In TF2, I usually wear smaller hats, especially as Sniper, to reduce my visual profile, so that I'm less likely to be seen.
But that leads me to another question: what if one is wearing a tall hat like Dr.'s Dapper Topper?
Obviously, a soldier's head only physically occupies the bottom half of Dr.'s Dapper Topper, so what happens when the top half is shot?
Does the soldier take damage from any shot anywhere in the hat?
Do non-set hats have any effect on where or how a player can be hit?