Sometimes it’s good to state the obvious: the team which scores more goals than its opponents wins more games. As such, we start by investigating a simple question: what is the relationship (the correlation) between a team’s goal difference and the number of points it can expect to earn over a season? We will look at some examples from the major European championships since 2002, looking for the general pattern and for what might constitute exceptions to the rule.

We start with the English Premier League, looking at seasons 2002-2003 through 2014-2015. You can hover over the graph to see to which team corresponds each data point (The year throughout will refer to the end of the season).

## It’s a line!

If you enjoy when things line up nicely, a picture like this should put a smile on your face. It’s not perfect, there is noise which we’ll talk about later, but the trend is clear and nicely approximated by the line of best fit (or trend line, or regression line) we added to the graph. This is a really good example 1 of a linear correlation.

Of course we knew there must be a general relationship between goal difference and points earned but the actual shape of this relationship has a couple of consequences we’ll take a look at. We start with the equation of the line of best fit:



If you remember your middle school math (I won’t blame you if you don’t, no judgment here!) you know that a line can be described by two parameters: its slope and its y-intercept, in our case about 0.6 and 52 respectively. What does each of these quantities mean?

The intercept has a simple interpretation: a goal difference of 0 will, on average, allow a team to accumulate about 52 points over a season. Two almost perfect examples would be Tottenham 2009 and Charlton Athletic 2004. In fact, since each season the average goal difference is necessarily 0, this also turns out to be the average number of points earned by teams through the last 12 seasons.

What about the slope then? It gives us the rate at which a change in the goal difference translates into a change in the number of points earned. To be more specific, an increase in goal difference of 1 goal will translate on average in an increase of 0.6 points in a team’s tally by the end of the year. If you don’t like fractions of points here is an example: we’ve seen that a team with a goal difference of 0 earns on average 52 points. Then a team with a goal difference of +10 can expect to obtain on average 6 or 7 more points and reach the 58 points mark (Liverpool 2005 is a close fit here).

## Some bold predictions

A surprising aspect of this relationship is how well it works even at the extreme ends of the spectrum: we can thank Derby County in 2008 for giving us a near perfect validation of our model at such low end, a true performance! At the other end, though it may be tappering off a little bit for the highest goal differences, Manchester City, Manchester United and Chelsea have all been performing according to expectations throughout the years.

This leads us to a prediction: in the future, a team may lose all of its games and end up with a grand total of 0 points. In order to achieve this anti-miracle, we project that our lousiest of all teams will have to be outscored by more than 80 goals. Maybe a perfect storm of all that went wrong for Derby County 2008, Arles-Avignon 2011, Pescara 2013, Freiburg 2005 and Cordoba 2015 will allow us to witness such a feat? Meanwhile, another team may win all of its games in the future and reach the 114 points ceiling. If our trend line is to be believed, such a team would have to score about 95 more goals than its opponents over the season 2.

This might look like an overkill, since it would mean our team would have to outscore its opponents by an average of 2.5 goals per game, which sounds like unnecessary violence. After all scoring one more goal than the opposition each game would achieve the same result. However, the goal difference should be seen as a measure of the intrinsic worth of a team. As such, history seems to be telling us that only a team that is able to win its games with an average goal difference nearing +3 per game has a good chance of being able to win them all by the end of the season. If it “only” scores one more goal than its opponents on average, odds are it will end up within 10 of the 75 points mark, which most of the time has meant finishing somwhere between 5th and 2nd place and is in any case a far cry from 114 points.

## So much noise…

What about the deviation from our line of best fit? From a statistical point of view it is relatively limited, however these small variations can have a large effect when we look at a team’s final ranking. In order to understand this noise better, we will look at a plot of the error, that is, the difference between the actual outcomes and what the line predicted, also called the residuals. We switch to the French Ligue 1, you’ll find a plots for all the major leagues near the end.



You can switch back and forth between the errors graph and the original one to get a feel for how they’re related. In the errors graph, the horizontal axis still corresponds to the goal difference, while the vertical axis now measures the error in number of points.

The key observation here is that the error, the variation about the line, seems to be truly random. It is spread about the horizontal axis uniformly, meaning there’s no difference in how teams translate goals into points whether their goal difference is -30 or +30 4. In addition there are more teams within 5 points of the line than between 5 and 10 and very few teams farther away 5. This is again a sign of “good” randomness.

