A real engine
Round-robins, double round-robins, and single-elimination brackets — including the season shape most leagues actually run, which is a round-robin that feeds a playoff. The rules your league actually runs on sit on top: rest days, venue blackouts, games per week, home and away balance, coaches who can't be in two places at once.
It's deterministic. The same inputs produce the same schedule every time, so when a coach asks why his team plays at 8am twice, there's an answer instead of a shrug.