Coover made baseball on the page seem three-­dimensional, exulting in what he called the game’s “almost perfect balance between offense and defense.” He captured what Philip Roth, in a 1973 New York Times essay on baseball, called “its longueurs and thrills, its spaciousness, its suspensefulness, its heroics, its nuances, its lingo, its ‘characters,’ its peculiarly hypnotic tedium.” (The jury is still out on whether Roth’s own madcap baseball novel, “The Great American Novel,” does the same.) Coover even relished the baseball-ish names of the players he invented — Swanee Law, Tuck Wilson, Hatrack Hines. The names were what gave the league “its sense of fulfillment and failure, its emotion,” Coover wrote. “The dice and charts and other paraphernalia were only the mechanics of the drama, not the drama itself. . . . Call Player A ‘Sycamore Flynn’ or ‘Melbourne Trench’ and something starts to happen. He shrinks or grows, stretches out or puts on muscle. Sprays singles to all fields or belts them over the wall.” That’s as clear and convincing a dictum for an essential part of the novelist’s art as anything in Flaubert.

Waugh takes obsessive care in shaping the verisimilitude of his invented game, a fanaticism that will be familiar to anyone who grew up playing dice-and-cards baseball games like APBA, Strat-O-Matic or Statis Pro. These are games that take the raw materials and events of the real world — actual baseball players who perform in particular ways — and seek, through a sort of organized chance, to more or less replicate them in the imagination. Why is it that for the smallest child, the height of pleasure lies in seeing the rules of the real world playfully subverted — the toy elephant made to fly, the playground tree made to talk — but as we grow older we find such pleasure in seeing rule-bound reality re-enacted onstage, in a book or in a dice baseball game?

Indeed, Waugh doesn’t just tally the season’s statistics. He maintains what he calls “the Book”: some 40 volumes of official archives, in which he writes a narrative account of what is happening, day by day, in the league. “Style varied,” as Coover writes, “from the extreme economy of factual data to the overblown idiom of the sportswriter, from the scientific objectivity of the theoreticians to the literary speculations of essayists and anecdotalists. There were tape-recorded dialogues, player contributions, election coverage, obituaries, satires, prophecies, scandals.” His created world is fake but true to real life; it feels real, like . . . a good book.

The genius of the novel is in how Coover revels in the sun-bright vitality of the world Waugh has created, full of drink and lust and dirty limericks and doubles down the line — and yet brings Waugh face to face with its darkest truths. Waugh may be the league’s creator, but he is also its slave, and the U.B.A. is as messy and tragic as life. Players marry and break up, start dueling political parties, grow wrinkled and diseased, and die. The young phenom Rutherford is killed by a bean ball, and Waugh’s growing obsession with the league in its aftermath costs him his job, perhaps even his life. By the end, Waugh virtually disappears into the game he imagined. The extraordinary Brad Holland illustration on the cover of an earlier edition, alas not used on Overlook’s reissue, captures all of this perfectly: the image is of Waugh, at once pulling the strings of his creation (players, mitts and balls, a naked woman) and being horrifically ensnared in those same strings.