Not so sure about that.
What most of us are familiar with would be the later edition of Fats. But back in his heyday I think he might have been closer to the Gleeson portrayal.
Lou Figueroa
Cool pic, very suave, Gleason looking. Tevis would've never seen this Fats, as he was less than 10 years old in those days, and living in CA. Twenty years later, by the time Tevis started writing pool stories, he inevitably based characters off of players he either knew, met, or simply heard about. So rumors about a cool fat hustler up in New York from back in the 1930's could easily of seeped into his writing.