He previously played in the National Hockey League with the Chicago Blackhawks, Tampa Bay Lightning, St. Louis Blues and the Colorado Avalanche.

[1] Kočí was assigned to the Blackhawks affiliate, the Norfolk Admirals, but made his NHL debut on March 10, 2007, against the Phoenix Coyotes, and amassed 32 penalty minutes in three fights.

[4] During the 2008–09 season, on October 21, 2008, David was claimed off waivers by St. Louis Blues after only playing one game for Tampa Bay.

[13] He finished the 2009–10 season with a career-high 43 games and was re-signed to a one-year contract by the Avalanche on June 2, 2010.

In leading Sparta with 132 penalty minutes, Koci also contributed with 5 assists, to earn a one-year extension with the club on May 21, 2012.