Who Handles Conventional Project Manager Duties in Agile Development?

Traditional project managers usually take on a great deal of responsibility. They are responsible for managing scope, cost, quality, personnel, communication, risk, procurement and more. Agile project management often puts the traditional project manager in a difficult position. He or she is told, for example, to make scope/schedule trade-off decisions knowing that a product manager or customer might second-guess those decisions if the project goes poorly. Agile acknowledges this difficult position, and distributes the traditional project manager's responsibilities. What is agile about this new paradigm is that many of these duties, such as task assignment and day-to-day project decisions, revert back to the team, where they rightfully belong. Responsibility for scope and schedule trade-off goes to the product owner. Quality management becomes a responsibility shared among the team, a product owner and Scrum Master. Other traditional tasks are distributed as well among a team’s agile project management roles. Do you think this is the right way to manage in an Agile environment?