The rivalry existed in a more official capacity after Houston joined the now-defunct Southwest Conference in 1971, in which Rice was a charter member. Since the breakup of that conference in 1995, the rivalry has continued. In 2005, Rice joined Conference USA, of which Houston was a member, and again made the rivalry more relevant for conference titles as well. The two schools were once again in separate conferences after the 2012–13 school year once Houston joined the American Athletic Conference.
The winner of the Silver Glove series between UH and Rice receives an award dubbed the "Silver Cup Trophy." The teams played against each other for the first time in 1948. Through the 2014 season, Rice leads the series 101–80.
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Since 2002, Rice and Houston have competed for an award dubbed the "Bayou Cup" in men's basketball. The series between the teams exists with Houston leading 51–14. The majority of Rice's wins have been within the last few seasons.
Football is the largest focus of the rivalry and is the sport in which the competition between the two institutions has run the longest. Both teams are part of the NCAA'sDivision IFootball Bowl Subdivision. For many years the competition included an annual regular-season football game between the schools. It has existed since 1971, when Houston joined the now-defunct Southwest Conference, of which Rice was also a member. The winner of the game wins the Bayou Bucket, which is a full-sized trophy with a golden bucket on top. Houston leads this series 29–11. Although the last Southwest Conference football game was part of the series, the teams did not compete against each other in football from 1996 to 1998, or from 2014 to the present, as the universities realigned themselves with other conferences.
Although the first official meeting between the teams in football didn't take place until 1971, a scrimmage took place between the inaugural 1946 Houston Cougars team and the Rice Owls. The Owls, having played football since 1914 and being a part of the Southwest Conference, were a much more experienced and accomplished team than the Cougars. In a front of a crowd of thousands, the Owls easily defeated the Cougars.