  A tournament is an orientation of a graph. Each edge represents a match,
directed towards the winner. The score sequence lists the number of wins by
each team. Landau (1953) characterized score sequences of the complete graph.
Moon (1963) showed that the same conditions are necessary and sufficient for
mean score sequences of random tournaments.
  We present short and natural proofs of these results that work for any graph
using zonotopes from convex geometry. A zonotope is a linear image of a cube.
Moon's Theorem follows by identifying elements of the cube with distributions
and the linear map as the expectation operator. Our proof of Landau's Theorem
combines zonotopal tilings with the theory of mixed subdivisions. We also show
that any mean score sequence can be realized by a tournament that is random
within a subforest, and deterministic otherwise.
