A system that displays performance data for a computing environment. During operation, the system determines performance states for a plurality of entities that comprise the computing environment based on values of a performance metric for the entities. Next, the system displays the computing environment as a tree comprising nodes representing the plurality of entities and edges representing parent-child relationships between the plurality of entities. Then, for each parent node in the tree, the system determines counts of one or more performance states for descendants of the parent node in the tree. Finally, the system displays a graphical representation of the determined counts while displaying the parent node. In some embodiments, displaying the graphical representation of the determined counts includes displaying a circular ring comprising visually distinct sections associated with different performance states, wherein the visually distinct sections are sized proportionately with the determined counts for the associated performance states.