[math-fun] tennis anyone?

suppose 16 tennis players enter an unseeded single-elimination tournament, and that the better player wins every match. after 4 stages and 15 matches, the best player (who we call W) wins. on average, which of the two following players is better? a) the player who loses to W in the first round, or b) the player who won the first match, but then was beaten by the player who was beaten by the player who lost to W in the final round? the answer, obtained by a 16-fold integral, surprised me. erich