How is it akin to rolling several dice specifically?
Each pair of dice has the same odds of coming up with a given number between 2 and 12 for each roll. Each variable in the shooting system (rifle + ammo + human) has a few variables; the odds of any one being somewhere between zero and maximum closely equate to dice rolling numbers from 2 to 12 for most of the Gaussian probability curve. The rolled dice numbers are on a line at some clock face value with 7 at the middle representing zero, 2 at one end for a maximum minus deviation from near zero deviation and 12 at the other end representing a maximum positive deviation from zero.
How many dice is "several"?
Several pairs are involved; each with different amounts of MOA values for each number of spots on the dies:
Pair 1 = Human holding the rifle; determines how far and what direction the bore axis at the muzzle moves from where it pointed when the firing pin strikes the primer. Each die number's worth 1/10th MOA or more depending on how well the human consistently holds and fires the rifle from shot to shot. Variation axis is mostly horizontal but some will be vertical.
Pair 2 = Bore axis offset from center of mass that holds the barrel; includes stock, action and shooter. The more that axis is off the center of mass that holds it, the more it will change the bore axis before the bullet exits. The bore axis does not point to a place above the aiming point equal to bullet drop at range plus sight height above bore axis when the primer fires It points there only when the bullet exits the barrel.
Pair 3 = Cartridge case effect on where muzzle points upon bullet exit. If the case head is out of square with the case axis and not parallel with the bolt face, it will smack the bolt face at some point around its perimeter. That shock makes the barreled action whip on the axis that point is from chamber center. How much depends on the force imparted as well as if it's in line with the bolt lugs. If 90 degrees from a 2-lug action lug center line, the whip amount will be the greatest. Die numbers are in 1/10th MOA increments. 3- and 4-lug actions reduce this problem.
Pair 4 = Bullet consistency in velocity, weight shape and balance upon exit from the barrel. If not perfectly balanced, they'll jump off the muzzle axis upon exit in some direction due to centrifugal forces and have lower ballistic coefficients. Faster ones will drop less than slower ones. Effect increases with range. Unit value can be from 1/100th to 1/10th MOA for each number on the rolled dice. It's mostly in the vertical plane. BC's for a given bullet can vary 1% in good match bullets, more in hunting and arsenal bullets. Bullets not started straight into the bore will be distorted and unbalanced a little bit; they'll take off in the same direction if their runout high point is consistent from shot to shot as it's indexed in the chamber. Primer and powder has to perform the same for each shot so the pressure curve is the same from shot to shot. Weak firing pin springs and/or shallow dented primers cause greater muzzle velocity spreads.
Pair 5 = Atmospheric conditions. Winds blow the bullet mostly sideways. Thicker air density slows the bullet down and it drops more for a given range. Amount per unit varies but can be calculated with ballistic software.
Pair 6 = Barreled action unrestricted in its vibrations; barrel totally free floated. If not, then this pair of dice represents how much the barrels vibrations are altered by some pressure point on it or the receiver is not positioned exactly the same in the stock for each shot. Unit amount per number on the dice can be 1/100th to 1/10th MOA depending on the severity of the issue.
What is the confidence interval of his ladder test? His group test? Both together?
What is the confidence level of his approach?
With only one shot per load, I think all are about as close to zero as one can get. He could've verified how good of a ladder test he made had he shot one or two more the same way. If their results had a 10% spread across them, then I think it would have a very high probability of being a good test. I've yet to see anyone's ladder test data from 3 identical sessions proving their worth having less than a 10% spread across them. One shot does not constitute a group.
During your design of load experiments, what confidence level and interval do you achieve?
I think a 95% confidence level is attained when I shoot 20 shot test groups with a given load that 19 out of 20 such groups will be no more than 12% larger to 11% smaller.
A 3-shot perfect triangle group at 100 yards with .5 MOA between shot holes has a real accuracy level somewhere in the range from approximately .2 MOA to .8 MOA according to:
Closed Form Precision - ShotStat
I've never worked up any load for .308 Win or a couple of 30 caliber magnums for different bullet weights save for one new bullet for which no load data had ever been developed outside of Sierra Bullets test range. Just used the same ones the match winners and record setters used. Shot test groups as small as any across several barrels.
Having oft times seen benchrest match results for the top 10% in aggregate group average sizes over the years, it's easy for me to see that their 5- and 10-shot group sizes fired at all ranges have the largest groups several times bigger than the smallest ones. And rarely is the smallest one in a given match the first group shot. Go to:
http://benchrest.com/showthread.php?93618-2015-NBRSA-Nationals-Complete-Results
. . .then open each file and check all the group sizes for the top 10% in each match. Do your own grade school math to see the range of sizes they are.
A favorite "statistical improbability" is the record 100-yard 5-shot group of .0077" held by someone who holds no other records
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