Rate of events (all sky and in the source frame) for a model that traces the star formation rate and normalized to 8  ×  10⁻⁵ events per year per Mpc³ (dashed line). The SNe rate has been re-scaled by a factor 10⁶ for presentation purposes. Also shown are the product of the rate times the optical depth for μ >  100 (solid line) and the rate of lensed events with the same apparent magnitude as a similar unlensed event at z = 0.3 (dotted line).