As an optically pumped device, the lasing characteristics of a spherical microcavity laser depend on the optical pumping processes. These characteristics can be described in term of the Q factor and the optical field distribution in a microsphere. We derived analytical expressions and carried out numerical calculation for Q factor and optical field. The Q factor is found to be oscillatory functions of the radius of a microsphere and the pumping wavelength, and the pumpingefficiency for a resonating microsphere is much higher than that for an anti-resonating microsphere. Using tunable lasers as pumping sources is suggested in order to achieve a higher pumping efficiency. Numerical calculation on optical fielddistribution in spherical microcavities shows that a well focused Gaussian beam is a suitable incident wave for cavity quantum electrodynamics experiments in which strong confinement of optical field in the center of a microsphere is requested, but higher order spherical wave should be used instead for exciting whispering-gallery-mode (WGM) microsphere lasers, for the purpose of favoring optical energy transferring to WGM in optical microspheres.