We experimentally investigate the emission of EUV light from a mass-limited laser-produced plasma over a wide parameter range by varying the diameter of the targeted tin microdroplets and the pulse duration and energy of the 1-μm-wavelength Nd:YAG drive laser. Combining spectroscopic data with absolute measurements of the emission into the 2% bandwidth around 13.5 nm relevant for nanolithographic applications, the plasma's efficiency in radiating EUV light is quantified. All observed dependencies of this radiative efficiency on the experimental parameters are successfully captured in a geometrical model featuring the plasma absorption length as the primary parameter. It is found that laser intensity is the pertinent parameter setting the plasma temperature and the tin-ion charge-state distribution when varying laser pulse energy and duration over almost 2 orders of magnitude. These insights enabled us to obtain a record-high 3.2% conversion efficiency of laser light into 13.5-nm radiation and to identify paths towards obtaining even higher efficiencies with 1-μm solid-state lasers that may rival those of current state-of-the-art CO2-laser-driven sources.