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Saturday, January 14, 2006

Basic Rating System

FRAN (Football Rating Assessment Number) is calculated as follows. Every team under consideration has an integer number which expresses its relative ability. The numbers are chosen so they average 1000. For example, if you were covering 92 teams as a closed system, the total number of ranking points available would be 92,000- to be divided between the teams.

The system is initialized by giving every team a rating corresponding to its status. In the simplest case, each team could start off with 1000 points but then it would take longer to settle down.
After every game played (league and cup matches) the FRANs for both sides are re-calculated to reflect the outcome. The adjustment proceeds as follows:

Each side contributes a fixed proportion of its rating to a 'kitty' or 'pot'- rather like placing a bet on the result. We suggest the home teams puts forward 7% of its strength into this pot and the away team contributes 5%. These contributions are rounded up to the nearest whole number.
The kitty is re-distributed between the two sides according to the result. (Winner takes all; draw splits the pot.)
If the home team wins, it takes the whole amount.
If the away side wins, it takes the whole amount.

If the game is drawn, half the kitty returns to the home team, and half to the away side. (To avoid fractional values, if the kitty contains an odd number of points, the away team is entitled to one extra point.)

Now the two teams have revised ratings, which can be used to help predict performance in later games.

A quick example: A home team with 1600 points meets an away team with 1755 points, and loses. The home team contributes 7% of 1600 (112 rating points); the away team contributes 5% of 1755 (88 rating points, rounded). The pot therefore contains 200 points. The victorious away team's new rating is thus 1755-88+200=1867 points. The defeated home team ends up with 1600-112+100=1488 points. A draw would have led to the following points redistribution:

Home team- 1600-112+100= 1588 points
Away team- 1755-88+100=1767 points.

Note the following points:

It is more beneficial to beat good teams than bad ones, since they contribute a greater amount to the kitty.
Drawing is somewhat more advantageous to the away than the home team, since the home side usually contributes a greater percentage of points.
There is no overall net gain or loss of points; what is lost by one side is won by the other, and vice versa.
Neither side fluctuates by more than 7% of its rating as a reult of a single game- i.e. there is a bias towards stability.

posted by Trilby at 8:48 am
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