The producer, in effect, has to work as a translator. You form a very tight relationship with the director and writer from the beginning, and then you are constantly communicating to the various people that begin to come into the process, as you are trying to manage to hold on to a vision that needs to be communicated over a long period of time.
Sports teaches you to understand the meaning of a team. You need to be able to work with everybody; you don't have to be their best friend. You can experience the fun of competition and driving toward a common goal without pushing to bond in some major way with each individual on a project.