Mutation analysis is a well-known yet unfortunately costly method for measuring test suite quality. Researchers have proposed numerous mutation reduction strategies in order to reduce the high cost of mutation analysis, while preserving the representativeness of the original set of mutants. As mutation reduction is an area of active research, it is important to understand the limits of possible improvements. We theoretically and empirically investigate the limits of improvement in effectiveness from using mutation reduction strategies compared to random sampling. Using real-world open source programs as subjects, we find an absolute limit in improvement of effectiveness over random sampling —13.078%. Given our findings with respect to absolute limits, one may ask: how effective are the extant mutation reduction strategies? We evaluate the effectiveness of multiple mutation reduction strategies in comparison to random sampling. We find that none of the mutation reduction strategies evaluated —many forms of operator selection, and stratified sampling (on operators or program elements) —produced an effectiveness advantage larger than 5% in comparison with random sampling. Given the poor performance of mutation selection strategies — they may have a negligible advantage at best, and often perform worse than random sampling – we caution practicing testers against applying mutation reduction strategies without adequate justification.