes knowing your gun real well, and it helps that the Discovery has a gauge..

    I know what you mean about shooting 125 shots with a spring gun of any type, being a job… That's what's so great about my 10 shot Air Arms S410 with the 1-2 pound side lever cocking… It is so easy and fun to do those 125 shots (on one 205 bar fill), in about 12 minutes. I can get way more practice in every night..


  15. Jony,

    The “bloop” tube makes the Condor pretty quiet. My guess is, it’s about 25% as loud… I got mine used from a commenter here, Jeff. So I don’t know where to get one…
    But Anthony also makes them for air guns, his number is 317-374-5679.. (he told me it’s ok to put his number up)..

    And yes, the use of this tool is to extend the distance to the front sight. 🙂


  16. Mr. B.,

    I didn’t shoot the 25-shot test group, but a 300 psi drop is about right.

    Seven shots will give some confidence in the group, but less than ten.

    Significance and confidence are two separate criteria for a statistic.


  17. Hi Wayne: just got off the phone with Anthony for a Discovery Shroud. A good man folks. Jony another place to look is Airhog.com and talk with Van or Martin. I have two of their products, ie, for a 12″ and 24″ .22cal. barrel Talon SS. They work well also. Mr B.

  18. David Enoch,

    You are right! That is another good reason why no writer likes shooting ten-shot groups. I shot about 50 of them when I tested a 10/22 customized rifle against the Ruger 10/22 Target for Shotgun news, because each type of ammunition needed its own chance to shine. It was very exhausting.


  19. Cowboy dad,

    I’m glad you are having so much fun with that PPK/S/.

    As for storing the gun with CO2, I store mine for years at a time. It doesn’t hurt the gun.
    Both my PPK/S pistols are several years old and both still hold and work well.


  20. B.B.

    On the subject of shooter fatigue, I read one article about a gun writer who had procrastinated on a comprehensive survey of big bore shotguns, and in the course of a marathon shoot, vomited all over himself. He had gotten a concussion from all the recoil. Anyway, I expect that shooter fatigue must become a factor for a single group of 30 shots although not so extreme as in this case.

    What is behind the saying that a gun is a hundred times more accurate than the shooter? If that’s the case, machine rested groups should be 100 times more accurate than bench-rested groups, but they’re not.

    On the subject of statistics, I wonder what it means when it’s said that statistics shows that 30 shots is a sufficient test for accuracy or any other such statement. What is the basis of truth in statistics? Has someone run endless trials to come up with this? Or is this based on some kind of mathematical proof based on the field of probabilities or something else? My impression of studying statistics is of endless formulae without it being clear as in other sciences of just where the formulae came from.


  21. Wayne,

    For your 5 shots at 25 targets on a single target sheet, I’d expect that the variation between the 25 individual targets would be insignificant. But you must remember that every variation is a potential source of error. Just matters if the error is significant to the overall error. So if you were shooting at 25 targets of different sizes at different distances, then obviously the target to target error would probably be significant.

    Up to now we’ve been discussing parametric statistics where you’re getting an actual measurement of how far the POI is different from the POA. There is also non-parametric statistics (like heads/tails for a coin flip) where you need a much larger sample size. So for a 25 shot group, you could measure the size of the major “one-hole,” and then count how many holes are not connected to the major hole group.

    The whole thing is that you need to establish some convention then follow it. If you vary distance, how many shots are in a group, or how you’re taking the measurement every time, then you can’t compare one group to the next. The whole idea of statistical control is make a measurement, adjust the process, and repeat the measurement. If the new measurement is better, then the the change was “good” otherwise the change was “bad.” Obviously the measurement has to be precise enough so that measurement to measurement error is insignificant compared to the measurement differences due to process changes.

    In other words, it would be a very frustrating task to adjust the scope after every shot. You’d never get the scope zeroed. But if you make a shot and you’re not even on the paper, its obviously stupid to shoot 4 more times just to “prove” that the scope is adjusted so badly that you’re missing the paper altogether.

