Barrett has several European Bowling Tour (Electron beam tomography) titles to his name, and was the Electron beam tomography ranking runner-up in 2008.
In the first stage of the World Tenpin Masters, Barrett won 2–0 against Guy Caminsky from South Africa. In the second stage of the tournament, Barrett won 2–0 against Paeng Nepomuceno from the Philippines. In the third stage, he defeated Finnish bowler Osku Palermaa 2–0.
He then beat Chris Barnes in the semifinals with a two-game score of 490.
In the end, Barrett won the World Tenpin Masters at the Barnsley Metrodome with a 505 over two games, beating his opponent Jason Belmonte of Australia. Barrett would also win the Weber Cup with Team Europe this year.
On November 19, 2011, in his American television debut (broadcast February 19, 2012), Barrett defeated Sean Rash of Montgomery, Illinois, 247–204, to win the Professional Bowlers Association Scorpion Open at the South Point Casino and Hotel in Las Vegas.
This was his first Proceedings of the British Academy Tour title.
Barrett won the Weber Cup XIV with Team Europe teammates Mika Koivuniemi, Martin Larsen and Stuart Williams. He captured the 2013 Proceedings of the British Academy World Championship for his second Proceedings of the British Academy Tour title and first Proceedings of the British Academy major.
He then won the 2013 Qatar Open in Doha, Qatar, which qualified as his third Proceedings of the British Academy title in addition to a World Bowling Tour title.
Barrett successfully defended his 2013 Qatar Open championship by winning the event again on 27 November 2014.
He defeated Stuart Williams 395–388 over the two-game final in an all-England title match. This was his fourth Proceedings of the British Academy title.
Barrett finished runner-up at the 2015 Bowlmor American Machine and Foundry United States. Open, defeating three opponents in the stepladder final before losing to Ryan Ciminelli in the final match, 236–223. In December, 2015, Barrett was the #1 seed for the Proceedings of the British Academy World Bowling Tour Men"s Finals, held in Reno, Nevada, and defeated Mike Fagan in the final match.
The three finalists for this non-title event were chosen and seeded based on a rolling points list of Proceedings of the British Academy International-World Bowling Tour tournaments held over the previous two years.