Partial quorum systems are widely used in distributed key-value stores due to their latency benefits at the expense of providing weaker consistency guarantees. The probabilistically bounded staleness framework (PBS) studied the latency-consistency trade-off of Dynamo-style partial quorum systems through Monte Carlo event-based simulations. In this paper, we study the latency-consistency trade-off for such systems analytically and derive a closed-form expression for the inconsistency probability. Our approach allows fine-tuning of latency and consistency guarantees in key-value stores, which is intractable using Monte Carlo event-based simulations.