We demonstrate that a simple silver coated ball lens can be used to accurately measure the entire distribution of radiative transition rates of quantum dot nanocrystals. This simple and cost-effective implementation of Drexhage's method that uses nanometer-controlled optical mode density variations near a mirror, not only allows to extract calibrated ensemble-averaged rates, but for the first time also to quantify the full inhomogeneous dispersion of radiative and non radiative decay rates across thousands of nanocrystals. We apply the technique to novel ultra-stable CdSe/CdS dot-in-rod emitters. The emitters are of large current interest due to their improved stability and reduced blinking. We retrieve a room-temperature ensemble average quantum efficiency of 0.87+-0.08 at a mean lifetime around 20 ns. We confirm a log-normal distribution of decay rates as often assumed in literature and we show that the rate distribution-width, that amounts to about 30% of the mean decay rate, is strongly dependent on the local density of optical states.