In Biometric Authentication Systems (BAS), the variability amongst population biometric data ensures distinctiveness, and helps minimizing false acceptance of non-subject data. However, higher variability implies temporal variations for a given subject, which can potentially reject subject data. Such variations are suppressed using feature extraction and Machine Learning (ML) techniques for improving the performance, but also reduce the adversary's effort in breaking the system (security strength) using forged data. Typically for BAS design, performance and security strength are evaluated in isolation using experimental analysis. This research provides an analytical approach to evaluate the BAS performance and strength, and their trade-off, by modeling the biometric data, and studying the effect of feature extraction and ML configurations on processing the data. Experimental analysis on 106 subjects' brain signal validates the analytical methodology results.