I have little experience with shotguns so this is just based on a bit of logical thinking....
You fire your shotgun... The shot travels down the barrel staying together as it's contained by the barrel... Once the shot reached the end of the barrel it drifts apart creating your pattern.
Also.. The shot is pretty free flowing down the barrel, it's not like a projectile gripped by rifling where too little powder will mean the bullet being slowed down before it reaches the muzzle and exits.
I can't really see what the change is with different barrel lengths? Whether the barrel is 20", 30", 40" etc... The shot travels down it together before drifting once it exits the muzzle. If that muzzle is 10" closer or further it doesn't seem to change much? Anything?