How many scrums should a ScrumMaster manage?

Capturing a snippet of conversation I had with one of the managers...

Manager:  What does a ScrumMaster really do and what is his role? 

I:  A ScrumMaster helps with planning meetings at the beginning of the iteration, conducts daily scrums, conducts retrospectives, organizes demo/reviews, and helps the team eliminate any impediments. 

Manager:  As far as I understand planning meetings take 2 days, retrospective and review might take additional 2 days - correct?

I:  Yes

Manager: I heard the daily scrums are for 15 minutes. Correct?

I: Yes

Manager: If the daily scrums are for 15 minutes, then what does the ScrumMaster do for other 7 hours?

I: [huh?] ScrumMaster works with the Product Owner to groom the product backlog, he ensures teams follow Agile and Scrum best practices [Unit test cases, Integration tests, Code Coverage, TDD], he also helps remove any obstacles the team has, ensures that team is self-organized and gels together, etc…

Manager: This shouldn’t keep the ScrumMaster 100% busy – do you think one ScrumMaster can manage more than one Scrum?

….

Honestly, I don’t think there’s a simple answer to this question. As a ScrumMaster, I have managed multiple scrums and I have noticed that it’s difficult to provide enough justice to all Scrums due to various reasons like conflicting priorities between teams, schedule conflicts, divided attention, etc.

I also did some research on what the experts have to say about the dedicated ScrumMaster Vs shared ScrumMaster responsibilities. I was equally amazed to see that even they have a dilemma in creating a convincing case for dedicated ScrumMaster. This thread at Scrumdevelopment forum captures different perspectives on this topic.

However, here’s my take on this question – For a new Scrum team, have a dedicated Scrum Master for the first 8 to 10 iterations. This is to ensure that this Scrum team gets full attention of the ScrumMaster while they are going through “Forming – Storming - Norming” stages and until they reach the “Performing” stage. The performing stage is when the team achieves consistent Velocity, becomes intensely collaborative, is Self-organizing and empowered to make decisions. Once the team is in “Performing” stage, the ScrumMaster can then assume additional responsibilities.

Thoughts?