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\title{Statistical and Mathematical Models of Sport}

\author{rttr}

\date{24/01/11}

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\tableofcontents

\section{Introduction}

The emergence of innovative mathematical models have vastly redefined the statistics behind sport. The possibility of technqiues such as the winning fraction and upset probability is rapidly gaining appreciation. Such approaches draw several conclusions of the data such as the relationship across the four football leagues in England.

\\The first mathematical model that will be used is the winning fraction. We find that a familiar pattern occurs between the competitivness of the leagues. In recent years the winning fraction shows us that the Premiership is less competitive than the other three leagues, furthermore the other three football leagues tend be similar in competitivness.

\\In this investigation we are going to relate predictibility and parity using a recent theoretical in which the underdog wins with a fixed upset probability, this will be the other method of competitivness. We will observe that there are less upsets in the premiership than in the other football leagues which makes it less competitive.

\\In the final part of the project we introduce a network graph to compare the standard of the footballers in every league to present day. This will be created by representing the players as nodes and if two players have played for the same team a link will be connected between them. We will discover that the players in the premier league tend to be connected to oher players in the premier league. However the players in the other 3 leagues will be more linked to each league.

\section{Winning Fraction}

The winning fraction is calculated by comparing the ratio between the number of wins in a season against the total amount of games in a season. This provides us with the strength of team, if they provide a small winning fraction then it is classified as a weak team, whereas if it has a large winning fraction it is classified as a strong team. This was computed for every team in each league from 1991-2010. And an average was calculated across the four english leagues.

\subsection{Mathematical}

The winning fraction for one league in one year is calculated by the sum of the total wins divided by the sum of the total games, which is the following:.

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Any help? Thanks.