**Analyzing
Accuracy**

There have been a number
of requests asking for the psi and CUP equivalents for several rifle cartridges. The list
shown contains the MAXIMUM ALLOWABLE for respective cartridges - NOT THE MAXIMUM AVERAGE.

For most of us, any
discussion of rifle or handgun accuracy is summarized in terms of groups - extreme spread
- or the measurement between the centers of the most widely spread bullet holes. Most of
the time, it is easy enough to just lay a ruler or caliper on the target and measure
between the centers of the widest bullet holes. If the group is somewhat clustered, it may
be just as easy to measure from the outside edge of the widest bullet holes and subtract
the caliber of the bullet. This is the best method and probably the only practical way to
measure a group that is little more than a one-caliber hole, albeit generally calipers
that are accurate to within .001 inch are required.

That’s how I
measured a one-holer that was fired from a stock off-the-shelf Remington Model 700 .30-06
with handloads using the then-new Hornady SST bullet. At first, I was satisfied that it
was basically a one-caliber hole, but when measured from the extreme edges of the hole and
subtracting .308 inch, the three-shot group actually tallied as .005 inch. I’ve been
shooting rifles since 1952, and that is the only one-holer to come my way.

Actually, the idea of
measuring groups from the center of the widest bullet holes is relatively new. For many
years, the U.S. Army used one of two measuring techniques: mean radius and figure of
merit.

Mean radius is sort of
involved and requires two lines, one drawn vertically through the bullet hole to the far
left, or right, and another through the center of the hole at top or bottom of the group.

Let’s assume I have
five bullet holes in the target, so I draw a vertical line through the hole on the extreme
left and a horizontal line through the lowest hole. Then I measure from the line on the
left to the center of each of the remaining bullet holes. Then I’ll do the same from
the horizontal line to the center of the holes, and then average the distances from the
vertical and horizontal lines. Let’s say the average shot is .5 inch from the
vertical line and .7 inch from the horizontal line. Add .5 to .7 and divide by 2, leaving
.6 - the mean radius.

The mean radius is a good
method for measuring groups because it tells us a great deal about the spread of the
bullet holes around the point of aim. In this example, we have determined that the five
shots landed, on average, within .6 inch of where the sights were pointed. Additionally,
that means if you aimed at the center of a golf ball at 100 yards, any one shot will hit
the ball, albeit within a .6 inch radius of the center, or point of aim.

I’m partial to this
method because it explains in easy-to-understand terms that a seemingly marginal 1.5-inch,
five-shot group from a sporting rifle actually means you can call the shot within .75 inch
from the point of aim based on a worst-case scenario. If most of the shots are clustered
within one inch, with one flyer, then the potential is there to put any one bullet within
.5 inch or so of where you want it. You can also state that rifle is capable of holding
shots within .5 inch of where the sights are pointed, indicating a bit better accuracy
than would be implied if accuracy is simply stated as the spread between the center of the
widest bullet holes.

Statistically minded
readers will also notice that mean radius is roughly the mathematical equivalent of
standard deviation and is used to measure the potential accuracy of a given load over
several samples, or groups. Either way, mean radius offers a bit more information than
group diameter, which has little to do with the field efficiency of sporting rifles.

Figure of merit was also
used by the U.S. Army but was usually
restricted to measurement of smaller groups that were somewhat clustered or contained a
larger number of shots that pretty much confused accurate measurements.

Figure of merit is simple
enough: measure the vertical and horizontal spread of the group, add them together and
take the average. So, you can have a 10-shot group that spreads 3.5 inches wide and 5.0
inches tall, for 8.5 inches and a figure of merit of 4.25 inches.

Likewise, you could have
a group that spans 7.0 inches vertical and 1.75 inches wide (I actually fired a group like
that at 80 yards with a .45 Colt revolver), for a figure of merit of 4.375 inches, a
number quite close to the sample above, but somewhat deceiving if both groups were posted
together.

No doubt, those who shoot
targets will continue to use group diameter
as the standard measurement of accuracy. For hunting, however, where we do not shoot
groups in animals, what we really want to know is how well any given rifle will hold its
shots to the point of aim or intended point of bullet impact.

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