This study investigates the optical characteristics of InGaN multiple quantum wells(MQWs) light emitting diodes(LEDs) on planar sapphire substrates(PSSs), nano-sized PSS(NPSS) and micro-sized PSS(MPSS). We obtain the results as the patterning size of the sapphire substrates approach the nanometer scale: The light from the back side of the device increases and the total light extraction becomes larger than the MPSS- and planar-LEDs. The experiment is conducted by Monte Carlo ray-tracing, which is regarded as one of the most suitable ways to simulate light propagation in LEDs. The results show fine consistency between simulation and measurement of the samples with different sized patterned substrates. Notably, light from the back side becomes larger in the NPSS LEDs. We strongly propose that the increase in the light intensity of NPSS LEDs is due to an abnormal optical distribution, which indicates an increase of extraction probability through NPSS.