I teach my clients that product managers in senior roles (VPs, product leads, or middle managers) concentrate on defining the vision and strategy for the teams based on market research, an understanding of company goals and strategy, and by looking at the current state of success of their products. The product managers without Scrum teams or with smaller teams (a UX designer and one developer, for example) help validate and contribute to that strategy for future products. After we validate the direction, we create larger Scrum teams around these people and build out solutions.