    So take one shot and make a crude adjustment. When you’re close enough to the center of the paper so that the next shot will be on the paper too, take 3 shots and adjust sights/scope. adjust towards center based on three shot group. Now that 3 shot group is close, take 5 shots. In order to make any real improvement in the average measurement due to sample sizes you’d need to double the sample size from one-size group to the next. So from 5 shots to 10. Obviously the difference between a 10 shot and a 11 shot group would be small. So from 10 shots to 20 and so on.

  22. Matt,

    The basis for statistics is EXACTLY what I DID NOT want to get into. It is there, if you want to look for it. It took me two semesters in college to appreciate the subject, and no, it is not hocus-pocus, despite what you hear or think.

    What it means is that you don’t need all the data contained within a population to predict certain things about the population. Things like averages, etc. No one has ever attempted to record the heights of every man in the world, yet you can find tons of data on that subject. Statistics provides the analytical tools for those findings.

    As for the saying that a gun is 100 times more accurate than the shooter – that’s a new one on me! I’ve seen some pretty good shooters in my life – people who could shoot to the limits of some guns.


  23. Matt61 & All,

    The main purpose guns were invented for, I would think, was to kill things…

    We practice so that when we shoot at something to kill it, we do it in a humane way.

    Shooting for fun came long after this main purpose, I would guess…

    Statistics, can be helpful to a degree, but the idea you gave me, of the 1/8" dot focus.. With 125 dots on a page, 5 shots per dot.. That is a very simple test that tells me if I'm ready to try and kill an elk, or knock over the field target…

    And I would rather spend my time shooting at the dots or hiking after game, or knocking over steel targets, than thinking about "Statistics"….


  24. B.B.

    The hundred times statement is a bit extreme, but I could swear I’ve seen versions of this in many places about guns being much more accurate than humans.

    As for statistics, I guess what I was getting at is that since the whole subject seems based on probabilities, to say that some probabilities reach some standard of certainty (30 shot groups) compared to others seems a bit rarified. But I have no doubt that this has been worked out by specialists. I give you credit for two semesters of this. One examination of an Idiot’s Guide on the subject was plenty for me. By the way, I love the conversions you gave for going between group sizes. I have wondered about this for a long time. The doubling of size from 3 to 5 shots is of particular interest and would explain a lot about the fantastic group sizes reported for certain AR-15s. I expect that the 3 shot groups would be especially inaccurate for rifles that tend to shoot badly when hot as the AR-15 system seems to do.

    Wayne, I agree with you that the fun of shooting is the key. However, you divide up your groups, I’m sure that there is plenty of data in the amount of lead that you’re putting out. I just hope you’re measuring CTC now instead of the whole group.


  25. Matt61,


    It doesn’t help me when trying to get inside the steel field target hole…. That 1/2 pellet still hits the edge of the hole and bounces off most times… leaving the field target standing and a score of zero for the shooter…

    Ashland Air Rifle Range

  26. BB,

    As always, this is an interesting topic. My opinion is still that someone with a new rifle which they intend to use should should shoot larger groups (at least 10) after sighting in, so that they aren’t taken by surprise. On the other hand, 5 shot groups are good enough for comparisons b/t rifles. I suspect one problem these days is that people are led to expect MOA performance (even for big game rifles), but due to the culture of “I’m OK, you’re OK” don’t realize that it takes a shooter some practice to get there. No doubt many shooters are disappointed in the performance of their rifles, which a professional shot, er, well, professionally.


    I like the story about the writer throwing up:). I wonder if he put that tidbit into the article? Sounds like he should seek another line of work or focus on rimfires and .410’s.

