At the age of three, Roberts learned to ski in Park City, and at the age of seven he competed for the first time in Moguls. From December 2001 he took part in the North American continental championship Nor-Am Cup. With a win and a second place he decided the Moguls discipline ranking of the Nor-Am Cup in the winter of 2002/03. Roberts made his debut in the Freestyle World Cup on January 11, 2003; in Mont-Tremblant he finished 28th and won his first World Cup points. The best result in its inaugural season was an 18th place.
Roberts celebrated his first World Cup victory on December 20, 2003 in Madonna di Campiglio . This was followed by a second place and several top 10 placements in winter 2003/04. On January 22nd, 2005 he won the second World Cup in Fernie . Due to inconsistent performance during the 2004/05 season, Roberts was not one of the favorites before the 2005 World Cup in Ruka . However, he won the gold medal in the Moguls competition just ahead of the Canadian Marc-André Moreau and the Australian Dale Begg-Smith . At the end of the season he was American champion in both Moguls disciplines.
Due to an injury, Roberts had to pause almost the entire 2008/09 season. In December 2009 he was back at the top of the world with a third place. He took part in the 2010 Winter Olympics and finished in 19th place. In the winter of 2010/11, a 10th place remained his best World Cup result.