Black hole quasi-normal mode spectroscopy with LISA

We present an improved estimate of the signal-to-noise ratio (SNR) for the gravitational waves from the ring-down phase of coalescing black hole binaries for the NASA/ESA space- borne mission LISA. The usual all-sky average assumption is relaxed. We replace the usual averages of the spin-weighted spheroidal harmonics and physical and geometrical variables by Monte Carlo values, that are computed randomly for detector---source directions, black hole orientations, polarization state, phases, etc. E.g., for a given ``radiation efficiency" $\epsilon_{\rm rd}$ we use a randomly generated ``radiation efficiency per polarization state" $\epsilon^{+,\times}$, that reflects our ignorance of the polarization state of a typical source. We then estimate the non--angle--averaged, polarization and phase dependent SNR for both Schwarzschild and Kerr black holes, and determine by how much they differ from their all--sky averages as a function of the population sizes.