How the IRB World Rankings are calculated
For illustration, we'll use the Six Nations match between Wales and Scotland in Cardiff on 14 February 2004, to describe the process.
Step One: Check pre match ratings
The top 10 countries in the IRB World Rankings, immediately before the match, are shown below. Wales were on a rating of 76.92 and Scotland slightly lower on 76.36.
Step Two: Allow for home advantage
To 'handicap' the home side, we treat them as though they are three points stronger than their current rating, which means that they will tend to pick up fewer points for winning, and give away more points for losing
This gives Wales a rating of 76.92 +3 = 79.92, against Scotland's rating of 76.36.
Step Three: Calculate the Rating Gap
The Rating Gap is the difference between the ratings of the two sides
Allowing for home advantage it is 79.92 - 76.36 = 3.56 (in favour of Wales).
Step Four: Check the possible Core Rating Changes
Core Rating Changes are based on the match result and the Rating Gap
As illustrated in the diagram below, with a Rating Gap of 3.56, if Wales won their Core Rating Change would be up, and Scotland's down, by 0.64
Again as illustrated below, if the game was drawn, Wales Core Rating Change would be down, and Scotland's up, by 0.36
And finally if Scotland won their Core Rating Change would be up, and Wales's down, by 1.36.
So Wales, as the higher rated side (especially allowing for home advantage) would pick up fewer points than Scotland if they won the match, and would give away more points if they lost.
Step Five: Apply weighting factors
If one side has won by more than 15 points, we multiply the Core Rating Change by 1.5. So if Wales won 30-10 the points exchange would be 0.64 x 1.5 = 0.96.
If the match was part of the World Cup Finals, we would then double the Rating Change.
What happened?
Wales won the match 23-10, so the sides exchanged 0.64 rating points, with Wales going up to 77.57 and Scotland going down to 75.72.