I'm a compass user from way back. When I arrowed the deer, I watched the direction it took. I watched exactly the last time the deer was in sight. Then I took a compass reading from my stand to that exact point.
I had a reading and a quadrant where it had gone. Not a 360 degree direction. So I would track to that point checking it on the compass, when I got to the location of last sighting. So even out of sight of my stand, in a heavily wooded area, I had a reading. Say it was in NW direction, I had the way it went. I would check, in small increments, to the left and right of the reading and look for the downed deer.
My theory was to look in small increments, first, and check the first 100 or so yards. If you made a good shot, you'd find a deer laying on the ground and not just a blood trail. If you didn't hit the broadside of a barn, only then would you only have blood.

Having a compass reading can then be used to backtrack exactly to where your tree stand is located. They can get lost too.