This paper focuses on the challenge of accurately estimating the subjective quality of multimedia content from noisy opinion scores gathered from end-users. State-of-the-art methods rely on parametric statistical models to capture the subject's scoring behavior and recover quality estimates. However, these approaches have limitations, as they often require restrictive assumptions to achieve numerical stability during parameter estimation, leading to a lack of robustness when the modeling hypotheses do not fit the data. To overcome these limitations, we propose a paradigm shift towards non-parametric statistical methods. Specifically, we introduce a threefold contribution: i) in contrast to the prevailing approach in subjective quality recovery assuming a parametric score distribution, we propose a non parametric approach that guarantees greater accuracy by measuring reliability per subject and per stimulus, overcoming the limits of existing approaches that measure only per subject reliability; ii) we propose ESQR, a non-parametric algorithm for subjective quality recovery, demonstrating experimentally that it has higher robustness to noise compared to numerous state-of-the-art algorithms, thanks to the weaker assumptions made on data compared to parametric approaches; iii) the proposed approach is theoretically grounded, i.e., we define a nonparametric statistic and prove mathematically that it provides a measure of score reliability. The code to run ESQR and reproduce the results in this paper is made freely available at: http://media.polito.it/ESQR.