Here's my chapter from the BIG BOOK OF GUN GACK II on the subject:

Chapter Five:
The Pros and Cons of Three-Shot Groups

Before World War Two many shooters fired 10-shot groups when testing rifles or ammunition, including Col. Townsend Whelen, author of the oft-quoted “only accurate rifles are interesting.” Even many hunters typically fired 5-shot groups when sighting-in, yet today 3-shot groups have become almost universal outside of formal competition.

What happened?

Before the war, most hunters used factory ammunition and iron-sighted rifles. Few owned a deer rifle capable of grouping less than 2-3 inches at 100 yards, yet still killed deer, so didn’t worry about tiny groups. In fact, many didn’t worry about groups at all, shooting only one round before adjusting their sights. Another factor may have been the war itself. As shooting supplies for civilians became scarcer, it made sense to use less ammunition.
Many older gun writers (including Whelen) were professional military men who helped develop rifles and ammunition. Many newer gun writers were primarily hunters, thanks to big game populations rising considerably after their low point around 1900. The most influential post-war writer was Jack O’Connor, who in his book The Hunting Rifle stated: “I consider the 3-shot group fired from a cold barrel indicative of the practical accuracy of a big-game rifle.”

During the 1950’s, handloading, rifle scopes and benchrest shooting all became far more popular. Many new handloaders read articles about using benchrest techniques to turn their scoped rifles into one-inch wonders, and discovered tiny clusters occurred more often when they only fired three shots.

This is exactly why so many 21st century deer hunters own “half-minute” rifles. The super-accurate handloads for most of these half-minute deer rifles are often range-proven by shooting handloads with slightly different powder charges, then picking the smallest cluster as The Load. I know this because so many friends and acquaintances “work up” hunting loads this way.

Recently, several of us had a short discussion after one guy showed off targets shot with a new .223 Remington, using handloads with different powder charges. The 3-shot groups ranging from slightly over half an inch to just under an inch, and the shooter wondered if free-floating the rifle’s barrel might improve accuracy.

Another guy said, pointing at the smallest group, “You’re not happy with a half-inch rifle?” I suggested (based on some experience) that ALL the groups probably represented the overall accuracy of the rifle—at least with 3-shot groups. The second guy looked me like I had two heads, neither with a brain.

Another friend gets almost irate whenever anybody suggests 3-shot groups don’t reveal a rifle’s accuracy level. He’s been testing ammo and sighting-in his big game rifles with 3-shot groups since reading Jack O’Connor as a kid, and taken a bunch of animals out to 350 yards, mostly with one shot.

So what’s the deal?

First, let’s look at the positives. Three-shot groups work for typical big game hunting because big game is by definition BIG. Even pronghorns and South Texas whitetails have a vital area the size of a volleyball. (If you didn’t know, the diameter of an official volleyball is slightly over eight inches.) As a result, any rifle averaging three shots in less than 1.5 inches at 100 yards will cleanly take big game out to 400 yards, and even farther. I know this due to range-testing, plus killing various animals at 400+ yards. (While 1.5 inches may seem like pretty sad accuracy, especially for a gun writer, we’re often forced to hunt with factory ammo in factory rifles. It’s tough work but somebody has to do it.)

For the same reason, 3-shot groups are sufficient for sighting-in the average big game rifle, whether scoped or not. Plus, several of my rifles are so accurate a single bullet hole at 100 yards reveals whether they’re still sighted-in. Why shoot twice more?

Now let’s look at the negatives of 3-shot groups:

Super-accuracy’s sometimes required for shooting distant targets, whether paper, varmints, or big game, and 3-shot groups aren’t enough to predict the spread of all shots from a rifle and load. With any rifle, 5-shot groups will average larger than three-shot groups, and 10-shot groups larger yet.

