Sport 45, my house is very different. I have a huge landing. I drop back to the south end and wait, and as they work their way up the stairs with their backs to me and then turn to face me that gives almost three seconds during which they couldn't even see me.
God help me if they reach that grand, central landing. They will literally own the home, with every door and every room a step or two away. Hunker down and guard the door, and if I have to save a kid, I'm almost bound to loose against several bad guys.
I have another stair well, a more traditional one, with a pantry at the top. A couple sweeps of my arm will dump about 100pounds of canned goods down the stairs into the basement(which will be black, as the light switch is next to me, and at night, there is literally no available light.
I have complete ambush and cover built in. I simply can't be hit until the bad guy has already been in direct line of sight for seconds. But I'm doomed if they bust in and catch me unawares. The rest of the home is wide open and the longest distance is maybe seven yards. I might not even make it to my concealed weapons.
Anyone who does have a traditional closed stairwell could keep a toy box, case of food, anything that could trip up a bad guy on hand. For that matter, the halon or co2 fire extinguisher will make it a pretty hostile place to be. Even a bug bomb.
The thing you have to convince yourself of is that either way, you wait in ambush, and own the high ground. They can't even hope to be prepared if they come after you, up or down stairs. You need to find out how and where to bake your stand, and if you can, put obstacles in the way aye. The kids box of wooden blocks and a couple bowling balls might just end the situation quickly and efficiently. He may be lying at the bottom, unconscious, with a broken ankle when the cops arrive. If you have three of them at ore on the stairs, good Lord, just imagine the chaos.
Sadly, in my situation, my probable choices will generally be to shoot and kill.