DJ; Only a pattern test will say whether a donut pattern is the result in your gun & load. Generally speaking slower shot columns stay together more. This is could be due to fewer damaged pellets to some extent, but is more to do with the lesser violence of the projection of the load from the muzzle. I can't show you any tests or refer you to any learned books, but I'll bet you can find this in some writing by Gough Thomas. (Or, see the link below, from 1767) No, I can't use a CAD program. It is shot on target that makes the KD fall, and I agree with DJ that a "sawdoff" has very poor pattern control.
The size of shot also has an effect. Generally, smaller shot give wider patterns, and heavier pellets larger ones.
PTERYPLEGIA; Or, The Art of Shooting-Flying, a POEM by Mr. Abraham Markland, 1727 (3d Ed. 1767)
http://www.archive.org/stream/pteryplegiaorart00mark#page/4/mode/2up flip through to page 4, and note the following passage; Apparently even 286 years ago less powder was known to increase pattern efficiency? This poem was apparently intended to convey the knowledge of wing shooting that the French had developed to our English forefathers
"One
Third the well turn'd shot superior must
Arise, and overcome the Nitrous dust"
See also; http://www.redriverrenegades.com/black_powder_shotgun_basics.htm