Stronger players win more balanced knockout tournaments (Q1116595)

A player is said to be stronger than another player if he has a better chance of beating the other player than vice versa and his chance of beating any third player is at least as good as that of the other player. Recently, \textit{R. B. Israel} [J. Am. Stat. Assoc. 76, 950-951 (1981; Zbl 0489.62064)] gave an example which shows that a stronger player can have a smaller probability of winning a knockout tournament than a weaker one when players are randomly assigned to starting positions. In this paper we prove that this anomaly cannot happen if the tournament plan is a balanced one.