A lot of money is involved with the transfers of top players in the big European football leagues. For various reasons, obtaining a good economic valuation of football players throughout the year is valuable, in other words, not just when a player has just transferred. Furthermore, it is relevant to consider how the market value of a player relates to the performance of that player. Both these factors again depend on the various parameters of the player, that might be gleaned from various public sources on the web. In this paper, we demonstrate how market value and performance of La Liga (the Spanish League) players can be modeled using extensive public data sources.
The transfer fees of football players are getting higher and higher each year. The
UEFA Financial Fair Play Regulations [
Consider the problem of economic valuation of football players. Most likely, the closest we can get to the real market value is the transfer fee of the player. This valuation is missing for most of the players, because players are not always moving from one club to another during transfer seasons. Furthermore, researching the market value individually for each football player can be quite hard work. We decided to approach this challenge by applying data-driven modeling techniques to attempt a proper valuation of football players.
Football is a team sport, thus it is quite hard to judge an individual
football player's performance. Di erent people have di erent opinions on a player's
performance. The responsibilities of each position are di erent, which leads to
performance indicators also being di erent by position. We took the votes on
\Who is the best player of this year?" by football experts [
The goal of this research is to nd the relationship between market value and the performance of players. In this paper, we develop regression models to predict the real market value and assess a player's performance. A fair market would assign a higher market value to a player with high performance. After we got the player's market value and his performance indicators, we look at the relation between the two. 2
For this research, we required data containing a player's basic information (name, team, age, height, weight, . . . ), market information (transfer fee, former team, duration of the contract, when the player joined the team, . . . ) and performance information (on pitch time, actions at the ball, fouls, scores).
After an extensive online search and browsing related work [
The market data are from Transfer Market, which is a website to discuss and
learn the latest news from the world of football. There is transfer news, rumors
and also statistics on the market value, for example the length of contract, the
former clubs. As for the real market value, we decide that the closest we can
have to a real market value of a player is his transfer fee at the moment he is
transferred from one club to another. This data was gathered from the European
Football Database [
The performance of the players data were collected from the website WhoScored
[
0 10000 Mar2k0e0t0va0lue from Tr3a0n0s0fe0r Market(in410000000euro) 50000 60000 0 500 10V0o0tes of best pl1a5y0e0rs by experts2000 2500 3000 (a) Q-Q plot comparing transfer fees and (b) Q-Q plot comparing Garter votes and market value from Transfer Market. WhoScored rating. In the previous section, we presented the real market value and performance indicators of players. But there is a common problem for both these variables. We have 381 players in La Liga, but not every player has been transferred this season and only some players will be on the candidate list of the voting. There are only 37 players who transferred this season and only 40 people in the voting list.
However, proxy variables for both the market value and performance have
been collected. For all the players, we have a Market Value estimation from
Transfer Market and a Rating from WhoScored. Market value is based on an
algorithm built by Transfer Market to estimate the transfer fee if the players
were transferred during the present season and is adjusted every year. Ratings
are calculated based on WhoScored's algorithm, using OPTA's statistics and
are updated during each game. The Rating variable is scaled from 0-10 where
10 indicates best. Both these algorithms are not public so we decided to collect
and compared them the closest we could nd about these variables [
The rst step of our study was to nd the relationship between proxy and real values. In Figure 1, we present the Q-Q plots crossing real and proxy values for market value and performance, for those cases where both values are available. The economical valuation of Transfer Market seems to match the prices paid for the transferred players. As for performance, the relation between real and proxy values appears to be non-linear but still monotonically increasing. Afterwards, we applied learning algorithms to a merged dataset containing all data sources, where proxy variables are put together with other variables as independent variables and the real variables are our target variables.
For each of our two targets, we included only those players in the training set for which the actual values were available. I.e., for Market Value we included the 37 players who actually transferred in that year, and for Performance we (a) Regression Tree using market value (b) Without using market value from from WhoScored to model transfer fee. WhoScored to model transfer fee. included the the 40 players that were nominated. The datasets used have 100 and 84 variables, respectively. This is because the performance-related variables were included to model the Market Value, but not the other way around. The rationale behind this decision is that performance cannot be in uenced by economical variables.
