No one was admitted to the lists, who could not prove himself, at least maternally, to be one of four descents and display a legitimate coat armour.

-From Inquiries into the Origin and Process of the Science of Heraldry in England by James Dalloway, p90

Essentially, in order to compete in a tournament, you had to have at least one great-great-grandfather, if not more, who was noble and bore arms.