  27. Oh lucky me,

    Our supply guy just told me we need more supplies…. I get to stop by the 200 yard center fire range with the Marlin 336RC 30/30, and the rim fire range, since we’ve been talking about the Marlin 60 .22 cal semi-auto .. I think I’ll do some “can walking” and shoot and see’s target shooting…

    Off I go now, shoo, shoo…

    Ashland Air Rifle Range

  28. B.B.

    I don't mean to belabor the statistics business, but I can't resist something else. I know that uber discussions about why a field of study works the way it does are irresolvable and generally lead to endless speculation. For instance, I don't think that anyone knows why the machinery of mathematics explains the physical world as well as it does. Hence, all of the sciences have an elaborate protocol for checking how mathematical formalism applies to the world. Pure math is a different animal where they seem to be able to verify their results internally. Statistics, though, doesn't seem to fit either category. I heard a physicist say that statistics was not really math although it makes use of mathematical techniques. Later I asked a couple of mathematicians about this distinction, and they just looked at each other. They told me that the distinction was apparent to them, but they couldn't really explain it…. So, if statistics is not really math, but no one is experimentally checking it like other sciences, that seems to leave us in a strange position with the way statistics saturates every aspect of life or at least the news media. Nevertheless, I'm all to happy to make use of the practical tools in general use.

    Speaking of which, is there a rule for converting group sizes from one distance to another? I know in theory, it is supposed to be MOA. So, someone who shoots 1 inch at 100 yards should be punching out a 10 inch group if paper was set up 1000 yards away. But in practice, I don't think it works out this way, and as per our recent discussion, groups tend to expand faster than MOA as distance increases. So, is there a way to convert, or does MOA work for 300 yards or less which is the distance most people shoot at? I've noticed that my MOA is pretty consistent between 25, 50 and 100 yards.

    Wayne, that's pretty intense, but I will make the conversion for you as I size you up for the next showdown. >:-) I do wonder now if I was shooting with a broken mainspring last time. After getting the gun back from PA, the sound of discharge was subtly different and the cocking effort was much easier. We'll see.

    Dr. G. did you ever find out the source of the burning smell with the gun that Rich tuned for you? I wouldn't really care if I got the results that you did. On the other hand, it would be nice to avoid if possible.

    BG_Farmer, the guy indicated that he solved the problem by spacing out his shooting sessions. I do wonder if there's a cumulative effect from high power shooting. After 6 clips from an M1 Garand, I was feeling just slightly dazed. And I read about a study wherein the Marine Corps was comparing the sustained fire rates of the 1903 Springfield with the M1 Garand. And after, 5 minutes or so of rapid fire, the Springfield people were completely incapable of shooting for some minutes.


  29. Matt,

    As long as the pellet remains stable, the rate of dispersion remains constant unless influenced from the outside (e.g. by wind). But when it becomes unstable, the dispersion accelerates. After that point, it becomes difficult to predict how fast it will diverge.


  30. B.B.
    How can I install a flashlight in my rifle w/out it affecting my vision through the scope during night hunting?????? Because I own a Gamo Wihpser VH, and the flashlight it includes is useless at night because it glares too much and I only see light through the scope…..


  31. Matt,

    Statistics is sort of like cooking a recipe. A cook can follow a recipe, but does not necessarily have the vision to create an entirely new menu. Being able to select a number of items which compliment each other and arranging the items to be attractive takes a greater skill level. That what separates a cook from a chief. But the distinction is fuzzy of course.

    Statistics is an area of applied mathematics, thought it is possible for a “real” mathematician to develop a new statistical technique.

    For another example, just because I can balance my check book doesn’t make me an account.


  32. Groups:

    The issue I have going much over five shots is that you lose your aim point, so I end up just aiming at a hole – and needing to estimate where the center was. This is assuming you are sighted in for point of aim.

    The Discovery:

    Finally got around to spending a little time with it today. My initial impressions of the furniture on it have not changed. Since it is useless to offer problems without solutions – here is mine. Send the stock blanks to shop classes through out the USA. Any 12 year old with a piece of steel wool and the desire to at least achieve a C- will make a better product. Win-win.

    Sorry, but I need to get it out of my system. Putting more effort in the box than the stock is just sad. Let people make a product they can be proud of.

    The noise level is less than the Webley. I suspect the lower charge level is to thank.
    The pump is very nice overall. It lacks the moisture filter of the FX model, but seems to be every bit as sturdy.

