J. Henry Waugh is an accountant, albeit an unhappy one. However, each night after he comes home from work, Henry immerses himself in a world of his choosing: a baseball league in which every action is ruled by the dice.
The novel opens with the excitement of a perfect game in progress. Henry, as owner of every team in the league, is flush with pride in the young rookie, who is pitching this rarest of rare games: Damon Rutherford, "son" of one of the league's all-time greats.
When the young hurler completes the miracle game, Henry's life lights up. Giddy with happiness, Henry pushes himself and his league to the limits as he plays game after game so that he can see the young boy pitch again.
As fate would have it, the rookie Rutherford is killed by a bean-ball, a rare play from "the Extraordinary Occurrences Chart" in the game that Henry has invented and has used to see fifty-six "seasons" to conclusion. That Henry is also fifty-six marks a turning point in Henry's life. The "death" of the young pitcher on the table-top affects the real-life Henry in ways unimaginable. As Henry's personal life spirals out of control, he finally arrives at the solution that will save his league, his creation, and, ultimately, his sanity.