The rule of thumb for 20" riot barrels and 9 pellet 00 buck loads, used to be 1" of pattern width for every yard of range from the muzzle. Today's buckshot, with plastic sawdust, "chilled" or plated pellets, etc, pattern a bit more tightly. The range will rarely be more than 10 ft from the muzzle of the shotgun in the home, so the pattern will be 3" wide.
That is really not any help at hitting anyone, swiftly, while under lethal stress, in the dark, on moving, cover using targets that are shooting back, throwing burglar tools at you, blinding you with a flashlight's beam or their muzzleflashes, your ears blown out from muzzleblasts, etc.