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Several parameters are proposed for describing the statistical thermodynamic component of the exchange of photons between a pump and a laser beam. They are based on the occupation probability of absorbing and emitting, pump and laser levels, and are complementary to the optical cross sections. The ldquooccupation factor,rdquo f 0 , is appropriate for describing an optical amplifier in the small signal regime. f 1 is appropriate for describing an amplifier in the large signal regime, e.g., a laser. They serve to facilitate a quantitative comparison of laser gain media, operating temperatures, and choice of pump and laser wavelengths. After a simple scaling, both occupation factors have a numerical value that coincides well, in most cases, with conventional usage of the terms two-, three-, and four-level laser. They can thus serve as an unambiguous, quantitative alternative to the quasi-two-, quasi-three-, and quasi-four-level terminology. The proposed definitions are general enough to apply to many types of gain media, but are particularly useful for comparing systems with discrete levels, pumped with a narrowband source, in near-resonance with the laser wavelength. Several low-quantum-defect combinations of pump and laser wavelengths are analyzed for Er3+ , Nd3+ , Yb3+ , and Ho3+ in YAG, as a function of temperature.