Here's the answer, taken from a great 2011 article by contributor and shooting expert Jay Langston.
A rule of thumb holds that you must put at least four pellets that retain about 4 foot-pounds of energy into a gobbler’s head and neck for a clean kill. Delivering that much force should cause enough trauma to kill the turkey.
When picking shot size, remember that the number of pellets in a charge makes a difference in how many fly downrange for a relative load. Again, more is better, with the caveat that you must pick a sufficiently large pellet to deliver the requisite energy and penetration at ranges at which you’ll be shooting. My favorite shot sizes are No. 5 for lead and No. 6 for various tungsten alloys. That preference comes after firing more than 11,000 rounds of turkey ammo at targets and game.
Pattern density, or the number of hits on target, is the best measure of determining the effectiveness of your gun and load. Years ago, I started using 10-inch circle patterning targets to test the effectiveness of turkey guns and loads. Previously, I’d used Winchester turkey patterning targets with 30-inch scoring rings. Those were holdovers from years of patterning shotguns for wing-shooting. They were designed to catch most of the load and determine the percentage and density of pellets fired at a clay bird. Depending on the percentage of pellets within a 30-inch circle, it also told the degree of choke: full, modified, improved or other. The larger targets also let you find the core density of the pattern and indicate the point of impact in relation to the point of aim. Determining point of impact ends their practical usefulness, however.
When comparing patterns, I shoot at blank paper at 40 yards and draw a 10-inch circle around the densest portion of the pattern. It doesn’t matter if the pattern is at the center of the spot where you aim, provided you can adjust the sights to compensate. If the center of density stays in the same place from shot to shot, sight adjustment will line things up later.
The area of the preferred 10-inch-circle target is many times smaller than the older, larger targets, so you can count fewer pellets to derive comparative results. This also saves time. Pellets outside the 10-inch area are wasted when it comes to killing a turkey. Conversely, using scoring ring smaller than 10 inches won’t provide enough information about the gun and load’s performance.
Using the outline of a turkey’s head for a scoring ring is a poor way to test a turkey gun. It’s not large nor concentric enough to give statistically comparable data, and it might penalize an otherwise good performer.
My rule of thumb for performance is whether a gun, choke and load can put 100 pellets inside a 10-inch ring every time. That many pellets assures that a bird will die quickly if your aim is true. It doesn’t matter which size shot you use, provided there are 100 pellets in the circle. Of course, smaller shot sizes with higher pellet counts per ounce will put more pellets in the ring than larger sizes. It’s wise to limit your maximum range to the distance where pellet count is less than 100.