Many hunters believe this occurs due to thin barrels heating up. While some barrels will warp when warmer, a properly stress-relieved barrel keeps laying bullets in there even when HOT. A good example is the New Ultra Light Arms rifles built by Melvin Forbes, partly because the Douglas barrels he uses are correctly stress-relieved. After a fellow gun writer test-fired his first NULA sporter, he simply had to call me, because he’d shot a group of 30+ shots into about an inch, never pausing to allow the barrel to cool.

This doesn’t mean some barrels aren’t correctly stress-relieved, but the contour doesn’t really matter. The worst warper I’ve ever owned was the varmint-weight barrel on a .22-250 Remington, made by a factory known for accurate rifles. The first 3-4 shots went into tiny clusters, but after that they could land anywhere within a three-inch circle—and yes, the barrel was free-floated. This doesn’t work when shooting prairie dogs, so the rifle went down the road.

The real reason 3-shot groups average larger is the laws of chance, and applies to super-accurate benchrest rifles as well as light-barreled sporters. Assuming a single 3-shot group represents the widest spread of any rifle’s shots is like driving a pickup from Boise to Spokane and averaging 15.2 miles per gallon, then assuming the pickup will always get 15.2 miles per gallon, no matter the road, speed or weather.

Even averaging several 3-shot groups doesn’t provide a real look at the possible spread. If you doubt this, on your next range visit shoot three, 3-shot groups with the same ammo, using a different target for each group. When you get home, place each three-shot target carefully over a new target, and use a pen to make a circle inside each bullet hole, ending up with a drawing of a 9-shot group. I’d be willing to bet a brick of .22 Long Rifle target ammo the 9-shot group will be larger than the average of the 3-shot groups—but it will also be a better prediction of your load’s true accuracy.

So when do we really need to know the maximum level of accuracy of a rifle and load? One example might be 1000-yard benchrest shooting.

The world record for a single 10-shot group was set in 2014 by Jim Richards, at the Northwest Sectional Competition in Missoula, Montana for the annual matches held by the Original Pennsylvania 1000-Yard Benchrest Club. The group was officially measured at 2.659 inches, smaller than the 3-shot groups most hunters shoot at 300 yards—if they ever bother shooting a target at 300.

Jim’s a member of the Broadwater Rod and Gun Club in Townsend, Montana, of which I happen to be a life member, and I’ve talked to him about his group. He’s actually a comparative late-comer to long-range benchrest shooting, but learned quickly, and like all serious competitors goes to extreme lengths to make every round exactly alike. But he differs from some other benchresters, since he set the record with a used 6mm Dasher purchased from a fellow competitor!

The main point, however, is Jim Richards did not depend on 3-shot groups to develop the record-setting load. Instead he depended on firing more than three shots at various ranges. (For those desiring more details, the rifle has a Krieger barrel, Borden action, Shehane synthetic stock and Nightforce Benchrest scope, and the bullets were 105-grain Berger Hybrids, weight-sorted and then tip-uniformed with a meplat tool.)

I’m not interested in competing in benchrest matches, preferring to spend my “spare” time hunting, something that can be done pretty much year-round in Montana. But I do like to see what sort of groups can be shot at distances from 100 to, occasionally, 1000 yards. (The Broadwater Rod and Gun Club’s range extends to 1000, one reason Jim Richards is a member.) But I do considerable small-varmint shooting, and after the experience with the barrel-warping .22-250 started testing my rodent rifles by firing 10-shot groups as fast as possible, both to test group size and see if the increasingly warmer barrel kept laying them in there.

In the process I learned that any rifle/load combination that couldn’t put 10 under an inch at 100 yards wasn’t accurate enough to consistently hit Richardson’s ground squirrels at 200 yards, or prairie dogs twice their size at 300. Today I try to work up loads that put 10 shots inside .8-inch at 100, which converts to 2.4 inches at 300 yards—about the diameter of a tennis ball, or the width of a mature prairie dog.

