Baz is one of the travelling adventurers in the world of Shovel Knight.
Shovel of Hope
Shovel Knight confronts Baz who is angry that he wasn't included in the Order of No Quarter. He sees Shovel Knight and realizes that if he could beat him, he could become a knight, which leads to a boss battle with him. After you beat him, he cries his loss and Shovel Knight leaves. He's later seen with the other wandering knights (excluding Black Knight) at the end.
Plague of Shadows
In this campaign, Plague Knight ran into Baz who, once again, was angry about being rejected by the Order of No Quarter, this time because he lacked intelligence. Upon confronting Plague Knight, Baz decided to fight him as per the ironically stupid reasoning that if you defeat a scientist, you become one. This then leads to a boss battle with Baz, after which you have the option to recruit him to work in the Potionarium (the hub world). Should the player decide to recruit Baz, he'll move into the Potionarium and give you Health Tonics for free.
Specter of Torment
Baz made a brief appearance in this campaign. After the player defeats and recruits two of the knights for the Order of No Quarter, Baz breaks into the Tower of Fate and asks Specter Knight and Dark Reize to let him join, only to be harshly rejected. Deeply hurt, Baz claims that they haven't seen the last of him before running away. This is, in fact, the last time Baz is seen in this campaign.
King of Miracles