Baba is a character who is first mentioned at the Coliseum in Coursair where Ryu learns that he is scheduled to participate in an upcoming fight against a girl. Ryu, wonders if this might be the same person who framed Bow, and determines to find a way to get into the competition to meet her. He eventually learns that Baba, an inhabitant of Tagwoods an annual contestant at the Coliseum, is the one who is scheduled to fight the girl. Since Baba also appears fighting Katt in the Coliseum in her prologue scene (which appears if the player waits long enough on the title screen without pressing any buttons), this suggests that the upcoming battle between them may actually be a rematch.
Ryu travels to Tagwoods to ask request Baba allow him to take his place in the Coliseum fight against Katt. Baba declines Ryu's offer and then challenges him to fight. Baba loses and accepts defeat, agreeing to Ryu's plan and gives him his axe, as proof of Ryu's identity. This will cause Ryu's name to appear as "Baba" in the menu screen until match at the Coliseum is completed.
Baba is short for Babaderu, which is Baba's full name. His full name is only shown during the fight with Katt if she is successful at taunting the player where a message will pop up exclaiming "Babaderu has lost focus." The shortening of his name is due to the character limitation with names.
Babaderu is also the romanization of his Japanese name ババデル.