Key infection is a lightweight key-distribution protocol for partially compromised wireless sensor networks, where sensor nodes send cryptographic keys in the clear. As the adversary is assumed to be present partially at the deployment stage, some keys are eavesdropped but others remain secret. To enhance the security of key infection, secrecy amplification combines keys propagated along different paths. Two neighbor nodes W₁ and W₂ can use another node W₃ to update their key. If W₃ is outside of the eavesdropping region of the adversary, the updated key is guaranteed to be secure. To date, the effectiveness of secrecy amplification has been demonstrated only by simulation. In this article, we present the first mathematical analysis of secrecy amplification. Our result shows that the effectiveness of secrecy amplification increases as the distance between the two neighbor nodes decreases.