  We study a stochastic process that mimics single-game elimination
tournaments. In our model, the outcome of each match is stochastic: the weaker
player wins with upset probability q<=1/2, and the stronger player wins with
probability 1-q. The loser is eliminated. Extremal statistics of the initial
distribution of player strengths governs the tournament outcome. For a uniform
initial distribution of strengths, the rank of the winner, x_*, decays
algebraically with the number of players, N, as x_* ~ N^(-beta). Different
decay exponents are found analytically for sequential dynamics, beta_seq=1-2q,
and parallel dynamics, beta_par=1+[ln (1-q)]/[ln 2]. The distribution of player
strengths becomes self-similar in the long time limit with an algebraic tail.
Our theory successfully describes statistics of the US college basketball
national championship tournament.
