A diligent, weak-kneed life of cagey, ferocious Ty Cobb (1886-1961)--probably baseball's most spectacular player, and maybe its craziest. Ohio U. historian Alexander maintains, reasonably, that Cobb didn't get all the facts straight in his own story, My Life in Baseball; going back to the daily papers, he assiduously chronicles the scrappy young Georgian's arrival at Detroit in 1905, his 21 turbulent years as a Tiger player (to 1926) and player-manager (1926-28), his comeback-vindication with Connie Mack's Philadelphia A's (1927-28), his capstone triumph as the first player elected (over Babe Ruth) to the Hall of Fame. Some episodes get straightened out en route--most especially the 1926-27 charge, regarded by Cobb as a frame-up, that he and Tris Speaker had conspired to fix a 1919 game. (Alexander goes into why American League president Johnson wrote Cobb off, why new baseball commissioner Landis delayed in clearing him.) And Alexander also gives a close accounting of Cobb's tight, fast, shrewd style of play--the bunting, base-stealing, hit-and-run game that dominated the sport until the 1920 advent of the ""fast ball,"" Babe Ruth, and home-run mania. But on the personal side, this is feeble stuff-mostly intended to counter the impression given by Cobb ghostwriter Al Stump (whose name is consistently misspelled), in his celebrated account of Cobb's macabre last days, that Cobb was ""psychotic."" Alexander, forswearing psychoanalysis, pronounces him a ""difficult,"" ""complex"" personality--""capable of warmth, compassion,"" etc. To Stump, Cobb was unhinged by his mother's accidental slaying of his father; he was climbing in the bedroom window (thinking to catch her with a lover), she took him for a robber and shot him. But the Cobb we see was an unruly kid, always bent on winning; and, from his earliest days in the majors, dislikable and disliked. In one of the earliest incidents, he attacks a black groundskeeper who holds out his hand (Cobb later said he thought the man was drunk), then beats up on the man's protesting wife; later, he taunts Babe Ruth for his ""carelessness with his personal hygiene"" and (with reference to his dark complexion) by calling him ""nigger."" The horror stories are numberless. Readers who want the full, flamboyant flavor of Cobb will have to go back to Stump, Ring Lardner, and other eye-witnesses; this will do, provisionally, for the record.