The rankings on this page are calculated with the Elo formula.
The Elo system is based on probabilities, each club has an Elo value based on its past performance. The difference between two clubs' Elo values represent the probability of one team winning against the other team. This probability can also be called result expectancy. Results and result expectancies can be expressed as percentages or fractions of 1. A victory is 1 (100%), a draw is 0.5 (50%) and a defeat is 0 (0%).
If two teams play each other, the result expectancy can be calculated according to the Elo formula:
E = 1 / (10(-dr/400) + 1),
where dr is the Elo point difference of the 2 clubs.
As football is a game of probabilities, where a weaker team can beat a stronger team occasionally, narrow victories are not as significant as landslide victories.
In these Elo ratings, the number of points exchanged will be multiplied with the square-root of the goal difference if there is a winner. For a draw, the factor F stays 1. The square-root-formula is inspired by WSASU.
Created: 23 Mar 2013 - Modified: 20 May 2012
The weight index determines how many points are exchanged per game. A low weight index (10 or lower) would lead to a long-term-ranking where results from the distant past still have an effect on todays Elo values. A very high value instead would be a good indicator on current shape of clubs and recent results.
This ranking uses the weight index that allows the best prediction for the next match. Simulations for every weight index have been performed and compared. At a weight index of 20, the difference between the actual results and the result expectations are at a minimum (least-squares).
In football as in other sports, the home field advantage has a measurable effect that is taken into account in these Elo ratings as well.
If the Elo formulas were applied without any home field advantage adjustment, home teams would win a lot more Elo points than away teams. To counter this effect, home teams have to be rated artificially higher until the expectation to win or lose Elo points is balanced between home and away sides. The following graph shows how many points the home team would win on average depening on how big the adjustment is.
Teams from different leagues play against each other in European competitions and exchange Elo points. This means that leagues exchange Elo points as well. However, when one observes the leagues' Elo differences over time, it becomes clear that leagues do not exchange enough Elo points just by the few European matches each year. The Elo values will then be very inert and it takes decades for formerly weak leagues to catch up with formerly strong leagues.
So these ranking will apply an additional measure: Every time a club exchanges Elo points with a club from another league, on top of the exchanged points from the clubs, the leagues will exchange points as well. A certain amount of points will be added to the league's clubs, uniformly distributed. To find out how many points are ideal, I tested what factor is required to provide the best predictability for European Cup games. The following table shows how many points are exchanged per team and per league in a European Cup game:
|Elo points factor: Team + League||NL||OP||1L||2L|
|Team's league not covered||2+0||2+0||2+0||2+0|
|Only national playoff matches covered||1½+½||1½+1½||1½+1½||1½+4½|
|One League from team's assossiation covered||1+1||1+2||1+5||1+5|
|Two Leagues from team's assossiation covered||1+1||1+5||1+5||1+11|
Clubs that are newly introduced in this system need an initial Elo value to start from.
Being relegated is defined here as not playing for one year because of real relagation or - if the league matches are not available - non-qualification for the European Cups. Teams count as relegated if there is already clear that they will not play a match in the covered competitions in the next 12 months.
A club that has not played for at least 12 months or enters the system for the first time is a promoted team. If a team is promoted it needs a new Elo value, which is set to the average Elo value of all relegated teams of its league. The club that was inactive for the longest time disappears from the system and the remaining relegated clubs are set to the same average value. In this way, no Elo points are won or lost, the league does not change its average Elo value just by promotion/relegation.
If there are more promoted clubs than relegated clubs, the last Elo value that has been given to a promoted team will be given to the new team as well.
Created: 23 Mar 2013 - Modified: 20 May 2012
The current method of calculating two-leg games takes into account the aggregate result, increases its weighting and subtracts the result of the first leg. Please see here for details.
However, there are some issues that I have with that method:
This article describes a new method of determining the home field advantage in club football. As opposed to the static method that has been applied so far, from now on home field advantage will adapt to results every day and will be different in every country and for international games.
This article examined the universal phenomenon of declining home field advantage and came up with a method to compensate for this effect. It was however a retrospectively applied manipulation and not future-proof. That is why we will introduce a new adaptive method of determining the home field advantage in Elo points.
The expected number of Elo points to be won by a club in a match should always be 0, regardless if the game is to be played at home or away. That is why the Elo value of the home side is increased by a certain number of Elo points to adjust the probabilities. If in the long run home sides won more points than away sides, then this home field advantage would be too small and would have to increase. Likewise, if in the long run away sides won more points, the home field advantage would have to decrease.
I have discovered that home field advantage can vary a lot depending on the country, so from now on every country will have its own home field advantage number. It is calculated in the following way:
For the first game historically, the home field advantage for a league is set to 100 (250 for international games). For every match, the number of Elo points that the home side won is multiplied by 0.075 and added to this value. 0.075 is not chosen arbitrarily, this is the number where the prediction accuracy is maximised.
This method creates a feedback loop that keeps the home field advantage always close to where it most realistically is. For a list of current and historic values for home field advantage, click here. Rankings will only slightly be affected, as every team plays as often at home as away, odds for single matches however will change.
Created: 23 Mar 2013 - Modified: 24 Mar 2013