clock menu more-arrow no yes

Filed under:

Elo Ratings - A Brief Overview

Explaining the Elo Rating and how it can be applied to the USL

Peter Macdiarmid/Getty Images

The Elo rating is used to try to give a numerical skill to a team that looks beyond how many points a team has gained throughout the year, taking into account things such as the goal difference in a match, opponent strength, and where the game is played.  This rating is very common in games such as chess, but has since been expanded to include other competitions such as soccer.

I am working with Ryan Allen to bring you Elo ratings for the USL this year.  We have assumed a starting value of 1100 -meaning that will always be the ranking of an average team - and used a K Factor of 10.  The K factor primarily serves to make adjustments after each game greater, but as the USL is a North American league, we have adopted a K factor of 10, per the American league norm.

By using a team's rating going into the game and the final score, the equation calculates new ratings for each team.  For example, if a team rated 1105 won 2-0 at home against a team rated 1095 the following would be calculated for the home team:

New Rating = (Old Rating)*(K*Goal Difference)*(Result-Expected Result)

The goal difference is 1 if the result is a draw or a win by a single goal, 1.5 if a game is won by two, and (11+N)/8 if a team wins by 3 or more, where N is the goal difference.

The expected result is 1/(10^(-dr)/400+1).

Dr is the rating difference, where the home team is given an extra 100 points by virtue of being at home.  In this case the dr value for the home team is (1105+100)-1095 which is equal to 110.

Plug that into the expected result and you have:

1/(10^(110/400)+1)

This gives you a result of .653, which means the home team is expected to do better than a draw.  If the home team draws, their result is 0.5, which means that they lose points.  In the early stages of the season, this means that any draw will benefit the road side.  For example in the West, if Vancouver (1114 rating) drew on the road at Seattle (1072 rating), Vancouver would still gain points.

As ties occur in our ratings, we will use the following system to break them:

  1. Total games played

  2. Total points gained

  3. Total wins

  4. Goal difference