Balbay spent the last two years playing on the Under-18 Turkish national team, and he helped the squad place fourth at the 2006 European Championships.

He led Brewster to a 29–6 record and a runner-up finish at the NEPSAC Class A Championship while averaging 13.5 points and 7.5 assists per game during his senior season under coach Jason Smith.

After Balbay signed a letter of intent with Texas, Longhorns' head coach Rick Barnes declared that "Dogus is an important pickup for our program, as he will provide us quality depth at the point guard position."

With his ball pressure, teams have a difficult time running offense against Texas, and Balbay has taken more than one quality point guard out of the game this season.

His strength, versality, defensive prowess and speed is said to resemble Fenerbahçe and national player Ömer Onan.