The first thing we have to be sure when dealing with SCRUM master is whether they have a full time Scrum masters, and the second question we have to ask is if what do they do?
We usually don’t find a full time scrum master. Scrum master is described by scrum guide as one who teaches, facilitates and removes impediments. When the team is relatively new it takes time and the team follows scrum religiously. This is when the team needs a scrum master who can teach scrum full time.
Facilitating is necessary, though it takes only 20 to 30 % of the time. The issues tend to lessen as the team learns to resolve them.
If a person puts 100% of his efforts being a scrum master, i.e. if he is training, facilitating that takes up only 20 to 25% of his time. He has to devote himself in helping the team with their work.
The first step is to train the project managers in Agile. Try to get them to be certified scrum masters, and agile project managers, preferably from Project Management Institute.
Thus the project managers become the first scrum masters. At first the scrum master shouldn’t be assigned to one team.
Probably assign two to three teams to one project managers. Their role is to train the team in Scrum.
This has to be followed for the initial six months, until the team gets used to the concept of Scrum.
Then once you are past the first 6 to 9 months have one of the team members to be a scrum master, it would be ideal if the team was allowed to select the scrum master from their team.
Then elevate the project manager to the level of program manager. This would enable them to become accountable for cross team initiatives,
Rearrange management structure, now instead of a functional manager we have a delivery manager.
The delivery manager is now accountable for training agile.
Thus Scrum Masters was underway as a position and evolved to be a role as the team becomes more Agile mature.
The bottom line here is we have less people doing same amount of work. This is without the need of a dedicated scrum master, Along with this we need to have a contingent plan.