Consistently hit means hitting rodents more than you miss. I’ve hunted prairie dogs with record-setting benchrest shooters, gunsmiths who build record-shooting benchrest rifles, top-notch military snipers and instructors, and nationally successful bullseye competitors. In a typical 5-10 mph breeze, none ever hit more prairie dogs than they missed much past 300 yards—and even at 300 you’d better have a very accurate rifle to hit more than you miss. (Another thing learned over the decades is most prairie dog shooters think they hit far more than they actually do, and to many any prairie dog they hit counts as consistently hitting ‘em, even if they took a dozen shots to finally get the job done.)

Eventually I abandoned three-shot groups when seriously testing most ammunition, because subsequent groups with any load that shot an initial tiny cluster almost never matched that first group, and the instances when they did were so rare they really stuck out. One of those rarities occurred when testing a bunch of different .25-06 Remington handloads in a Ruger No. 1AH. The first three-shot group with the 75-grain Hornady V-Max and 58.0 grains of Accurate 4350 measured .39 inch, so I loaded up nine more rounds and shot three more 3-shot groups. They measured .41, .39 and .37, for a four-group average of .39.

But that’s as rare as a pro-gun Democrat from San Francisco. More typical was the first group with the 156-grain Norma Oryx and 60.0 grain of H4831 from a .280 Ackley Improved. The three shots spanned exactly the magic half-inch, but three more groups with the same load averaged .93 inch, good but not magic.

So how many shots are required to truly predict the accuracy of a given rifle and load? A few years ago a guy named David Bookstaber contacted me about some new statistical analysis being done on exactly this subject. He’s a professional statistician (one of his recent jobs was as a “financial engineer”) who realized no major work had been done on accuracy analysis for a number of years. Eventually he was joined in the research by an actual rocket scientist (the director of one of the major U.S. government research labs), plus two more professional statisticians from Europe. You can look up the technical stuff on the website ballistipedia.com, but here are some Bookstaber’s main points:

First, statistical analysis of groups is designed to predict within a certain confidence level how a particular rifle/load will continue to perform. This confidence level is expressed as a percentage, such as 60% or 95%, with 95% obviously preferable to 60%.

Bookstaber confirmed my empirically-derived distrust of 3-shot groups, but one of his main points is that measuring the widest-shot spread in a group is a relatively poor way of analyzing accuracy: It assigns the same value to a one-inch group whether all the shots are evenly scattered inside than inch, or several cluster into half an inch, with a single “flier” outside the cluster. Instead, computing the standard deviation of the radius of each shot, from the center of a group, results in more confidence in any prediction of future accuracy.

Bookstaber mentioned the standard rifle accuracy test used for decades by the American Rifleman magazine, the average of five, 5-shot groups at 100 yards. Statistically, he found this pretty good—but if it used the standard deviation of all shots in a group, rather than extreme spread, the same confidence level could be determined by shooting fewer shots.

Shooting fewer shots is exactly what most hunters are after with 3-shot groups, but they don’t understand how the size of a typical big-game animal masks errors. What we can say is 3-shot groups averaging an inch are sufficient to produce a 100% confidence level for shooting volleyballs at 400 yards, but not enough for 100% confidence in shooting tennis balls at 300.

Many prairie dog shooters think 3-shot groups work because they expect to miss some prairie dogs anyway, but Bookstaber found “a single 3-shot sighting group will, on average, be .6 MOA from the true center.” Which is why three 3-shot groups almost always result in a much larger 9-shot group.

Around 1990, ballisticians at Speer calculated a seven-shot group provided the same amount confidence level as a 10-shot group. Bookstaber points out the “analysis was based on key parameters from very small Monte Carlo simulations done by Frank Grubbs in the 1960s. When you use better numbers – like those from the million-iteration simulations I ran for ballistipedia – you discover that 6-round groups are actually the optimum and 5-round groups are practically as efficient.”

However, most shooters won’t understand any of this, or even care. It’s been so long since ten-shot or 5-shot groups were standard, very few shooters understand they’ll always average larger than 3-shot groups from the same rifle. And neither results in many bragging-size “half-minute” groups from a deer rifle!


“Montana seems to me to be what a small boy would think Texas is like from hearing Texans.”
John Steinbeck