There have been many discussions on this forum where this topic has been discussed. I have participated in many of them. I wanted to get a thread started completely on this topic so that future forum visitors may find it. Plus I would really like to get others input on this.
I looked through the scrum guide. No where is velocity mentioned. All I actually found associated to measuring teams productivity is this statement in the section on Product Backlog under a sub-title of Monitoring Progress Towards Goal.