At the Breeders' Cup World Championship, fractions of a second and tiny strokes of luck define legacies. Flipping through the past performances, it's easy to see only the numbers: the morning-line odds, post positions and speed figures that quantify each race. But for the people who know these athletes best—the grooms who understand their quirks and habits, the riders who have their stride memorized, the assistants who have thought through every nuance of their daily routine--these horses represent something else entirely. "Horses are like your family," said Tony Gutierrez, who...