On 4 October 2014, it was announced that Baz would move into MotoGP, with Forward Racing.[3] At Misano in September, Baz achieved his best result with 4th place in changeable conditions.[4] Baz finished his début season with 28 points, and was 17th in the final championship standings.
He made a one-off appearance at the 2018 British GP, replacing the injured Pol Espargaró in the factory KTM team.[6] However, the race was cancelled due to dangerous track conditions following heavy rain and resurfacing.
On 2 February 2021, American racing series MotoAmerica announced Baz would join the HSBK Racing Ducati team to compete in the United States during 2021, riding a Ducati Panigale V4 R.[8] Baz finished the season in fourth place.[9]
Superbike World Championship (2021–2023)
Baz acted as a replacement for the injured rider Chaz Davies, finishing 6th in race one and 9th in race two at Jerez, Spain in September. After a rider death in World Supersport, there were two main Superbike races only, with no Sprint (short distance) race.[10]
Endurance World Championship
Whilst in Europe and following-on from riding World Superbikes, Baz rode as part of a three-man Moto Ain team on a Yamaha YZF-R1 in the last round of the 2021 FIM Endurance World Championship at Most, in the Czech Republic. Together with Randy De Puniet and Corentin Perolari,[11] the team finished last (21st position) after progress was delayed by mid-race damage to the bike when being ridden by Perolari.[12]