By Carlos Pena-Lobel
In what will hopefully be a 3 part series, I will take a look at parity in European Soccer. But parity is a buzz word without a well-defined meaning. In this post, we look at 2 different types of parity: the distribution of wins between teams in a season, and a measure to see if the same teams are winning each year. Put another way, we look at the spread between the best and worst teams over time, and how long past performance predicts future performance.
In this first post, we will look at both of these types of parity in the English Premier League. The motivation here is the oft-heard claim that the Premier League is the deepest league, and that explains their failures in Europe. In order to dissect this I will go through some measures of parity applied only to the Premier League in order to explain fully what they are measuring and what they can help us understand. In my next post I will use these same metrics to compare the EPL and other European leagues, but for the other major European leagues often an explanation is needed in how the data was treated because of tainted data. For example the German scoring system used to award 2 points for a win, or in Italy there was a cheating scandal that removed Juventus from the upper flight, or in Portugal the league is constantly changing size, etc.
Comparing the EPL Today to the EPL of Yore
For the first part, we take the Gini score, a classic economic measurement of equality. A measure of 1 indicates perfect inequality (1 team would have all the points, which is impossible in soccer), and a measure of 0 indicates perfect equality (every team has the same number of points). In soccer scheduling, each team plays every other team once at home and once on the road. With 3 points awarded to a win, 1 to a tie and none for a loss, it is impossible to have a Gini score of 1, since the worst teams have to play each other.
To find the maximum Gini in a 20 team soccer league, we take the approach of finding the optimal distribution of wins/ties/losses with n dominant teams. That means that if there is 1 dominant team, it if fairly obvious that we need them to win all 38 of their games, and then each of the remaining 19 teams tie their 36 other games. With 2 dominant teams, it isn’t as clear, but after some thought it can be seen that the dominant strategy is to have the first team win all 38 games, the 2nd dominant team then wins 36 games with both losses to the best team, and now the remaining 18 teams all tie their remaining 34 games. Extrapolating this we produce the graph seen below.
This gives us a maximum Gini Score of .377 when there are 11 dominant teams. This illustrates that with a schedule in which bad teams are required to play themselves, it is hard to have a very unequal league. And without further ado, the Gini score of the EPL over time.
Some things to note. First of all, the data for the most recent season is not complete, not every team has even completed 15 games. Also, our first 3 years of data on the EPL consists of a league of 22 teams. While a huge advantage of a Gini score is that it stays constant irregardless of a scaling factor (number of games played or number of teams), and even though these scaling factors can’t be the same because team’s performance aren’t completely independent, the strength of the Gini method can be seen on the graph above as there isn’t a discernible difference for the years in question. However, as some other methods aren’t as rigorous, we remove these years from further analysis unless denoted.
For example, below is a graph of the point total of every team marked in blue, the average score marked in red, and 2 standard deviations which are filled in red. Traditional measures clearly do depend on games/teams. However it is still clear that ignoring the first 3 years, the spread in data is increasing.
Now, ignoring these 4 years, we can regress the Gini score of the league on the year. With a p-value of .005, and a positive coefficient, it is clear that this is significant, which tells us that the league is getting more and more unequal. However, we do not find any significant result when regressing the mean point total on the year. Since each game is either a 3 or a 2 sum-game, an increase in average score in time would tell us there are less ties. This isn’t the case. Instead, we can say that the number of ties hasn’t changed, and so this change in Gini has to come from somewhere else. If we look at the average points scored at each final position of the league table in the first 6 years of the 20-team EPL vs the more recent years, we see a remarkably clear trend. The best teams have been outpacing themselves, while the worse teams are doing worse and worse.
Does this matter in European Competition? Using the idea of Championship points towards the EUFA Champions League can tell us. The idea of championship points works as follows: if a team wins the cup they get 1 point, if they come in 2nd they get ½ a point because we say they had a 50% chance of winning the cup if the winning team hadn’t been a part of the competition. Likewise for a semi-finalist they get ¼ point because they would have had to win 2 more games. Summing this for the EPL in Champion League Performance since 2000 (the first year where there were 32 teams competing) gives us this graph:
A quick regression confirms the initial suspicion, that there is no relationship between the Gini score of the EPL and the success of English teams in the Champions League. However as any good analysis does this only looks at the EPL Gini score and not the relative Gini scores between England and another major European soccer league. For example, maybe the Gini score is a significant predictor, but the Gini score of La Liga or the Bundesliga has been changing much more rapidly than that of the EPL score and thus obscuring this effect. With this we can say that the claim that the EPL does poorly in Europe because it is so deep is similar to mostly any random sentence that Byron Scott says, probably ridiculous, but every once in a while, an outrageous claim is actually true.
Comparing the Man U of Today to the Man U of Yore
(Sorry if you are an Arsenal, Liverpool, or Chelsea fan, I could have easily inserted you guys above). Since we now know that the best teams are doing better, and the worse teams are doing worse, the question is now whether these are the same teams. Is it Manchester United, Chelsea, Liverpool, and Arsenal who are outperforming the 90’s versions of themselves, or is this more of Manchester City outperforming the 90’s Wolverhampton Wanderers?
This also addresses the socialism aspect of American sports. Except for potentially the Lakers, Celtics, Yankees and Patriots, there are very few teams that have dominated their respective leagues for decades. Likewise there are very few teams that have been terrible the whole time, even the Hornets have gone to the playoffs 9 times in their beleaguered 26 years. This is enforced by giving draft picks to the worse teams rather than relegating them, or by imposing contract limitations so that big market teams don’t have more purchasing power than smaller teams etc, which isn’t true in European Soccer. Now, we graph the position of a team in the current year vs their position in prior years. If a team was relegated either in the current year or previous year, we assign them a ranking of 21 (since we don’t know where they placed in the Championship, and this isn’t of great worry for us). Below is the graph of comparing a team’s performance in one season vs the next.
The size of the circles are a measure of frequency of that occurring. To understand the 3 large top right circles, those are instances of a team placing 18th, 19th, or 20th in year n-1, and then being relegated in the next year. That in itself is very unremarkable because this is 100% by design, but it shows how to read the graph. The bottom left most point, is the frequency of repeat champions etc. Lastly, the more that the circles lie on the line y=x, the more predictive the year is, and in this case, it is very predictive.
While saying that performance in the previous year predicts performance in the next year, won’t win you any awards, maybe the graph at 10 years will.
Even looking at performance 10 years apart, we don’t have any of the top 2 teams every being relegated, and (with the exception of Leicester City) we have very few teams that weren’t in the league making the top 5 within a 10 year time frame.
To measure how long this relationship lasts, we take a look at the p-values of a regression YearN ~ YearN-k, where our x axis is our k (years prior), and our y axis is our log(p-value). We use log p-values because with numbers so close to 0, this spreads out our data for computational accuracy and better visualization. I have added the line of log(.05) to show what are level of significance is, with everything below the line being significant.
This also illustrates why Leicester City shouldn’t be leading the Premier League. Just two years ago, they were in the Championship. In the 2008-2009 season, they were in League One (the 3rd level of English soccer). Teams in any sport rarely make ascents that large that quickly, much less the Premier League. Behind phenomenal play by Vardy and Mahrez, Leicester City is destroying the trend.
And I will finally end on this note. As the graph shows, (especially the zoomed in portion), performance 19 years ago is predictive of current performance in the EPL. If only the same thing could be said about my Lakers…
The data used for this post can be found on our GitHub here.