Binaural systems seek to convey a high-definition listening experience by re-creating the sound pressure at both of the listener's ears. The use of a rigid spherical microphone array (RSMA) allows the capture of sound pressure fields for binaural presentation to multiple listeners. The aim of this paper is to objectively address the question on the required resolution for capturing an individual space. We numerically evaluated how binaural synthesis from RSMA recordings is affected when using different numbers of microphones. Evaluations were based on a human head model. Accurate synthesis of spectral information was possible up to a maximum frequency determined by the number of microphones. Nevertheless, we found that the overall synthesis accuracy could not be indefinitely improved by simply adding more microphones. The limit to the number of microphones beyond which the overall synthesis accuracy did not increase was higher for the interaural spectral information than for the monaural one.