So if you were hit with an arrow in a place that won't cause immediate death, such as the shoulder or thigh, what do I have coming ahead? Will they really do the whole breaking it off about six inches from the body like you see in movies? Will they cut it open to be able to pull the broadhead out? Will they sear the wound shut with a hot iron like in Braveheart? What's my outlook and likelihood of recovery?
Here is a historical account of a surgery performed on the future Henry V's arrow wound to the face.
https://medievalreader.wordpress.com/2012/06/12/when-henry-v-almost-died/
It shows that medieval medicine was reasonably practical and not nearly as thoughtless as popularly depicted. I don't think a guess at recovery chances is practical given little statistical evidence available in period sources. The best we can say is that recovery was not at all certain but far from automatically fatal.