The Economic Design of Sporting Contests

What is the optimal number of entrants in a race, or the optimal number of teams in a baseball league? What is the optimal structure of prizes for a golf tournament, or degree of revenue sharing for a football championship? How evenly balanced should the competing teams be in the NASCAR or Formula One championships? What is the maximum number of entrants per nation to the Olympic Games that should be permitted? What quota of qualifying teams to the soccer World Cup should be allocated to the developing nations?