Write amplification is a critical factor limiting the random write performance and write endurance in storage devices based on NAND-Flash memories such as solid-state drives (SSD). In this paper, we present a novel probabilistic model of write amplification for log-structured Flash-based SSDs. The impact of garbage collection on write amplification is influenced by the level of over-provisioning and the choice of reclaiming policy: we quantify the impact of over-provisioning on write amplification analytically and by simulation assuming workloads of uniformly-distributed random short writes; we propose modified versions of the greedy garbage-collection reclaiming policy and compare their performance. Finally, we analytically evaluate the benefits of separating static and dynamic data in reducing write amplification, and how to address endurance with proper wear leveling.