Caches are commonly employed to hide the latency gap between memory and the CPU by exploiting locality in memory accesses. The cache performance strongly influences a system's overall performance, as this gap is large and ever-increasing. The efficiency of a given cache architecture - usually measured by its miss ratio - varies greatly depending on the software being executed. We present an efficient method to estimate the miss ratio using a stochastic model. The model takes into account the parameters of the cache architecture and a concise characterization of the software's locality. In contrast to previous approaches, we consider the replacement policy as an important component of the cache architecture. To this end, we introduce policy tables as a concise representation of replacement policies. The software 's locality is characterized by stack histograms or our extension thereof: History stack histograms, which refine stack histograms by distinguishing contexts of accesses. Simulation results on the SPEC benchmarks demonstrate the strong influence of the replacement policy on the miss ratio and the precision of our estimates: average absolute errors between 0.18% and 2.92%.