The path-based coverage of a wireless sensor network is to analyze how well the network covers the sensor field in terms of paths. Known results prior to this research, however, considered only a single source-destination pair and thus do not provide a global outlook at the given network but a local feature for the given source-destination pair. In this paper, we propose a new coverage measure of sensor networks that considers arbitrary sourcedestination pairs. Our novel measure naturally extends the previous concept of the best and the worst-case path-based coverage to evaluate the coverage of a given network from a global point of view, taking arbitrary paths into account.