Like Tommy Heinsohn and Togo Palazzi, who both consider themselves Celtics for life, Bill was from NJ, specifically Passaic. He had very weak eyesight which prevented him from playing basketball himself but his love of the game led him to become one of the pioneer promoters, historians and authors of the game.
After graduating from the University of Rhode Island, he became public relations director at Rhode Island State College and joined the Celtics in the same capacity in 1946. Mokray gathered statistics and wrote articles for Converse's Basketball Yearbook, founded and was editor of The Official NBA Guide and authored the history of basketball for the Encyclopedia Britannica.