In this entry I try to establish a relationship between the strength of a club (measured by Elo ratings I calculate on my humble, little site) and the money spent on players (measured by their market values). It can be shown that there are underachievers (lots of money spent, relatively little success) and overachievers (little money spent, relatively big success) among the football clubs under consideration. I finally derive a simple metric $α_{%}$ which aims to reflect the degree of over- and underachieving and hence might serve as a proxy for the quality of the management.
The Y: The case for Elo ratings
First things first, the value of Elo ratings with regards to predicting the outcome of a single event is concedingly limited for a number of reasons:
- Firstly, as in any game, the outcome of a single football match can be influenced by random events (undeserved send-offs, doubtful penalties, offside goals, actual goals being called offside etc.) which don't necessarily reflect the strength of the contestants.
- Secondly, Elo ratings only reflect past results without taking into account the circumstances of the current match (other than home court advantage), that is, the absence of key players due to injury or rest will not affect the prediction. The formula expects the contestants to be as strong as their past outcomes indicate - with increasing weight on more recent results.
- Thirdly, the real life motivation/mindset might be different depending on the magnitude of the contest (in April 2017 Barcelona lost 2-0 in Malaga (rated 1439), yet two weeks later overcame Real (rated 2044, ranked 1st) in Madrid 3-2) or the importance/timing of the actual match (In 1974, Bayern already clinched the league title ahead of Mönchengladbach prior to the last match day. On 17 May, Bayern won their Champions League final re-match against Atletico 4-0. Yet, despite having a higher rating, they lost their subsequent final league game against Mönchengladbach 0-5 most likely because the game had no value whatsoever. That this match was played merely one day after the Atletico game didn't help much either.).
These events can be regarded as the reflection of some error term $ε$ in the prediction of a single match. But they tend to cancel out over the course of a season such that $E(ε)=0$: Clubs benefit or suffer from bad officiating, one day a club is hurting from their star player being absent, the other day they profit from the opponent's star player not playing etc. To maintain the notion that certain clubs get a systematic bonus while others are systematically discriminated against, one would have to subscribe to some of the conspiracy theories floating around.
For a more thorough justification refer to the first entry of this blog.
The X: Market values of a clubs squad
Since players happen to be the main capital of a football club it seems obvious to take their market values as the X. For this analysis I make use of the market values which are published by transfermarkt.de. That site uses a comprehensive review system factoring performance, past transfer fees, injury proneness, age as well as the opinions/assessments of numerous users to estimate a player’s market value. Research for 2012/2013 found that for players which changed a club for a fee the estimated market values correlate strongly with the subsequently realized transfer fees, $r=0.93$. The seven countries I am going to consider in this entry (Spain, England, Italy, Germany, France, Portugal and the Netherlands) have a reasonably high exposure and should be researched well enough.
Interdependencies and timing of events
The transfer periods are usually between 1 July and 31 August in summer and between 1 January and 31 January in winter. To measure the impact of the investment into a squad, I take the earliest market value after the closing of a transfer period ($t=1$) and regress it against the Elo ratings on the last day before the next transfer period ($t=2$) (see graph below).
It does not make sense to take the Elo rating in $t=1$ because the team has been newly assembled and the Elo rating at this point does not reflect the strength of this particular combination of players. Likewise, I will not use the market value in $t=2$ because it might already reflect the performance of the team since the last transfer period. In other words, the relationship is two-fold: market value does influence the performance but obviously performance also affects the market value, $MV_{t=1}=f(ELO_{t=1})↖{+}$.
Results
Like the proverbial hen and egg problem, one can ask the question whether goals generate value or money scores goals? I will confine my efforts to the latter question, namely if and by how much the performance can be explained by the money spent on the team and what might explain the difference between estimated and actual values? To this end I take all 281 teams in the 14 first and second divisions of the top 7 countries ordered by average league strength ascending – market values are as of 1 September 2016, Elo Ratings as of 1 January 2017 – and plot every league individually. The regression lines tend to become flatter with increasing strength which implies that there are diminishing returns to scale for each additional Euro spent.
