It's in writing.
Section 4.5.3 of the BYU Department of Athletics Policies and Procedures Manual states: "Athletic participation, including practice and competitions, is prohibited on Sundays."
The foundation for the policy is Exodus 20:8 — "Remember the sabbath day, to keep it holy," and faith that the commandment is the word of God revealed through His prophet Moses and reaffirmed continually by prophets through the modern day.
The reason for the policy is faith-based, according to Janie Penfield, BYU associate athletic director and senior woman administrator.
She said during a recent Church News interview, "As a university that's not only funded by, but also represents the LDS Church in many ways, we have that accountability that we're straight in alignment with not only what the prophets teach but what the scriptures say. We need to be that firm example and I'm so grateful that we can have the opportunity to do that."
She added that there are individual LDS athletes at other schools around the country who do their best to live the gospel and are good examples, but at BYU, the entire institution must be the example.