"I'll take a shot at it (no pun intended). The large buckshot like 00 Buck has too few pellets and leaves gaps in the pattern that a coyote can literally walk through at longish ranges. Or worse yet, you just poke a hole or two somewhere... maybe in the paunch, or jaw, or who knowns where and the coyote runs off wounded. Some guys rely on what I call the "Magic Pellet Theory" in which they hope for a single lucky strike from one of the big balls to somehow hit a vital area. It's a poor plan indeed, as luck makes for a poor partner and will more than likely lead to lost coyotes. At close ranges where the pattern has held together the large buckshot can absolutely flatten a coyote - but no better than a more versatile load of mid-range shot like BB/T/No. 4BK. At long ranges the large buck is a real handicap because of the low number of pellets. Large buck such as 00 Buck really has little to offer a coyote hunter.
The smaller shot lacks anchoring power much beyond 30 yards or so. Coyotes are tough - period. Coyotes can take a lickin' and keep on tickin'. They also have thick fur which soaks up blood. Little pellets make little holes which don't leak much fluid. Coyotes have soft feet and do not cut the ground with tracks that are easy to follow like a hard hooved animal like a deer. All this adds up to lost animals unless the ranges are short to low mid-range with the small shot sizes. I've shot somewhere around a dozen with turkey loads and they ALL RAN OFF! I found most of them with some tough tracking jobs and a heaping measure of luck on my side. None were much under 100 yards, some over twice that distance. That is too far to look for one in the thick cover we normally use a shotgun in. Wounded coyotes will crawl into logs and under rock overhangs and creek banks ect. You will loose coyotes this way. If I were restricted to shot size under BB, then I would select the absolute largest shot size allowed by law and shoot the fastest load of "denser than lead" stuff like Hevi-Shot or Remington HD. AND, I would restrict the range of the shot to where I could reliably get at least a dozen of those smaller pellets within a 6" circle at point of aim in the center of the pattern. Think no more than 35 yards to at the very most 40 yards even with such a great pattern and at least 3" .12 ga magnums.
There's a good reason most experienced coyote hunters think of shot sizes from BB, T-shot, and No. 4BK for coyotes... Because these are the absolute best combinations of pellet count, hole punching size, energy retention, and penetration, for reliably anchoring coyotes. They are a reliable and historically proven recipe when combinined with a proven choke for shotgun coyote hunting. Why look elsewhere? After all, this is the end result we seek... "-----------GC
There was the nugget of information I was looking for. Thnals guys!!