Using Massey Constant Rating Model: The Australian Footy League (AFL)

Introduction

Australian football is a physical game played on an oval-shaped ground between two teams of eighteen players in each team on an oval ground. A team scores six points by kicking a ball through the goal posts. The team with the most points at the end of the game wins. Australian football is the most popular sport in Australia. The Australian Footy League (AFL) is one of the most distinguished sporting series in the country. In this assignment, we are using the data related to the teams involved in the AFL. In this assignment, we have built plots and tables using Massey Constant Rating models which include a common home ground advantage H.

Aims

This assignment, using Massey Constant Rating models, aims to observe how H has varied

Methods

In Massey's Constant Rating Method, each team has a rating which is assumed constant during the window of time being examined. The ratings are chosen to give a best fit between the expected results and the actual results. If the rating of team A is RA and the rating of team B is RA, then the expected margin in favour of team A is EA = RA − RA

If the observed margin in favour of team A is OA then the difference ΔA between the observed and expected margins is

ΔA = OA − EA

We fit the model by minimising the sum of the squares of the ΔA values over all matches played.

Constant Rating Method - Building the Model I have first created a lookup table consisting of team name and a guessed rating for each team. Then I calculated the sum of squares of the ΔA values over all matches played. I have then used the Excel solver to find the team ratings which minimise the sum of squares and the common home ground advantage

Then a table of team ratings for each team in each year is created. With the help of a scatter plot, the team ratings for the current year is plotted against the team ratings for the following year and analysed. We have used the correlation formula and function to calculate and interpret the correlation coefficient.

To find any evidence for increasing consistency with team rating, I have used a scatter plot to plot the absolute value of Signed Diff as a function of Rating A. For this we have stacked all the Massey Constant Rating models of each year that we had created. I have then used Pivot Table containing three columns, Team A, Rating A, Standard Deviation of Signed Diff where the calculation is separated for each of the years 2012 to 2017 to plot Standard Deviation of Signed Diff for each team/year as a function of Rating A.

Results

• It is observed that except for years 2015 and 2016, H has varied substantially over the years.

• The table below shows the team ratings for each team in each