Driving factors behind the cool-core fraction characteristic curve. The left and central panels correspond to results from the Magneticum simulation (Box2b), where cool-core clusters are shown in blue and hot-core clusters in orange. Solid lines indicate moving medians, and dashed lines indicate 16% and 84% percentiles (1σ). Left panel: Ratio between the energy injection from the central AGN feedback and the bolometric luminosity in the [0.01−100] keV band for gas particles inside the core region. Central panel: Number of mergers undergone by the central black hole of the brightest cluster galaxy (BCG). Right panel: Sketch to illustrate the concept of how the driving factors combine to produce the characteristic shape of the cool-core fraction curve.