Scrum Master is a greatly misunderstood and under appreciated role. On most teams I’ve encountered its taken on by the PO or its ignored entirely. I’m guilty of this sin myself and when I am not ignoring it, I’m playing scrum master across way too many teams, in addition to way too many other duties, so its not done terribly well…better than nothing I suppose, but better is possible, and, I think, a good investment.
It seems to me that a Scrum Master is like a personal trainer for a group of people. Some people are disciplined and are able to get a good workout on their own, some people are less disciplined and struggle to get results at the gym. But where ever you are on the spectrum, having a personal trainer who spends time with you, helping you use the right technique and offering motivational support to help you push a bit harder on the workout or when controlling your eating habits, can have a huge impact on your rate of progress and your final result.
Without a personal trainer the groups’ results suffer not just a little, but a lot. A personal trainer that’s spread out over 20 people is better than no personal trainer at all, but much better results may be achieved by adding another personal trainer.
My guess is a good scrum master that’s not spread out can boost their team’s productivity by 20-50% depending on their proficiency with scrum, their level of interruption, and their seniority. Besides that, its more fun being more productive, so there is a morale benefit. In short, a good scrum master per scrum team readily pays for themselves.