I think Walderone had it wrong. It wasn't Tevis who used him as a basis for Minnesota Fats. I think it was Gleason. They were both from New York and both hung out in pool halls and probably knew each other, or at least, knew of each other. Many of Gleason's mannerisms in the film were similar to Walderone's, particularly a neck twitch.
Very astute observation here Fran. Gleason and Fats were hanging out in NYC poolrooms during the same time period. I always wondered about that twitch. It made me think that Tevis or Gleason had to know Fats. I was friends with Tevis and he absolutely swore he had never seen Fat's play. In fact he modeled his character more on Eddie Taylor who he did see play in Louisville.
Unlike Cruise, Gleason could play! Danny D. used to play 14.1 with him in Florida and Jackie could still put a couple of racks together.