This paper presents the Convex Goalkeeper Theorem: in a non-ergodic, single-elimination competition, managing the defensive tail adds convex value to terminal outcomes independently of time spent in the mean zone. It applies the investment philosophy developed at Convex Strategies — non-ergodicity, tail magnitude, capital liberation — to a domain where outcomes are observable, data is public, and the test environment runs for 104 matches across six weeks. Spain ranked #1 in the theorem’s structural measurement from their first group match. They won the World Cup. The model held.