Raced as a 2-year-old
This is the granddaddy of all qualifiers. At least one race at age 2 is essential if a horse is to win the Derby. Only Apollo in 1882 won the Derby without racing as a 2-year-old; only one Derby winner (Fusaichi Pegasus in 2000) since 1967 raced only one time.

Why do trainers keep trying to beat this? And, why do betters keep betting on them?