Disregarding a hit on a wall stud, paneling, exterior wall, or insulation a 2 3/4" 12 gauge Foster slug will penetrate 12 sheets of 5/8" drywall fired from 20'. As mentioned above that is 6 walls. If you are going to be using slugs as your boogerman ammo then soft slugs like a foster with a hollow point is your best choice and don't miss. Poor ballistic coefficient maybe but at 15' that does not matter, an ounce of lead is going to take some persuading to slow down.
As for heavy set semi armored heavily clothed boogerman invading your house, its more likely to be a cop at that size. Most goombah's breaking into houses are younger, not overly well dressed and usually smaller than the average well fed suburbanite. Unless he is on something really dumb like PCP or meth a load of anything from #4 to 000 shot in their bread basket is going to stop them or at least slow them down enough the average 11 year old girl could kick his tail up around his ears. a couple of quick follow up shots to the initial shot and it will be "Clean up on aisle three." and then a trip to Sears for a new carpet.
As for heavy set semi armored heavily clothed boogerman invading your house, its more likely to be a cop at that size. Most goombah's breaking into houses are younger, not overly well dressed and usually smaller than the average well fed suburbanite. Unless he is on something really dumb like PCP or meth a load of anything from #4 to 000 shot in their bread basket is going to stop them or at least slow them down enough the average 11 year old girl could kick his tail up around his ears. a couple of quick follow up shots to the initial shot and it will be "Clean up on aisle three." and then a trip to Sears for a new carpet.