American University of Armenia
Analyzing soccer’s transfers and
predicting footballers’ transfer price
June 15, 2020
Analyzing soccer’s transfers and predicting footballers’ transfer price Page 1
The purpose of this project was to create a machine learning-based model which could
predict the transfer fee of football players based on some range of data. Nowadays, concepts
of AI are widely used in almost every sphere. Many football clubs use such techniques
to maximize their proﬁt. The paper demonstrates one way to develop such a technique.
The ﬁrst phase of the project included data collection for having a high precision model.
Then various machine learning algorithms were applied such as linear regression, decision
tree, deep neural networks, and others. The models were evaluated based on some speciﬁc
measures. After model evaluations, respective conclusions and interpretations were made.
Keywords: Machine Learning, Deep Learning, Soccer, Sports Analytics, Regression,
Networks Science, Transfers
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1 Introduction 3
1.1 LiteratureReview................................. 4
2 Methodology 8
2.1 DataCollection.................................. 8
2.1.1 DataDescription ............................. 9
2.2 DataAnalysis................................... 14
2.2.1 Exploratory Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 NetworkAnalysis............................. 50
2.2.4 Insights .................................. 56
2.3 DataPreparation................................. 57
2.3.1 Data Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.2 Missing Value Imputation . . . . . . . . . . . . . . . . . . . . . . . . 59
2.3.3 FeatureSelection ............................. 60
2.4 Modeling...................................... 61
2.4.1 MachineLearning............................. 61
2.4.2 DeepLearning............................... 62
2.5 Findings...................................... 67
2.5.1 Predictive Power and Interpretations . . . . . . . . . . . . . . . . . . 67
2.5.2 Comparisons and best model selection . . . . . . . . . . . . . . . . . 71
3 Summary 77
3.1 Interactive Dashboard Application . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Recommendations................................. 77
3.3 Conclusion..................................... 78
Analyzing soccer’s transfers and predicting footballers’ transfer price Page 3
Nowadays, soccer teams buy and sell thousands of players during each transfer window,
spending millions of dollars to buy them. The top players of the game are even worth a
couple of hundred million dollars. With the increase in resources spent on football players
during transfers, football teams aim to maximize the eﬃcacy of each transfer. Some football
teams use AI-based technologies to predict football players’ transfer fees and market value.
According to an article published on BBC, if a player transfers before their contract expires,
the new club pays compensation to the old one. This is known as a transfer fee (Quick,
2017). While a player’s market value is an estimate of the amount for which a team can sell
the player’s contract to another team (Herm, Callsen-Bracker, & Kreis, 2014). The market
values attached to the players do not play a key role as in many cases a player is sold for a
much higher price than his market value or much lower price. At the moment of his transfer
from Barcelona to PSG Neymar’s market value was 100 million euros, but PSG paid more
than double the price to sign him. So, what are the main qualities of the player or other
factors, that decide his transfer price? Also, when is the best time to sell the player? Which
of the transfers paid oﬀ for the teams? And in general, are there any special connections
among the teams or leagues of the transfer market? Those are some of the questions that
we are going to provide answers to. We want to use simple statistical measures and ratios
(such as goals, minutes per one goal and etc.) of the players’ performance for predicting
his transfer price. One of our main goals is to identify whether the easily interpretable
statistical measures of the players are solid predictors for his transfer fee and how well can
these variables predict the player’s price. As the importance of a statistical measure varies
depending on the position of the player on the ﬁeld, we will implement the predictions
for each position separately. In the end when we ﬁnd the best prediction model we can
investigate the underrated and overrated players based on their transfer fee.
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1.1 Literature Review
Various studies and projects conducted by individuals or organizations for diﬀerent
purposes, which tried to investigate the features that may impact the transfer fee of the
football players and conduct predictive models and methods.
First of all, there is a study conducted by CIES Football Observatory. They published
a document called “Scientiﬁc assessment of football players’ transfer value” in October 2018.