Having said that, 10 points above or below is a large margin. For example, if we take a look at Monaco, in 2003 their goal difference was 33 and they underperformed slightly ending up earning 67 points, about 8 points below what they could have hoped for. In 2014 however, their goal difference was one goal lower at 32, yet they ended up with 80 points, about 5 points higher than expected. That’s a 13 points spread for roughly the same goal difference. Still, in both cases Monaco finished at second place, due to the mysterious relationship between points and ranking, but that’s a story for another article.

And then we have the most striking outlier: the Olympique de Marseille 2013. They finished the season with 71 points and a goal difference of only +6! That’s more than 15 points above the prediction, meaning we could have expected them to end up with about 56 points. This would have meant ending at 7th place that season, just above Bordeaux, which had the same goal difference and “only” 55 points. Instead, they finished 2nd with a goal difference that is 17 points lower than Lyon at 3rd place. In fact, Saint-Etienne which finished 5th could have been even more disappointed with a goal difference of +28, 22 goals above Marseille’s and the second best that season. It would be interesting to see how they managed to buck the trend so strikingly and we’ll try to spend some time analyzing their season some time in the future.

## The other championships

Finally, we’ll let you compare the various European championships, see what the trend line is in each case and how much the real outcomes deviate from the model. Some remarks:

• The Bundesliga consists of only 18 teams and as such cannot be compared exactly with the other championships. For a similar reason, our record starts with the 2005-2006 season for Italy, corresponding to the extension of the Serie A to 20 teams.

• For the Italian Championship, we removed the points penalties for the teams that were ensnared in the infamous 2006 Serie A scandal. This might have affected slightly the outcome of these seasons.

• We added the coefficient of determination $R^2$ for each graph. If you don’t know what it means (yet!), suffices to say that the closer it is to 1 the better our line fits the data. Anything above 0.9 is a sign of an extremely good correlation.



We won’t go over each championship’s specificities for now, but here are a few pointers:

1. The slope of the line varies greatly between championships, from 0.60 for Germany and Spain to 0.74 for Italy. This means that goal difference translates into points at a higher rate in the Serie A than in any other championship, which may related to its low scoring nature.

2. The errors graphs exhibit similar features of true randomness in all cases, except possibly for extremely high goal differences, where teams may have a harder time translating goals into points. The exception to the exception is Italy again, but no team having had a goal difference above +60 in the Serie A, it is not yet clear how far the trend can be extended.

3. You may notice the vertical axis corresponding to a goal difference of 0 is shifted to the left for Germany and Spain. This is partly explained by the recent performances of the Bayern Munich, the Real Madrid and the Barça, which have all outscored their opponents at a rate never seen before.

## Not the end of the story

This was a first discussion on goal difference and how it relates to the actual outcome of a championship. There’s a lot more to say though, so as a food for thought here are a couple of questions:

1. Is the trend line stable over time or does it change as the championships evolve?
2. What are the differences in the trend between the championships and how can they be explained?
3. Are there teams that have consistently beaten the trend over several seasons, and can this be explained by more than random chance?
4. A subtler question: can we detect during a season whether a team is under or overperforming by looking at its goal difference? This is related to the concept of regression to the mean ubiquitous in statistics.

We’ll probably get to talk about some of these questions in the future, meanwhile if you have an opinion, a request or would like to tell us about your favorite team’s amazing season (Pescara 2013 anyone?), leave a comment below!

1. In fact, together with the computation of this line, we also obtain a number between 0 and 1, called the coefficient of determination. It measures how good our fit is, how close our prediction (the line) is to the actual data. In our case the coefficient of determination is above 0.9, which is sometimes interpreted by saying that about 90% of the variation of the data is "explained" by the trend line.

2. To obtain these values we just invert the equation of the line to get the goal difference in terms of points

$GD=\frac{1}{0.65}(P-52.12)$

and then plug in for $P=0$ and $P=114$ respectively.

3. This might no be true for the highest goal differences where few to no teams seem to be able to overperform. We have very few data points though so it’s a matter of interpretation, and it depends on the championship, as you can check for yourselves with the next graph.

4. all of them above, which might indicate a small bias toward greatly overperforming teams

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