Nicknamed "Steady Eddie" for his ability to consistently contribute 12 to 16 points a game, with the special knack of netting most of them in clutch situations, Parchinski served as co-captain during the 1952-53 and 1953-54 seasons when the Rams put together back to back 18-6 campaigns.
 
During the 1953-54 season, Parchinski was the Rams second-leading scorer behind Ed Conlin and helped Fordham clinch an NCAA at-large bid with a win over NYU in which he dropped in 25 points. He was awarded the Maroon Quill Trophy for his high-scoring performance against the Violets. He ended his career with 947 points.