Randomized is the fourth foal of the unraced French Passport (Elusive Quality), a half-sister to Smooth Air (Smooth Jazz), a triple Grade 2 winner who was also placed in several Grade 1 races, and to the Grade 2 winner Overdriven (Tale of the Cat). Another half-sister, the winner Super Phoebe (Malabar Gold), is the dam of Got Stormy (Get Stormy), a triple Grade 1 winner. French Passport's produce also includes Rayas (American Pharoah), and Randomized is a half-sister to winners by American Pharoah and Shackleford.

Second dam Air France (French Deputy) won twice and bred ten winners from 15 foals, headed by Smooth Air and Overdriven.

Third dam Twin Propeller (Known Fact) was a stakes winner and had three winners from five foals, among them Air France. She is a half-sister to the Grade 2 winner Penny's Reshoot (Turkey Shoot).

French Passport has a two-year-old colt by Justify, Marginal Cost, besides a filly by Frosted plus a yearling filly by Maxfield.