    The open sights are fair at best, but since most will scope it that is of little consequence.
    I have not scoped it yet, so the accuracy remains to be seen.

    The dual fuel idea is intriguing, but it needs a couple items that are not included to run off of CO2. I do have to question the name. Since “dual fuel” ranges have been available for about a decade, I keep envisioning a range with gas burners and an electric oven.


  33. Just had a chance to read the days comments. Wow. It’s amazing how we can get hung up on statistical what if’s. The maze of hypotheticals. I’m a simple guy so I’ll offer an observation.

    I’ve seen many people shoot their favorite gun and be impressively accurate. I’ve seen them hand it to a guy/gal watching/admiring nearby and allow them to shoot it. Many times these people are disappointed in this “magically” accurate gun in their hands because it’s not performing the same as it was in its’ owners hands. Apparently this gun wasn’t the elusive “silver bullet” of accuracy either that they have been looking for for a long time.

    The moral: some guns are more accurate than others “out of the box” but a five shot group with any gun with only one type of ammo isn’t going to tell you much. A 30 shot group with a variety of ammo will tell you more. But, with rare exception, if you want an accurate gun you need to put your slide rule away, disregard statistics, ignore quantum physics and shoot the gun until you gain enough confidence and consciously or subconcously recognize/ingrain the nuances of that gun. It may be possible to verbalize these nuances or they may be so subtle that you’re not aware of them. But until you shoot the gun a lot you’ll never have the chance to know. With some guns you will never create this symbiotic relationship.

    Please realize that this perspective is primarily from a firearm background but from my little experience with air guns I still believe it applies.

    God bless all. Please pray for all of us for the next four years in America.


  34. Kevin,

    Don’t let me be your only source of information.

    There is a video review of the Discovery on PA’s web site. I guy named Paul makes them I think. Check it out if you have time. Another resource is the yellow forum – they have a Discovery link.

    Some of these guys do seem to love them. To each their own.

    Maybe it will grow on me?


  35. Kevin,
    Amen. You could give a goofball the rifle that won competition X without telling him and he would shoot a scattergun group and probably complain about the trigger pull.

    Send the stock — nay the whole rifle and pump — to me, and I will refinish the stock within 6 months to something which can be compared to a Weatherby Mark V. I wont charge for this service, although ebony endcaps are extra:).

  36. Matt61,

    I assume the smell is dieseling, and it continues to occur after about 10 shots. You obviously have a lot on your mind.

    It is not and has never been unpleasant, simply interesting.

    Regarding the bloop tubes (Airhog) and Anthony’s tubes, I have one of each for my Condor. One of them is definitely quieter than the other, and is worth the extra money that is charged.

    Also, the purpose of using averages is to handle large amounts of data. For example, it is easier to say that a baseball player has a .250 average than to say that he was 122 for 488 at bats. However, it is more descriptive to say that he was 3 for 12 than that he batted .250, although both are correct.

    Now, how does this apply to group sizes? BB’s use of averaging his group sizes has a fundamental flaw. Here it is..Is is more descriptive to say that the average group of 6 groups composed of 5 shots each was 1 1/2″ or is it more descriptive to write that 3 of the groups were 1″ and three were 2″?

    The point I am making is that important information is lost when averages are used for group size, as the flyers are not reflective of what you are actually trying to measure (the True Value of the Gun + Pellet Accuracy), but rather are reflecting noise. You do not want the noise to be averaged in, you simply want a way to identify it and then eliminate it from measurement.

    Another way of saying this is that it is more helpful to know that 17 out of 20 shots will fall within a 2″ radius (with 3 flyers, viz. more than 2 standard deviations from the norm) than it is to say that the average of the 20 shots is 2 1/2 inches.

    – Dr. G.

  37. Volvo,

    My bias isn’t solely based on your opinion.

    Read an awful lot about the discovery. I really like the price, the package that includes the pump, mid-range report, etc. It just won’t be my entrance into the pcp world. Can’t quite put into words what my hesitation is. Guess springers are satisfying my craving right now.