The study tried to understand the predictive perspective of the transfer values of the foot-
ballers, mentioning that there is some predictable logic which is possible to model. The data
that they have collected consists of over 2,400 transfers, involving top-5 league players be-
tween July 2011 and August 2018. The number of features is 36 including information about
footballers’ contract duration, year of transfer, book value, loan status, nationality and eco-
nomic level of the releasing club. They used multiple linear regression which included only
signiﬁcant features, leading to the overall model to be very signiﬁcant (p−value < 0.00001)
with adjusted coeﬃcient of determination evaluated as 0.86. The study concluded that the
model is useful for deﬁning the starting value, initial salary of the players, as well as under-
standing the value of the club in the future based on the price of the players (Polim, Ravenel,
& Besson, 2018).
The next approach to understand the players’ transfer value was done by Lukas Bar-
buscak with the study called “What Makes a Soccer Player Expensive? Analyzing the
Transfer Activity of the Richest Soccer” in 2018. The data that the author used consists of
quite a small amount of 49 players, including features such as number of google searches,
number of years on contract left, rating of the players by the community, number of goals
and assists and ﬁnally race of the players. The sample consists of the most valuable players
on the market by the year of 2018. The models that he used are the two multiple linear
regressions, which concluded that the most essential independent features to predict the
transfer value are Contract Left and Race. First model included all the players, however
the second one excluded Neymar, since he was the most valuable player at that time. The
models are quite similar in terms of the adjusted coeﬃcient of determination evaluated as
0.92 (Barbuscak, 2018).
Another study we examined was “Football player’s performance and market value”
published by Ricardo Cachuchino, Miao He and Arno Knobbe, published in 2015. The
authors of the paper wanted to understand the relationship between the performance of the
player and his market value. They also underlined the current problem of player’s economic
valuation and deviations in the market values and transfer fees. Their dataset included
information about the player’s performance, his ratings from WhoScored, market information
from TransferMarkt and some other performance assessment metrics gained by juries. The
scope of the project only included LaLiga players for the half of the 2014-2015 season. The
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authors built their model of evaluating the market value using Lasso Regression. They
emphasized the importance of choosing the right lambda in ﬁltering the important features.
Later they ﬁgured out the importance of evaluating the players based on their position and
continued their work putting the main emphasis on evaluating the forwards. They came out
with a simple linear model for evaluating the forward’s performance based on his behavior
on the ﬁeld (fouls, yellow or red cards), shots from diﬀerent areas, goals (underlining the
goals from penalty area as a big plus), successful dribbles and other attributes relevant to
the forwards position. Later, they studied the relationship of the performance and market
value and came up with a conclusion that economical valuation of the player is dependent
on his performance but his performance cannot be aﬀected by economic factors (market
value, transfer value). They also indicated that the undervalued or overvalued players can
be found using the diﬀerence between the real and estimated market values of the player
(M. He, Cachucho, & Knobbe, 2015).
We also found another similar study that tried to predict the market value of the
footballers with linear models. This study included only EPL data about footballers in the
season 2017-2018. It also included the ratings of the player from Fantasy Premier League
and also the number of the player’s Wikipedia page views. The overall formula of their model
was based on the ability of the player and his performance. They regarded the number of
page views as a proxy variable for ability. The model had R squared a little bit higher than
0.7. Overall, this model emphasized the importance of the proxy variables for accounting
the player’s ability (Maurya, 2018).
Another similar project was made by Yuan He. This project was the ﬁrst case where
the data was collected not only for one season, but for 5 seasons. They divided the data into
multiple parts, one for the player’s personal information such as his nationality year of birth,
race, height, position and other similar attributes, and also, they had a dataset aligned for
the player’s performance metrics such as the number of games played, the number of goals,
the number of clean sheets for the goalkeepers and other metrics. Also, this project included
the national stats of the players. Yuan Hee’s project used mainly two models, OLS (ordinary
least squares), KNN (k nearest neighbors) and also Ridge, Principal Component Regressions.
The authors used 10-fold cross validation techniques and used RMSE as a main criterion for
judging their models. The authors also added various performance ratios after the EDA, such
as international caps to age and other interconnected attributes. According to the author
the PCR model with a K value of 15 was the best among the chosen options. The authors
advanced with that model in later developments. The authors started to do predictions and
check the accuracy of the model using multiple approaches. The approaches chosen were.
