Baba is the leader of the B-Kings Gang; a small crew of thugs that extort money from pedestrians on the streets of Kamurocho and do small time dirty work for various Tojo Clan families (most notably the Atobe Family). Baba, along with the rest of his gang, has a great passion for baseball; a sport he practices constantly at the Yoshida Batting Center.
In 2005, B-Kings member Takashi tried to leave the gang to elope with his girlfriend Kyoka Atobe; the daughter of the Atobe Family patriarch for whom the B-Kings frequently did grunt work. Since Kyoka had stolen some of her father's money to facilitate their escape, the Atobe Family had men prowling the streets of Kamurocho to find the couple. They also tasked the B-Kings with aiding in tracking down and capturing their runaway member and the patriarch's daughter.
Baba and a group of his lackeys managed to find Takashi in the Yoshida Batting Center right after he'd gotten into a fight with Kazuma Kiryu. Since Takashi was the illegitimate son of the Florist of Sai, whom Kiryu owed a favor, the yakuza protected Takashi from his former gangmates and fought off Baba and his friends to give Takashi time to escaope.
Later on, Kiryu would run into Baba and his friends again while they were being shaken down by some yakuza from an unspecified family. Feeling bad for having beaten Baba and his crew before, Kiryu helps them fend off the men who'd been harassing them. Though Baba is still somewhat angry with Kiryu for beating him before, he nonetheless thanks him for the help.
In 2010, Kiryu received an email calling him to the Yoshida Batting Center for a meeting with somebody who referred to themselves as the "Twisted Curve King". As it turns out, the email was from Baba, who; in the years since his showdown with Kiryu, has left the gang life behind and become a professional baseball player.
Despite his success, Baba's defeat at Kiryu's hands 5 years prior still haunts him, so he challenges Kiryu to hit a homerun against one of his famous "twisted curve" pitches. Having a little time on his hands, Kiryu agrees and; much to Baba's shock, he manages to homerun one of his curveballs.
Impressed by the fact that Kiryu has managed to beat him again in spite of the fact that he had the advantage, a newly invigorated Baba decides to take a break from baseball so that he can perfect his pitching even further; hoping that someday he'll finally be able to beat Kiryu.