  38. Bf –farmer,

    Tempting offer. Could you throw in a brass trigger? : )

    With standard pellets it is on par with the Webley. With the 28.4 Eun Jin’s it averages 648 fps for 26.4 ft lbs.

    I saw a Discovery on a forum with a $400 custom stock along with other upgrades that came close to $1200 total. Once again, to each his own.


  39. Kevin,

    I have put several thousand rounds through my IZH 61 and believe that I have felt the resonance of this particular gun. It is very gratifying and akin to appreciation. I feel it a little bit with the M1 Garand.

    Dr. G. Ha ha. I have kind of an overactive imagination. Thanks for your analysis of the smell. I recall B.B. saying somewhere that you will get dieseling in guns above a certain velocity no matter what, so I guess that it’s nothing a tune can fix. As to your remark on statistics, I think the tool that is used for analyzing variance in samples of the kind you are talking about is the standard deviation. And if I remember correctly, with large enough collections of samples, the SD shows that statistical noise gets reduced.

    I have wondered about the exact meaning of a flyer. I’m guessing from your description that it refers to shooter error which is one meaning I have heard. And to the extent this is true, your point is very well-taken. However, I’m not so sure that such a flyer is always easily distinguished from generally bad shooting or perhaps buried somewhere in the shooter/gun interface that Kevin describes which would make it almost a property of the gun. For example, I notice that flyers are more common for me with lighter guns both rifle and pistol.


  40. Matt,

    Yep, the standard deviation is how the precision (spread) of a population is measured.

    As far as outliers, the notion is to measure standard deviation with and without the outlier. First you decide how confident you want to be that finding a difference is “correct.” Typically a 95% confidence interval is used in science. Thus 95 out of 100 times when the experiment finds a difference there is truly a difference.

    Trowing a shot out reduces the sample size, so you have to make a correction to the new standard deviation. You compare the ratio squared of old standard deviation with the new, and use the correction factor from the sample size to calculate the experimental F ratio. You then look up in a F-ratio in a table to see if the difference is significant or not.

    In order to remove the “outliers” you don’t have to figure out what is causing them. But you have to figure out why they occur to eliminate the source of such outliers (eg unusually light pellets) from the sample.

    If you were doing some sort of experiment and you know you had an oops (eg you know that you shot accidentally while trying to take up the first stage of the trigger) then the deviation is due to a known assignable cause. For that kind of error you can throw the data point away without doing an F-test. You just have to be sure that you always throw such points away. You also have to be honest and only use such a removal when appropriate.

    Look up the F-test in statistics if you’re really interested in more about this. For more than one-factor at a time the technique is ANOVA (analysis of variance).

    For a PCP with an ANOVA test you could test kind of pellet, starting pressure, and number of shots between refills all at he same time taking a minimum number of shots. You could of course do the tests one at a time with the F-test, but you’d have to shoot a lot more to get the data.

    You could also recalculate the F-Table to be for group size and an outlier for a given group size, or various group sizes by making some assumptions. Thus you could compare the group size of a four hole group to the size of the five hole group to decide if the worse shot is an “outlier.”


    PS – My daughter refers to this as the “dad” answer. The “mom” answer would have been just the first paragraph!

  41. B.B.,

    Along this idea, do you think that group size and magnification are related?

    Would seem to be no question but that a scope helps over open sights.

    But it would seem that too much magnification is bad too. I haven’t studied it yet, but with 9X magnification at 10 meters I can’t hold sights steady, but at 3X, the sights APPEAR to be steady. I’m guessing that at 9X my subconscious brain is working against me by signaling my muscles to twitch to try to center the scope. It just seems more tedious to shoot at 9X, though I haven’t statistically analyzed the group size. Make sense?

    I assume that a really good shooter can allow for how sights are moving and anticipate when to pull the trigger. Also a good shooter is “settled down” and subconscious isn’t overly active. I’m struggling to get a decently steady hold now.


  42. B.B.
    Sorry to be so far off subject, but while cocking my webley patriot the barrel slammed shut breaking the stock in two. I don’t think the gun was damaged. Were can I pick up a new stock.

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