Kocinski showed exceptional ability from a young age: by seventeen he was already a factory rider for Yamaha in the AMA Championship Cup. He won the AMA 250 Grand Prix Championship three consecutive years from 1987 to 1989. At Daytona in 1989 he won the Supersport race after starting 53rd in a field of 80 riders, a result that underlined both his speed and his capacity for recovery riding. He also placed fourth at the 1988 250cc US Grand Prix after taking pole position, and fifth at the 1988 250cc Japanese Grand Prix.
Kocinski made his 500cc World Championship debut in 1989, then contested four different championships in 1990. The highlight was the 250cc World Championship, which he won in his first full season at that level, riding a Team Roberts Yamaha YZR250. The title was a breakthrough result that established him as a genuine world-class talent.
After the 250cc title, Kocinski moved into the 500cc class full-time. He finished fourth in 1991 and third in 1992, winning the final round in both seasons. During his first year in 500cc racing, he made the widely reported statement that any rider who had not won the World Championship within two years of entering the class should quit. The comment would return to haunt him repeatedly as his own 500cc title never materialized despite six seasons of effort.
In 1993, Kocinski began the season in the 250cc class with Suzuki, taking the manufacturer's first ever podium at that level, before switching back to 500cc mid-season following a falling-out with the team. He went on to win Cagiva's first ever dry-weather 500cc Grand Prix victory at Laguna Seca. After opening the 1994 season with a win in Australia and finishing third in the championship, he stepped away from Grand Prix racing when Cagiva withdrew, spending a period as a professional water skier.
Kocinski returned to world-level racing in 1996 by joining the factory Ducati team in the Superbike World Championship. Despite a difficult relationship with Ducati, he came close to winning the title in his debut season in the series.
For 1997, he moved to the factory Castrol Honda squad, delivering one of the most dominant championship campaigns in the series' history at that point: nine wins and seven additional podiums over the course of the season. The 1997 title was sealed under controversy at the final round at Sentul in Indonesia. Going into the last lap of the first race, Kocinski led teammate Aaron Slight. Slight needed the win to secure second in the championship, and briefly passed Kocinski during the lap, but Kocinski repassed him in an aggressive move that nearly made contact, taking the race win. The incident caused a permanent rift between Kocinski and both Slight and the Castrol Honda team.
Kocinski returned to the 500cc World Championship in 1998 with Sito Pons' Movistar Honda team, and again in 1999 with Erv Kanemoto's team, but did not win a race. In 2000 he raced in the AMA National Championship for Vance & Hines Ducati, then spent two years testing for Yamaha before retiring. In January 2008 he was reported to be seeking a professional ride in the AMA, SBK, or 250cc categories.
Kocinski remains one of the most naturally gifted motorcycle racers of his generation, a two-discipline world champion whose career was marked as much by its moments of brilliance as by its interpersonal controversies. His 1997 Superbike title campaign stands as one of the most effective single-season performances by an American rider in international motorcycle road racing.