2008-09: Buddy Robinson played high school hockey for Gloucester Catholic in New Jersey and skated for the Hollydell Hurricanes U18 AA team. He was a teammate of Calgary prospect Johnny Gaudreau and both teams were coached by Gaudreau's father, Guy Gaudreau.
2009-10: Robinson moved to Ontario to skate for the Hamilton Red Wings in the CCHL junior A league. He scored 11 goals with 12 assists and had 62 penalty minutes in 49 games. In ten playoff games he had 1 assist with 8 penalty minutes.
2010-11: Robinson began the year with the Hamilton Red Wings before skating for the Tier 1 Nepean Raiders. In 19 regular season games with the Raiders he scored 5 goals with 19 assists and had 20 penalty minutes. He scored 2 goals with 1 assist and 2 penalty minutes in five playoff games. Robinson played 32 games with the Red Wings and scored 15 goals with 23 assists and 39 penalty minutes. He committed to playing college hockey at Lake Superior State in 2011-12.
2011-12: Robinson played in 39 of 40 games for Lake Superior State as a freshman. He scored 5 goals with 5 assists and was +1 with 37 penalty minutes. Lake Superior State finished seventh in the CCHA and swept Alaska in a first round series before falling to Western Michigan in the CCHA quarterfinals.
2012-13: Robinson signed a three-year entry level contract with Ottawa as a free agent in March of 2013 following his sophomore season at Lake Superior State and made his pro hockey debut with the AHL's Binghamton Senators. He scored 2 goals with 2 assists and was +2 with 8 penalty minutes in six regular season AHL games. The Senators were second in the East Division and had the league's fourth-best record before being swept by Wilkes-Barre/Scranton in a first round series. Robinson played in two of three playoff games with no points nor penalty minutes. He played 38 games for the Lakers in his final college season, scoring 8 goals with 8 assists, and was -10 with 48 penalty minutes. Lake Superior State finished eighth in the CCHA's final season and lost to Bowling Green in a first round series after shutting out the Falcons in the series' first game.
Robinson signed an entry-level contract with the Ottawa Senators in March of 2013.