  On being told that a piece of work he thought was his discovery had
duplicated an earlier mathematician's work, Larry Shepp once replied "Yes, but
when {\em I} discovered it, it {\em stayed} discovered". In this spirit we give
discussion and probabilistic proofs of two related known results (Moon 1963,
Joe 1988) on random tournaments which seem surprisingly unknown to modern
probabilists. In particular our proof of Moon's theorem on mean score sequences
seems more constructive than previous proofs. This provides a comparatively
concrete introduction to a longstanding mystery, the lack of a canonical
construction for a joint distribution in the representation theorem for convex
order.
