At age seventeen, Kocinski was already a factory rider for Yamaha, in the American Medical Association Championship Cup. He would also place fifth at 1988 250cc Japanese Grand Prix. Middle years
1989 was also the year of his 500cc World Championship debut.
In 1990 he raced in four different championships, but the highlight was winning the 250cc World Championship in his first full season on a Team Roberts Yamaha YZR250.
He was a full-time 500cc racer for the next two years, finishing fourth and third in the championship and winning the final round in both seasons. Kocinski started 1993 in 250s, taking Suzuki"s first-ever podium at this level, but switched back to 500cc mid-season after falling out with the Suzuki team
After Cagiva pulled out of Grand Prix racing, Kocinski concentrated on becoming a professional water skier. Later years
Kocinski came back to world-level motorcycle racing in 1996 when he joined the World Superbike series on a factory Ducati and came close to winning the title in his first attempt, despite falling out with Ducati during the year.
In the final round of the season at Sentul in Indonesia, Kocinski led team mate Aaron Slight going into the last lap of the first race.
Kocinski"s actions caused him to fall out with both the team and Slight. He raced at home in American Medical Association National championship in 2000 for Vance & Hines Ducati, and tested for Yamaha for the next two years before retiring. He is currently a property developer in Beverly Hills, California.
In January 2008, he was reported to have been looking for a professional motorcycle racing ride for 2008 in the American Medical Association, SBK and 250cc sections.