Wooden-Spoon Theory

Dr. Andrew Broad
Wooden-Spoon Lists
Explanation of the Theory

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:

	Monica Seles beats Jelena Dokic
	Iva Majoli beats Karina Habšudová

	Monica Seles beats Iva Majoli
Obviously 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:

	Monica Seles beats Iva Majoli
	Daniela Hantuchová beats Iroda Tulyaganova
	Jelena Dokic beats Vera Zvonarëva
	Maria Sharapova beats Karina Habšudová

	Monica Seles beats Daniela Hantuchová
	Maria Sharapova beats Jelena Dokic

	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:

	Iva Majoli loses to Monica Seles
	Iroda Tulyaganova loses to Daniela Hantuchová
	Vera Zvonarëva loses to Jelena Dokic
	Karina Habšudová loses to Maria Sharapova

	Iroda Tulyaganova loses to Iva Majoli
	Vera Zvonarëva loses to Karina Habšudová

	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:

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