The stairs are a choke point. If the BG (s) are coming for you they will be forced to come through a narrow space
the target zone for the perp(s) is also much smaller and he can even improvise if necessary.
in your bedroom he has no clue where to shoot and really cant except thru the door anyways. he(or they) is absolute toast if he tried to enter. I am outside naked on a cold morning with the stairs scenario...the odds are upped bigtime but I guess its doable....