About AFL Glicko Ratings

May 29, 2020

Hello all. After discovering Footy Maths Institute a many number of years, and having a deep passion for footy analytics, I decided to make my own predictive model for the AFL at the beginning of this year. This first post will discuss how my model works.

1. Glicko Ratings

Glicko ratings are a rating system created by Mark Glickman as an improvement on traditional Elo ratings. Glicko ratings differ from Elo ratings because of the new parameter introduced by the former, rating deviation, which measures the reliability of the ratings.

2. Determining Rating Deviations

Rating deviation is found from this formula:

RD=\min \left({\sqrt {{RD_{0}}^{2}+c^{2}t}},350\right)

where RD is the new Rating Deviation, RD_0 is the old Rating Deviation and c is a constant based on a reliability of a team's rating over time and t is the amount of time periods that have passed.

3. Determining the New Ratings

The new ratings are calculated by these formulae:

$r=r_{0}+{\frac {q}{{\frac {1}{RD^{2}}}+{\frac {1}{d^{2}}}}}\sum _{i=1}^{m}{g(RD_{i})(s_{i}-E(s|r_{0},r_{i},RD_{i}))}$

where:

$g(RD_{i})={\frac {1}{\sqrt {1+{\frac {3q^{2}(RD_{i}^{2})}{\pi ^{2}}}}}}$

$E(s|r_{0},r_{i},RD_{i})={\frac {1}{1+10^{\left({\frac {g(RD_{i})(r_{0}-r_{i})}{-400}}\right)}}}$

$q={\frac {\ln(10)}{400}}=0.00575646273$

$d^{2}={\frac {1}{q^{2}\sum _{i=1}^{m}{(g(RD_{i}))^{2}E(s|r_{0},r_{i},RD_{i})(1-E(s|r_{0},r_{i},RD_{i}))}}}$

Where RD_i is an opponent's Rating Deviation, r_0 is the old rating, r_i is an opponent's rating, and s is the result of a match.

As shown above, this calculates the expected value that each team wins over the other and this is where my predictions come from. This formula may look familiar to you, this is because it is the same as the formula used for the Elo system with the added function to adjust for Rating Deviation. Not listed above in the formula is the addition of a 30 rating point bonus to the home team in calculating the expected value.

4. Determining the New Rating Deviations

New Ratings Deviations is calculated by this formula:

RD'={\sqrt {\left({\frac {1}{RD^{2}}}+{\frac {1}{d^{2}}}\right)^{{-1}}}}

5. Variables

The only variable in these formulae which can be altered is the c value. I have chosen 20 after some experimentation.

6. Margin Prediction

As this is an Elo-based model, I have used The Arc's margin formula (sorry for the theft I guess).

7. Goals

The main goal of this blog is to make it into Squiggle's tipping competition. I hope to be able to maintain this blog and to post weekly updates on the model. Currently, I am unable to make my Round 2 predictions as AFL Tables has not updated yet.

AFL Glicko Ratings