Baba Torasada served as a bushō during the Sengoku period. Torasada was a retainer of the Takeda clan of Kai Province. He received the honorary title of Governor of Izu.
Torasada served as a senior retainer of Takeda Nobutora, a sengoku daimyō, shugo daimyō, and eighteenth head of the Takeda clan of Kai. Nobutora was also the father of Takeda Shingen. Torasada received one of the characters in his name from Nobutora. However, in 1529, after the family admonished Nobutora for the killing of Kagami Toramitsu, Torasada incurred the wrath of Nobutora, and, along with Naitō Torasuke, Yamagata Torakiyo, and Kudō Toratoyo, was executed. Kudō Sukenaga became the successor to the Naitō family and adopted the name of Naitō Masatoyo. Obu Genshirō, the younger brother (or nephew) of Obu Toramasa (a senior retainer of the Takeda), became the head of the Yamagata family and adopted the name of Yamagata Masakage. The Baba family was later inherited by Kyōraishi Kagemasa, who adopted the name of Baba Nobuharu.