Evolution of the false detection rate in the eRASS1 simulation. Top panel: spurious fraction as a function exposure time and background level in the eRASS1 simulation. Each bin containing more than 100 sources is color-coded by the false detection rate. Lower panel: correction of the prediction of the spurious fraction for the eRASS1 data using the simulation due to the 10% overestimate of the background. The x-axis is binned with a progressive 10% increment. The total number of spurious sources in each bin is written as text.