Most large companies with an engineering department have rules that require anyone at a given level of engineering management to have a certain minimum number of direct reports. After some thought, I have realized that this is because there is a staggeringly exact analogy between the task of engineering management and the problem of thermal management on spacecraft. A stationary spacecraft will freeze on its shadow side and boil on its Sunward side. A spacecraft wholly in the umbra of some other object needs to have its own source of heat to replace radiated losses. All temperature-sensitive equipment needs to be mounted and monitored with careful thought to internally generated heat. The spacecraft is covered in foils, paints and blankets designed to reject solar radiation. Complex arrangements of fins and heatsinks are required to dump internally-generated heat, plus whatever solar radiation leaks in, out the night-side of the craft.
Replace the concept of "solar heat" with "ire from upper management" and the analogy is clear. A successful manager spins gently at all times, like the Apollo Command and Service Module in lunar coast mode, so that no single surface receives 100% of incident anger. The anger wattage decreases exponentially as the manager moves further away from upper management.
Direct reports are a manager's heatsinks; they cling to the main body of the craft and increase the surface area available for radiating anger away from the craft. Under some circumstances, they also form the basis of a sublimation cooling system; the coolant absorbs as much heat as possible, then is boiled into space.
Since incident anger is directly proportional to the manager's stature in the company, the heatsink area required to dissipate that anger naturally also has to increase as the manager is promoted. Company policies about the number of direct reports necessary for a manager to hold a specific title reflect the amount of anger that title is required to dissipate.