A wooden-spoon list is a compact representation of a tournament draw. It takes the form of a list of the players, ordered according to who beats whom in the tournament. Obviously the champion is first in the list. I call it a `wooden-spoon' list because any draw has exactly one `wooden-spoonist', defined as the player at the end of the longest losing chain, and that player has the `ignominy' of being identified as the last player on the list.
A simple example illustrates the theory. Suppose Monica Seles, Iva Majoli, Jelena Dokic and Karina Habšudová are the players in a four-player knockout draw. Suppose the results are as follows:
Semi-finals: Monica Seles beats Jelena Dokic Iva Majoli beats Karina Habšudová Final: Monica Seles beats Iva MajoliObviously Monica is the number one player on the wooden-spoon list for this tournament (as well as number one in every other sense of the word). Iva is second, because she lost to Monica in the final. Jelena is third, because she lost to Monica in the semi-finals, and Monica went on to win the tournament. Karina is last on the list, because she lost to Iva, and Iva lost to Monica, so Karina is at the end of the longest losing chain - the `wooden-spoonist' of the tournament.
Study the following example of an eight-player draw to cement your understanding of wooden-spoon theory:
Quarter-finals: Monica Seles beats Iva Majoli Daniela Hantuchová beats Iroda Tulyaganova Jelena Dokic beats Vera Zvonarëva Maria Sharapova beats Karina Habšudová Semi-finals: Monica Seles beats Daniela Hantuchová Maria Sharapova beats Jelena Dokic Final: Monica Seles beats Maria Sharapova Wooden-spoon list: 1. Monica Seles 2. Maria Sharapova 3. Daniela Hantuchová 4. Jelena Dokic 5. Iva Majoli 6. Karina Habšudová 7. Iroda Tulyaganova 8. Vera Zvonarëva
The wooden-spoon list has some neat properties:
Quarter-finals: Iva Majoli loses to Monica Seles Iroda Tulyaganova loses to Daniela Hantuchová Vera Zvonarëva loses to Jelena Dokic Karina Habšudová loses to Maria Sharapova Anti-semi-finals: Iroda Tulyaganova loses to Iva Majoli Vera Zvonarëva loses to Karina Habšudová Anti-final: Vera Zvonarëva loses to Iroda Tulyaganova
The algorithm for constructing a wooden-spoon list from a given draw is as follows. This is how you assign players in a 128-player draw to positions in the wooden-spoon list: