Some years back older guys at the club showed me how improving my shotgun's fit improved my bird shooting. Clay and otherwise. There it was rough and ready. Wood glued on the stock and covered with moleskin. But if you had the money and wanted a best gun made the maker took your measurements and built the gun to fit you.
I am wondering how much gun fit affects a rifle shooter's accuracy. The adjustable stocks of Anschutz target unmentionables suggest it is a factor. Do any custom rifle builders take and use the customer's measurements?
I did gun fittings for the Orvis Company at the Orvis store in San Francisco in the 90's. A properly fit gun makes a HUGE difference in performance with a shotgun. The object of the gun fitting is to get the eye of the shooter directly over the center of the barrel and just slightly above it. As the shooter the only thing you should see would be the bead and about 4 to 6" of the barrel preceding it.
The the big trick is to get the shooter to mount the gun correctly consistently. If you can't mount the gun correctly every time, then all bets are off. When the shooter mounts the gun correctly with a gun that is properly fit, he doesn't have to make any sighting adjustments at all. At the Sandanona Shooting grounds in Millbrook, New York, Orvis offers Sporting Clays (open to the public) as well as some live hunting (if you are a member) and they also offer their shooting lessons (open to the public with reservations for lessons at scheduled dates) utilizing the instinctive shooting method. This is similar to the Churchill method but not quite so strict about stances.
If you have a gun that fits you perfectly this is a simple method. You are taught a couple of stances you can use depending on how they feel to you, but most importantly you are taught to focus on the bird or clay you are shooting at. You typically start with the shotgun held "at the ready" which has the rear stock under the arm with the muzzle pointing up just below eye level. Using clays, you call the pull and the clay launches. The point is to focus entirely on the front edge of the clay and then mount the gun. When the butt of the shotgun hits the pocket of the shoulder, if you've mounted it correctly and the gun is fit correctly, the bead will be on the front edge of that clay. Then you pull the trigger and the clay turns to dust or the bird falls to the ground.
I would use a Spot Shot in the barrel of the try-gun I used at Orvis San Francisco (no longer there) because we couldn't very well fire shotguns in the store in San Francisco. But this Spot Shot worked very well. It worked with a reflective target so I could see where the light beam hit when triggered. With someone who mounted the gun correctly I'd work out the length of pull with the clothing they expected to wear (thick jacket for winter waterfall had to be accounted for). After length of pull I'd start adjusting the drop at heel and drop at comb on the shotgun until it was hitting at the correct level but off to the side.
Once we reached that point, I'd take the shotgun and open the breech to make sure there was nothing in it hand it back to them and then to stand in front of the target. I would caution them not to touch the spot shot button (laser in the eye is no fun), but to stare at my finger the tip of my finger I was holding in the middle of my right eye, and then to mount the shotgun. From there I could see whether their eye was too high or too low in relationship to the barrel, and how far off center it was (they were not allowed to tilt their head over the stock when mounting the gun).
Usually at this point their eye was right above and just slightly to the side of the barrel. From here I could see about how much offset (for right handed shooter) they'd need. I'd then take the shotgun back and adjust the offset in an attempt to get their eye directly over the center of the barrel without tilting their head. With most people about 1/4" would do but some were as little as 1/8" and one fellow was a full 1/2" offset. So I'd check the breech, hand them the shotgun and have them mount the shotgun again staring at the tip of my finger in my right eye.
So this measurement "offsets" the stock from the straight plane of the barrel allowing you to see directly down the center of the barrel without tilting your head over or making other sighting adjustments. This is really the magic of a custom fit shotgun.
Once I adjusted the offset (or onset for a left handed shooter) with their eye centered over the barrel at the correct height with the bead in the center of the pupil of their eye, I'd move out of the way and have them mount and shoot the target about 10 times fairly quickly. When fit correctly, that red dot would hit the bullseye every time - 10 out of 10. If they missed the correct mount, it would always miss.
Then I would take the shotgun and using a level flat glass tabletop measure and write down the specification for the shotgun that would fit them. It was not uncommon for them to come back a year later to have measurements taken and a custom fit shotgun ordered for their spouse or other member of the family. It really makes a huge difference to be able to hit what you're looking at by just focusing on it and mounting the gun correctly. I could usually get the fitting done in anywhere from as little as 45-minutes to as much as an hour and a half.