Carril, who leads posh Princeton's underfinanced, overworked, almost A-one basketball team, generally tops in the Ivy League and recently (1975) the surprise winners of the National Invitational Tournament, isn't everyone's idea of The Coach even if his idol is Vince Lombardi. A guy who calls the Admissions Office ""Heartbreak Hotel,"" reads the poetry of Hardy and Sassoon, and cultivates a public image as the ""little schlemiel"" isn't the type to compete successfully with flashy recruiters carrying big wads and bigger promises. And he doesn't even try, White, who has succeeded in making Carril an exceptionally vivid sports figure, focuses on the man and his surroundings: Princeton is too venerable to give athletic scholarships or to relax its academic standards. So everyone works harder because Carril ""plays to win""--all the time--even though his pool of potential talent is small and the players can expect not to be lionized. Basketball cognoscenti also differ on Carril's very deliberate, methodical style of play, a style that emphasizes defense defense defense. Carril, we're told, is famous for being a prophet of doom around his school but somehow this is a very up book.