Large-scale survey assessments (LSAs) such as NAEP, TIMSS, PIRLS, IELS, and NAPLAN produce plausible values of student proficiency for estimating population statistics. Plausible values are imputed values for latent proficiency variables. While prominently used for LSAs, they are applicable to a wide range of latent variable modelling contexts such as surveys about psychological dispositions or beliefs. Following the practice of multiple imputation, LSAs produce multiple sets of plausible values for each survey. The criteria used to determine the number of plausible values remains unresolved and is inconsistent in practice. We show analytically and via simulation that the number of plausible values used determines the amount of Monte Carlo error on point estimates and standard errors as a function of the fraction of missing information. We derive expressions to determine the number of plausible values required to reach a given level of precision. We analyze real data from a LSA to provide guidelines supported by theory, simulation, and real data on the number of plausible values. Finally, we illustrate the impact with a power analysis. Our results show there is meaningful benefit to the use of greater numbers of plausible values than currently generated by LSAs.