The Sector Championships were championships between sports teams who competed in racquetball.
When Julian Bashir was the captain of his team at Starfleet Medical Academy, they won the Sector Championships in his final year. When questioned by Miles O'Brien about playing against other medical students, Bashir responded that they played against everybody. This included a Vulcan in the finals, whom Bashir didn't think ever actually broke a sweat. Bashir won by taking on the Vulcan with a back wall riser shot. (DS9: "Rivals")