A second-team All-American as a senior forward, Bâby is one of just two two-time winners of the ECAC Hockey Defensive Forward of the Year Award since the honor's inception in 1993. He was also the 41st player in program history to eclipse 100 points in his career. Bâby was extremely durable, racking up his 115 points over a school record 134 games. A two-time captain, he was a key contributor to the Big Red's vaunted defense and special teams. The Big Red ranked first in the country in team defense and on the penalty kill in 2003, racking up a program-record 30 wins en route to its second straight Ivy League championship, an ECAC Hockey championship and a trip to the Frozen Four. Bâby earned the athletic department's Ronald P. Lynch Spirit Award in 2003, and he was an All-ECAC Hockey second team selection as well. He was also a two-time winner of the team's Joe DeLibero-Stan Tsapis Award (2001 and 2003), which recognizes skilled efficiency, unselfish dedication and hard-nosed competitive application, and was the 2003 winner of the Mark Weiss Memorial Award, which is given to the player who best exemplifies determination and passion. A seventh-round selection by the Atlanta Thrashers in the 1999 NHL Entry Draft, Bâby signed with the team after his Cornell career and played professionally for four seasons with the American Hockey League's Chicago Wolves and Springfield Falcons.