The right span of control

What is the ideal span of control for a people manager?
i.e. how many direct reports should a manager ideally have to ensure the success of the team as a whole?

Fairly complicated question and too generic in nature to make a fair analysis. So lets' get more specific. Lets' assume that we are referring to an ITeS provider in urban India. Lets' also assume that the manager is competent enough and the overall infrastructure (support systems such as HR, finance, hardware/software needs, training programs, etc.) provided for doing the job are also appropriate. So the real question is... what may be the ideal team size for this manager, such that the team's output is consistently high?

To analyze this, I would look at the situation in 2 parts. As mentioned above, assuming all other factors are conducive and fairly constant, it really comes down to two main aspects (1) The nature of work to be performed (2) The skills and talents of the team members collectively and individually.

Here are my observations based on my real world experience over the last several years.
(1) The nature of work may be broadly classified into 4 main categories, viz. Easy, Medium, Difficult, and Complex.
EASY: These tasks would involve following pre-set procedures and rules to perform certain predictable tasks. eg. Following a pre-set script to respond to callers on the phone OR updating provided content into a webpage following a defined standard operating procedure  web template OR performing quality checks on a piece of software following pre-defined test cases.
MEDIUM: Building on the EASY category definition, medium tasks would involve using one's judgment and experience to favorably respond to non-standard situations that represent a slight deviation from predictable tasks. eg. Having to manage an aggravated caller on the phone when the pre-set script does not help OR having to modify the web template slightly to meet the precise needs of the client OR combining 2 or more test-cases to check the software in a more creative way.
DIFFICULT: Building on the MEDIUM category definition, difficult tasks would involve using one's judgement and experience heavily to favorably respond to non-standard situations that represent a major deviation from predictable tasks. eg. Having to manage a caller who is requesting for a new product / service that is just recently introduced and you do not have proper information OR having to re-write the web template completely to meet the precise needs of the client OR write new test-cases to check a piece of software.
COMPLEX: Building on the COMPLEX category definition, complex tasks would involve using one's judgment and experience to favorably respond to  situations never experienced in the past. eg. Responding to a caller's request that is in line with your business but is regarding a product / service that your organization does not yet provide OR having to architect a brand new web design strategy, a sub-set of which would be creation of several different web templates for different sections of the web portal OR having to understand the software product specifications in detail to appropriately arrive at the accurate test-case strategy, which would eventually lead to the creation of test-cases.

(2) Now let me try and plot the skills and talents corresponding to each of the 4 main categories of work complexity, viz. Easy, Medium, Difficult, and Complex. The following are generalizations assuming that the worker possesses an average to good intelligence and emotional quotient appropriate for his/her age, education and experience.
EASY: Basic education (graduation, diploma, etc) with about 0 - 6 months experience in the relevant domain should be sufficient. A lot of supervision and mentoring (~0.3 to 2 hours per day) is needed for such workers as they are typically new to the job itself and have probably just begun their careers. This individual is strictly an individual contributor.
MEDIUM: Relevant yet basic education (graduation, diploma, etc) may suffice; however about 1 to 3 years' experience in the relevant field would be necessary to proficiently handle medium level tasks. Some direct supervision and mentoring (~0.3 to 1 hour per day) may be needed. Such an individual may grow rapidly if he/she is asked to guide / mentor his junior subordinate to some extent (about 10% to 20% of his time). This person is still an individual contributor but may display inklings of people and/or project management.
DIFFICULT: An additional professional diploma, certificate or a bunch of courses relevant to the domain of specialization may be helpful, besides the basic education. About 3 to 6 years' relevant years of experience with a good mix of project types during this tenure would be preferred. Some direct supervision and mentoring (~1 to 3 hours per week) would be needed, especially in the area of working with clients and a diverse set of team members. Such an individual will grow rapidly if he/she is asked to guide / mentor his junior subordinates in a formal manner... probably with a direct line of reporting as well. This person may be an individual contributor but may also be in a junior to mid-level management position in the organization.
COMPLEX: More than any further formal education, demonstrated competence on a wide variety of complex deliverables across a diverse set of clients (national and international) becomes very necessary. 6 or more years of relevant experience is typically necessary for the individual to have accomplished the above. While some direct supervision and mentoring (~1 to 3 hours per week) continues to be necessary, more of mentoring / coaching rather than direct supervision and especially the tone and texture of mentoring is crucial. Such individuals are typically subject matter experts in their fields and/or could be in mid to senior level management positions.

Now draw a grid. X axis defines the level of complexity of tasks, therefore the approx. duration of weekly supervision/mentoring needed. Y axis defines the number of people you have on your team, per level of complexity. This should give you a fair idea of the amount of time you may need to spend directly with your teams, thereby the ideal number of people who should report to you.

Of course, you could get creative in several ways to optimize and improve your management.
(A) You may have group mentoring sessions and optimize your mentoring time. However avoid the pitfall of tending to overlook individual one-on-one sessions just because you've had team meetings.
(B) If you have a bunch of folks in the same job function / domain, at the same level of proficiency... you could improvise on your teams' reporting structure and reduce some of your direct supervision time.

While mature organizations across all industries and businesses have used several strategies like the few illustrated above; what I have shared here would hopefully help someone get started in this area of ideal span of control... in case you are looking for a starting point.