A Monte Carlo simulation of electron transport is used to predict the dependence of the ionization efficiency on the magnetic field strength of a planar magnetron. This offers insight into the operation of the magnetron, and it also provides two valuable practical results. First, the efficiency increases with field strength only up to a saturation level. Operating a magnetron with a stronger field strength would only lead to an undesirable loss of target utilization. Second, a scaling law is found that is useful for designing magnetrons of different sizes.