Authority

A commander’s stars: +5 Hit and Avoid per star for its whole army.

Authority is a unit’s command level, in stars. Only an army’s commander’s stars count: every unit of its army, the commander too, gets +5 Hit and +5 Avoid per star, anywhere on the map, as long as the commander lives.

Your army’s commander is the chapter’s; enemy, allied and other armies have commanders of their own, whose stars give their armies the same bonus. When a commander falls, the next unit able to lead its army takes over, and a unit that changes sides fights under its new army’s commander. Parity cancels the bonus in its fights.

A unit’s own stars do nothing while it doesn’t command, and they add nothing to its skill capacity: the classes of a unit with stars already include their extra.