Depending on arrow design and tip weights, recovery can happen extremely fast. I had made some arrows up recently, that I knew should be overspined for my bow by a fairly substantial margin. The arrow seemingly flew great, hitting right where I was aiming, very consistently. As I shot it though, I noticed that it seemed pretty sensitive to my release, and anything less then absolutely perfect, id notice a slight wagging. EASY to overlook. So I shot through a paper tuner at close distance.....ugh. Huge tear showing massive stiffness, yet for the most part, my eye couldnt pick it up. I then bare shafted it....you got it....very stiff as well. I increased 50gr of head weight to begin seeing a change take place, and was still a bit stiff. With feathers alone, because of my arrow design, it was very difficult if not impossible to see without proper testing.
I took an average penetration measurement with the fletched stiff arrow in my target. Later I did the same with the properly tuned and spined arrow, being very close in weight. The tuned arrow got an average of 1 1/4" better penetration in dense foam. There is a difference, trust me.