I don't think it was the function of barrel length. It was the lack of a choke.
My understanding, from what I've read not direct experience, is that you get optimum performance around 13-14 inches as the barrel is long enough for the powder to fully burn and reach maximum velocity. Much less and you're sacrificing some velocity.
Barrel length in and of itself has no bearing on pattern.
But, I've got to ask.......why would you select the 15" pattern over the 7" pattern as the "winning load"?