If we put all 281 teams of these leagues into one graph, this decreasing marginal return becomes quite apparent. To fit the data points I use a power law function of the form ${ELO}↖{∧}=b↖{∧}MV^{z↖{∧}}$ with $b=956.4166$ and $z=0.1054$ ($R^{2}=.83$). Now, aside from there being a clear positive relationship, there is also quite some inequality, the GINI coefficient being $GINI=0.68$ (even the most unequal societies won't match this number). Approx. half of the 281 teams have a market value of less than 20 million EUR, around 90 teams have values between 20 and 100 million EUR, and the remaining 50 teams are valued between just over 100 and up to almost 800 million EUR.
Another observation relates to the rather broad dispersion of points around the curve. The actual rather than the estimated Elo rating of a club follows the form $ELO=b↖{∧}MV^{z↖{∧}}+α$ with $α=ELO-{ELO}↖{∧}$ representing the part which cannot be systematically explained by the market value. My interpretation would be that $α$ somewhat measures the quality of the management in the broad sense, that is front office activity like scouting and picking players which are undervalued relative to their potential, and the actual work on the training ground in developing said players. In that sense, teams above the line, $α>0$, could be said to be overachievers while teams below the line are underachievers, $α<0$. The relative degree of over- and underachievement would then be $α_{%}=α/{ELO}$.
This sortable table contains the data for all clubs with a market value of at least 20 Mio. EUR. Some observations:
- A lot of teams depend on identifying and developing talent which can be sold for more value in subsequent transfer periods. Not surprisingly, all Dutch teams have a positive $α_{%}$. It is part of their business model to generate revenue by posting a positive transfer balance. For example, FC Utrecht whose players had a market value of less than 30 Mio. EUR overperformed in a way that would imply a market value of 55 Mio. EUR.
- On the other side of the equation we find clubs who chose the ensemble approach and largely rely on buying already developed talent. Yet, quite often they still manage to underachieve, indicating that the whole can actually be less than the sum of its parts. Notable examples are the two Manchester clubs. City and United both started the season with market values of comfortably above 500 Mio. EUR. But by the end of the year, they underperformed by 150 Mio. EUR and 120 Mio. EUR, respectively. (Cf. Juventus whose squad was valued 420 Mio. EUR and who played arguably more successful in the time frame considered.)
- RB Leipzig is under constant scrutiny for its controversial ownership structure. A popular talking point refers to the team "buying success". However, if we look at the numbers, we have to concede that the club is a massive overachiever. The squad largely consisted of players who were already part of the team in their second division campaign of the previous season. After the closing of the transfer window on 31 August, there were 12 Bundesliga clubs in total with higher market values than Leipzig! By the end of the year, the club overachieved by around 115 Mio. EUR, meaning that they performed like a 183 Mio. EUR club while being valued only 66 Mio. EUR. (Compare this achievement with that of perennial underperformer Hamburger SV who started the season being valued around 80 Mio. EUR.)
Scheduling
Considering the discrepancy between the abundance of money English clubs have at their disposal and the relatively ordinary success in international competition it has been suggested that the schedule of English teams is too tight (no winter break, re-plays of drawn cup matches, league cup) compared to other countries. The reduced number of games might also explain why Chelsea won this year's Premier League with relative ease seeing that it didn't have to face the likes of Real, Barcelona et al. every other week. In one of the future entries I will try to somehow factor the schedule density into the equation.
What else?
On a completely unrelated note: Another interesting idea for a blog entry would be to estimate the strength of non-European leagues like the US Major League Soccer or the Chinese Super League. Unfortunately, there are no competitive games between the European universe and the rest of the world (ROW) apart from the very few contests during the FIFA Club World Cup. Mostly, I will look at international club friendly matches (weighted considerably lower than competitive matches) between European and ROW teams and try to find ratings for the ROW teams which minimize the Elo rating change as small changes in the Rating suggest that the result of the game is already reflected in the pre-match ratings.
