Excited state absorption (ESA) is a process that occurs in many laser gain media and can significantly impact their efficiencies of operation. In this work we develop a model to quantify the effect of ESA at the pump wavelength on laser efficiency, threshold and heating. In an analysis based on the common end pumped laser geometry we derive solutions and analytical expressions that model the laser behaviour. From these solutions we discuss the main parameters affecting efficiency, such as the laser cavity loss, pump ESA cross section and stimulated emission cross section. Methodologies are described to minimise the impact of pump ESA, for example by minimising cavity loss. It is also shown that altering the pumping geometry can significantly improve performance by improved distribution of the population inversion. Double end pumping can approximately halve the effect of pump ESA compared to single end pumping, and side pumping also has the potential to arbitrarily reduce its effect.