Babinski pent the last two seasons with the Omaha Lancers of the USHL. The Midland (Mich.) native talied 16 points on eight goals and eight assists in an injury-shortened 34 games during the 2010-11 season. The 2010 USHL Entry Draft selection came back to record 24 points on 11 goals and 13 assists in 53 games played this past campaign. He had both two game-winning goals and two power play markers while totaling 49 penalty minutes for the Lancers, who reached the USHL Western Conference quarterfinals. Babinski played for Midland High School prior to joining the Lancers and led the Chemics with 40 goals and 37 assists, including a five-goal game in the state semifinals as MHS earned state runner-up honors in 2009-10.