We present the first analytic study of stream tapping protocols, a family of protocols that provide the most efficient way to distribute videos on demand at low to medium request arrival rates, say, less than ten requests per hour for a two-hour video. The main results of this study are analytical solutions for the optimal operational points of stream tapping, stream tapping with small client buffers, stream tapping with partial preloading and stream tapping with proactive streams. In addition we introduce a new stream tapping protocol with batching that caps the bandwidth requirements of stream tapping at high to very high arrival rates.