Seeding in the 2006 World Cup

Below is a table showing how the rankings (current and past standings) were used in combination with the previous World Cup performances of national teams, to determine their seeds for the . It uses the points obtained from the and the averaged in a 1:2 ratio respectively, added to the average amount of points that each team has at three given dates (at ratio 1:1:1), December 2003, December 2004, and November 2005. This generates a view to how well the teams have performed over the last ten years (since the rankings in 2003 include results from eight years previous to that) with a specific focus on how the teams have performed in the FIFA World Cup on previous occasions. If a team did not qualify for the previous two World Cups, their final total will be significantly less, hence the Czech Republic received a low score for seeding, despite being ranked sixth, fourth, and second in the world at the given dates.

Criticism

Pre-tournament betting odds for 2006 FIFA World Cup show enormous discrepancy between the comparative likelihood of victory in the tournament and the FIFA rankings at the beginning of the tournament, particularly for Germany, Ukraine, the USA and Iran. Comparison of one betting table with the rankings list gives Spearman's ρ=0.69.

One thing that has been criticised is that the rankings consider the performances of teams over an eight year period, and that teams' ranking positions do not correlate to their recent performances. This criticism should lessen with the introduction of a new formula, reflecting results over a four year period, from July 2006.

The perceived flaws in the FIFA system has lead to the creation of a number of alternative rankings from football statisticians including the World Football Elo Ratings and the rec.sport.soccer Statistics Foundation rankings.

FIFA's change of system for calculation of these rankings and their adoption of a different formula for World Cup seedings may be seen as an implicit admission of the shortcomings of the current formula.

The current calculation method

Calculation method from 1999 - 2006

The points allocated did not depend solely on whether a team wins, loses or draws their match, but also on the importance of the match and the strength of the opponent. A win over a weak opponent will result in less points being awarded than a win over a much stronger one. This means that a match will not result in the two or three points for a win and one for a draw, as is standard in most national league competitions. The calculation is more complex since it has to incorporate the other aforementioned factors.

Since the Rankings were revised in 1999 changes have taken place, one of which FIFA has dubbed the "scaling up", where the points on offer for a match have been roughly multiplied by ten, with the addition of more factors. Now teams can receive between zero and thirty points for a single match, and the leaders of the rankings have over eight hundred points.

Overview

The rankings were intended by FIFA to give a fair ranking of all FIFA member associations’ senior national teams. For the ranking all matches, their scores and importance were all recorded, and were used in the calculation procedure. Only matches for the senior national team were included, separate rankings were used for other representative national sides, such as the woman’s and junior teams, for example the FIFA Women's World Rankings. Interestingly, FIFA did not use the same formula to determine its rankings for women's football. The women's rankings are based on a procedure which is a simplified version of the Football Elo Ratings.

For the purposes of calculating the importance of matches, each match was divided into one of six categories. Competitions that were not endorsed by the appropriate continental association of FIFA are counted as friendlies. Each category is given appropriate weighting in the calculation in order to correctly include the importance. The six categories were:

• World Cup finals matches
• World Cup preliminary matches
• FIFA Confederations Cup matches
• Continental championships final matches
• Continental championship preliminary matches
• Friendly matches

A computer program was used to calculate the rankings, points were awarded according the following criteria:

• Winning, drawing and losing
• Importance of the match (multiplication factor)
• Regional strength (multiplication factor)

In order to try and remove the obvious advantage of having more matches, only the best seven matches each year were taken into account, as seven was the average number of matches a team plays per year. Older matches were given diminishing importance within the calculation, in order to reward teams most recent form, until after eight years, they were completely discarded, so the calculations only take into account teams performances over the last eight years.

At the end of each season two prizes were awarded by FIFA; Team of the Year and Best Mover of the year.

Winning, drawing or losing

From July 2006, three points will be awarded for a win, one point for a draw, and no points for a loss but in order to create a better ranking system, the calculations will also take into account the relative strengths of the two teams. This results in more points being awarded for beating a stronger opponent, than a relatively weaker one. It also enables weak teams to earn points despite a defeat if they manage to play well (i.e. they score goals, or there is low margin of defeat), though this is a small amount and will not secure as many points as the team that beat them. In the event of a match being decided on penalties, the winners will receive the correct points for the victory. The losers will receive points for the draw which they earned in normal time.

Number of goals

To prevent "overweighing" goals, and huge amounts of points being dealt in runaway victories, far more weighting is attached to the initial goal by each team, and progressively less points for any subsequent ones. This is done in the agreement that the goals scored are important but the most important factor is the win or loss, as in normal championship games.

Home and away games

Status of a match

Regional strength factors

The weightings (shown below) are applied in the form of multiplication factors for teams from the same continent. If teams from two different confederations are involved in one match then the factor applied is the average of the two continental weightings.

For 2005, the following weighting factors were applied:

After the 2006 FIFA World Cup, these weighting factors were amended. They now reflect the number of wins each confederation has recorded against other confederations at the last three World Cups.

Summary

Where:

• w = Points for winning, drawing or losing
• g = Points for goals scored in this game
• c = Points for the goals conceded
• a = Bonus for the away team
• s = Appropriate factor for the status of the match
• r = Appropriate factor for regional strength
• m = Points Received

( w + g + a − c ) s r = m

The number of points for a win, draw or loss, as well as for the number of goals scored or conceded is dependent on the strength of the opponent. In order not to punish a lack of success too severely, a negative points total is rounded up to 0.00.

These examples have also been used on the Elo football ratings for a fair comparison. Here are some calculation examples to show the formula being used. For simplicity in this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Note:no away team bonus, nor continental or status multiplication factors are applied.

Before the tournament the three team have the following point totals:

Example 1

Example 2

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table shows how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

As is shown in the .

Comparison with Elo ratings

Assuming team B drew with team A and lost to team C the table now stands (decimals rounded);

As you can see, as the criticism suggests, the FIFA rankings have been slow to respond to Team Bs considerable drop in form, with despite Team Cs underdog victory, the margin between it and Team B is still ten points, whereas in the Elo rankings, team C has overtaken team B. Also in the FIFA rankings, team A despite having drawn with a team significantly lower ranked than itself, has still gained 8 points, whereas in the Elo rankings has lost 4. However in the Elo rankings, team B who managed a draw with significantly higher ranked team A, have lost a position in the rankings due to only a single poor result, and have overall lost almost ten points.

Further criteria

The number of matches played

In order to prevent teams with fewer fixtures than this been disadvantaged, the calculation initially considers only the best seven results of a team. To include further results an average of them must be calculated.

For example, if a team played twelve matches, the calculation would run as;

• The best seven of the 12 results are identified
• The total score for these seven matches is calculated (X)
• The total score for all 12 matches is calculated
• This total is divided by 12 and multiplied by seven (Y)
• The total for the seven best results is added to the seven "average" results (X+Y)
• This total (X+Y) is divided by two for the final score

Previous results

Calculation method from 1993 - 1999

Awards

Team of the Year

Best Mover of the Year