OP here. I've fallen many times, but never sprained my ankle. Usually if I have an injury from a fall at all, it's that I've skinned my knee or the palms of my hands (you can wear fingerless leather gloves if you're worried about that).

I have had two injuries that required medical attention. Dislocated my pinky finger once.

The other time I was crossing a wet wooden bridge. On the down-slope of that bridge, my feet went out from under me and I fell on my back. It hurt, so I walked a mile or so back to my car. Hadn't gotten better after a few days, so I checked in at an ER. Turns out I had cracked a rib, and that had caused a small pneumothorax. I was in the hospital for three days while they suctioned it and waited for the lung to heal. (The MD was amazed at my ability to breathe well despite everything.) When I come to that bridge now, I change to a walk.