This research explores how to improve the molecular-replacement method in crystallography, particularly for challenging cases. By using a likelihood-based function, performance could be significantly improved. There is an ambiguity in the relative phases of contributions from symmetry related molecules in molecular replacement. The required likelihood function depends on the translation searches. Correlations between sequence identity and coordinate error can be used to calibrate parameters for model quality in the likelihood functions. By setting up the true and model structure factors joint probability distribution, multiple models of a molecule can be combined. It is shown that likelihood-based targets are more accurate and sensitive. The study demonstrates that likelihood-based targets offer enhanced sensitivity and accuracy compared to previous methods, with the new multiple-model likelihood function significantly improving success rates. A new likelihood function is suitable for rotation searches.