Directed evolution (DE) is a versatile protein-engineering strategy applicable to proteins like enzymes, antibodies, or viral vectors. Starting from a library containing billions of random variants, DE screens them against a chosen task over multiple rounds until they converge onto a few variants with desired properties. Today, DE benefits from deep sequencing, allowing us to monitor millions of distinct variants through the screening iterations. Nevertheless deep sequencing data are noisy and it is often difficult to understand if the selection process has yet converged onto reliable results. As a consequence, experimentalists are compelled to increase the number of selection rounds or even to replicate the experiments. Here, we propose ACIDES (Accurate Confidence Intervals to rank Directed Evolution Scores), a combination of statistical inference and in-silico simulations to: (i) reliably estimate the selectivity of individual variants and its statistical error using the data from all available rounds; (ii) identify which variants among the best ones are worth keeping for further tests; (iii) quantify if DE has converged onto the few variants with desired function or if additional experimental rounds/replicates or deep sequencing are needed. The latter point allows for integrating ACIDES into the experimental pipeline to avoid unnecessary, costly and time-consuming experimental efforts. To showcase our method we re-analyze public datasets ranging from DE of viral vectors to phage-display or yeast competitive growth experiments. Lastly, we benchmark our method against previously proposed approaches in the literature.