Problem Statement Our main task is to nd good regression models for both Market Value and Performance. More formally, we assume a wide dataset with both performance and/or economic related variables, as well as an evaluation function (R2) that can evaluate the quality of the model, with respect to the target variables (real Market Value and Performance). The task is to nd good models such that: { The score of R2 is high, where 0 R2 1. { The complexity of the model (number of variables) is low.
{ The models are interpretable for further analysis. 3.1
The datasets for estimating Market Value and Performance have both numeric
and nominal variables. Most of the regression algorithms cannot deal with
nonnumeric variables, but regression trees can [
If we consider the subset of our dataset for which we have the real values
of Performance and Market Value, there are more variables than observations.
This makes it impossible to apply least squared methods [
LASSO is a well-known regression technique for these cases [
In the R package Glmnet [
There are negative values for the predicted real market value when we using min as threshold. Clearly, it goes against common sense when you pay money for selling your players. However, 1se is too restrictive by only introducing one variable.
According to Figure 3.1, the mean-squared error will be smaller when lambda is bigger. By taking all these issues into consideration, the criterion for is: min( min ) provided that all the predicted market values are non-negative. Based on the above criterion, we decided for = 3247:0. It is the closest model to the best which would never cause negative market values. It is indicated by the vertical red line in Figure 3.1. It is in the interval of the best model and simple model. The model is:
M^ = 231:26 + 0:89 M arket:value + 2723:26 Assists 4.2
There are signi cant di erences in performance between positions. It has been
suggested [
In addition, we have used the t-test to test whether there are signi cant differences between positions when it comes to market value. When considering the market value between the four categories, p = 0:001 which indicates a very signi cant di erence between the four positions. Furthermore, when comparing the market value between speci c sub-categories within each group (e.g. comparing various types of defenders amongst each other), we get p-values above 0:8, which suggest it makes sense to group such very similar sub-categories. Hence, also from a market value perspective, the four categories are justi ed. 20 25 Age 30 (a) Market value and age.
0 1 2contractlengthinyears3 4 5 (b) Market value and contract duration.
We attempted modelling the performance over the entire set of players, but failed to nd satisfactory results, due to the variance of performance per positions. Focusing on the forward players speci cally, it becomes possible to model their performance. Forward players play an important role in the valuation of players. Although they only represent 30% of all players, they appear as winners of the FIFA World Player of the Year (since a few years called the Ballon d'Or) in 17 out of 24 years. No goalkeeper has ever won the prize.
In this case, we use LASSO to train the forward players. Five-fold cross validation was used. The threshold is min. The KPIs for forward players have been selected as follows. A good player should have few Fouls (F ). Shots and Goals in Penalty area (SP &GP ) are a big plus for player performance. Shots on Target (ST ), Goals from out of Box (GB), Dribble successfully (D), Assists total (A) also contribute to the nal results. The model for forward players now is: Since we have predictions for the market value and performance assessments of players, the relation between the two can be studied. The over-all trend of market value follows the trend of performance. The better performance, the higher the market value will be (Fig. 4). There seems to be a ceiling for market value, where the top performing players have similar market values and very di erent performance ratings.
For the transferred players, we calculated the di erence between the real market value and the estimated market value based on performance, = ln(M ) ln(M^ ). The smaller is, the more proper market value for the players is according to his performance. We also considered that if > 0:3 the player is over-valued and if < 0:3, the player is under-valued. In general, the majority of over-valued players are also high-performance. This might be due to the marketing value of high-performance players. Normally, high-performance players also bring revenues to the clubs in terms of publicity and merchandise sales. This market variables are not incorporated in our model. We have built a model to value economically all the players of La Liga. Furthermore, the method could be applied to other leagues. As for the performance, the operational model for now applies only to forward players. We believe this could be extended to other positions if a unique model is created for performance across di erent leagues. As part of future work we would like to scale up the project to all European leagues.
Even considering covering all leagues, this project will keep on dealing with incomplete data because not all players are valued every year (by being transferred), neither are all players' performance evaluated by the voting system. In the future, we would like to consider semi-supervised methods to solve the tasks of Performance and Market Value estimation.
Finally, the voting system to access performance is biased towards forward players and good players. We would like to explore other data mining techniques that account for this problem, such that we could create an Elo Rating model alike for performance of football players, across positions and leagues.