2015-06-28

The case for the Football club Elo ratings

TLDR: Common metrics to measure team strengths such as titles or points are insufficient and sometimes misleading as they do not sufficiently account for the random nature of football nor opposition strength.
The Elo ratings on this website provide a strength estimation based on results for every European club in past and present while trying to consider these factors optimally.

Where wide-spread metrics fall short

It is said that anything can happen in a single game. Even when clubs are classes apart, the outsider might win once in a while. When the difference in quality is smaller, the outcome of a single game is even less predictable.

Titles

Greatness is often measured in the number of trophies collected. While certainly better clubs win more titles than worse clubs, it is still a very unprecise measure.
In a knock-out competition - a series of single or two-legged games - only the winner survives each round, with the big random element in each single game influencing the outcome drastically.
League titles are not the best metric either. Due to the randomness of the game, winning a league by a few points makes it only a bit more likely for the first placed team to be actually better than the second placed team. If the points difference is bigger, then it is a lot more likely. In your trophy cabinet, this does not matter, both count equally and the second club gets nothing just like every other team.

Points

So should we rather look for the number of points that a club achieved in a league to determine how good it is? There are a few problems with that as well:
Firstly, the three-point-rule. Winning and losing is worth more than drawing twice while both actually mean that you are on average as good as the opposition.
Secondly, points do not take into account quality of opposition. You get more points against weaker teams than against strong teams, measures like points per game ignore that completely. You could say that in a full season this equals out for all clubs but then you still have the problem of comparing clubs from different leagues.
Thirdly, the arbitrary cut-off point. When looking at points, a game at the beginning of the season counts as much as the game last week even though the game last week tells us probably more about the current strength of a team than a game months ago. Points or points-per-game ignore that.

What Elo can do about this

Elo estimates the strength of a club based on the results against opponents and their strength.

Quantify quality

The Elo system works with only a single number, the Elo value. The difference in Elo points between two teams directly translates to a likelyhood of winning against that team. When a club with a 20% winning probability (and 80% losing probability, draw counting as half win/ half loss) wins it will gain 4 times more Elo points than when it loses so that the two clubs Elo values will remain stable relative to each other if the club actually wins 20% of the games. Should the club win more than 20%, their Elo values will converge accordingly.

Recognise over/underperforming

The expected number of Elo points gained from the next match is always zero. That means that over and underperforming over one or more games can be recognised by the number of Elo points won or lost in this/these games. That makes it very easy to actually judge how good a result or set of results has/have been.

Recent results are weighted more strongly

Every game's influence decreases when new games are played. In this way, a club's Elo rating is a combination of all its past results with games from the distant past having only a microscopic influence and newest games influencing the rating most. This effect can be increased or decreased by changing a parameter in the Elo equation and is chosen so that predictability is maximised.

Where Elo falls short

Elo does only consider results, it completely ignores how the game went. There are metrics that are less affected by randomness that actualy look into what happens on the pitch. These methods can however introduce a bias as the result is what clubs play for. How big the reduced randomness and introduced bias compare depends on the method and is not always easy to quantify.

Conclusion

In a very heterogeneous entity like European club football, Elo ratings put a club's results into perspective. Leagues vary greatly in quality and a metric that takes opposition strength into account is indispenable to compare clubs across leagues.