Full-duplex radio technology is becoming mature and holds potential to boost the spectrum efficiency of a point-to-point wireless link. However, a fundamental understanding is still lacking, with respect to its advantages over half-duplex in multi-cell wireless networks with contending links. In this paper, we establish a spatial stochastic framework to analyze the mean network throughput gain from full duplex, and pinpoint the key factors that determine the gain. Our framework extends classical stochastic geometry analysis with a new tool set, which allows us to model a tradeoff between the benefit from concurrent full-duplex transmissions and the loss of spatial reuse, particularly for CSMA-based transmitters with random backoff. We analytically derive closed-form expressions for the full-duplex gain as a function of link distance, interference range, network density, and carrier sensing schemes. It can be easily applied to guide the deployment choices in the early stage of network planning.