The demand and usage of 360 degrees video services are expected to increase. However, despite these services being highly bandwidth intensive, not much is known about the potential value that basic bandwidth saving techniques such as server or edge-network on-demand caching (e.g., in a CDN) could have when used for delivery of such services. This problem is both important and complicated as client-side solutions have been developed that split the full 360 degrees view into multiple tiles, and adapt the quality of the downloaded tiles based on the users expected viewing direction and bandwidth conditions. To better understand the potential bandwidth savings that caching-based techniques may offer for this context, this paper presents the first characterization of the similarities in the viewing directions of users watching the same 360 degrees video, the overlap in viewports of these users (the area of the full 360 degrees view they actually see), and the potential cache hit rates for different video categories and network conditions. The results provide substantial insight into the conditions under which overlap can be considerable and caching effective, and can inform the design of new caching system policies tailored for 360 degrees video.