•Taking overall mean as a sole prediction. RM SE ≈54.7
•Taking the responsive model for each player. RM SE ≈27.27
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•Using value from last year. RM SE ≈25.64
•Training original data matrix without cross validation. RM SE ≈21.27
The authors concluded that the last year value of the player had the highest contri-
bution to the response. Goals, Assists, International caps and other similar attributes also
had high contribution, while the personal information of the player and the ratios added by
the authors did not have high signiﬁcance (Y. He, 2012).
There were also other similar studies done, but the results and scopes were in general
similar to the mentioned works. Also, initially trying to ﬁnd similar projects’ implementation
in other team sports, we did not ﬁnd any similar projects in scope. The reason is that except
soccer there are multiple team sports based in the USA, that have huge ﬁnances involved
in the game. Those are Basketball, Baseball, American Football and others. However, in
almost all of these sports, there are some limitations included on the team’s budget from
the according sport’s federation of the country. A great example is the application of salary
limits of the players in almost all the American team sport games. In addition to this in
many sports the teams are getting their players from the junior leagues, and in baseball’s
case the worst team has the ability of picking the best junior player ﬁrst. So, in general
the “trade” practices in American sports and their occurring problem solutions will not be
helpful for analyzing soccer’s market.
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Year Authors Overall data scale Methods applied Final Results
Top 5 leagues.
2011 - 2018.
of the club:
The year 2017.
Top 6 EPL,
market value, and
google page views.
one season data.
Table 1: Previous work summary
Most of the approaches used a small number of observations. Also, many projects used
some external information about the players’ performance such as FPL scores or WhoScored
ratings. The most popular algorithm used in the mentioned projects was Multiple Linear
Regression. Most of the projects used R2and RMSE for estimating their model’s predictive
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power. The projects that provided the results had mostly pretty high R2(Table 1).
2.1 Data Collection
Data collection was one of the most important phases of the project. As a model based
on machine learning algorithms, a considerable amount of data was necessary to achieve high
After thorough research, we found all the necessary data on the Transfermarkt web-
site 1. Python modules were written in order to scrape data from the website. Overall, we
obtained data about 18000 players from various leagues. Transfermarkt provided historical
data of the player’s performance since the beginning of his professional career and also his
market value history starting from 2005. We also scrapped players’ injury history and tro-
phies from the Soﬁfa website 2, as this information was no structured in Transfermarkt. Later
we connected the two sources by string distance algorithms in players’ names, nationality,
and clubs. The scrapping was done using python’s Selenium and beautifulSoup packages.
The scrapped data contained a lot of messy information and gaps. We have cleaned
up all the information and assigned the correct data types for each variable.Overall, there
are around 4 categories.
•Datetimes(DOB of a player, date of a transfer, ...)
•Floats(points per game, minutes per goal, ...)
•Integers(height of a player, number of goals scored, ...)
•Categorical variables(strong foot of a player, continent of a player, ...)
1Transfermarkt website link
2Soﬁfa website link
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2.1.1 Data Description
The main sources of information about the players are based on multiple categories
each having according ﬁgures about the players’ details.
•Player’s physical,racial and playing attributes.
–Position on the ﬁeld
•Player’s market value history
•Player’s trophy history
–Number of trophies won
–Number of times player’s team was a runner-up(second place)
•Player’s performance attributes
–Number of goals scored
–Number of goals scored from penalties
–Number of assists made
–Number of yellow cards received
–Number of second yellow cards received
–Number of red cards received
–Number of substitutions into the pitch
–Number of substitutions oﬀ the pitch
–Number of minutes played on the pitch
–Number of elections into the team squad
–Number of appearances in the starting eleven
–Number of own goals scored
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–Number of clean sheets(only for Goalkeepers)
–Number of goals conceded(only for Goalkeepers)
–Points per game team earned when the player was playing
•Information about the transfer
–Transfer’s window type
–Transfer’s year type(Tournament year or not)
(Number of games won/Number of games played)
(Minutes played on the pitch/Minutes elected in the squad)
–Minutes per goal
–Minutes per assists
–Minutes per yellow cards
–Minutes per red cards
–Minutes per conceded goals
–Minutes per clean sheets
–Number of clean sheets per conceded goals
(Number of goals the goalkeeper has conceded per a game of not conceding any
–Number of goals per penalty goal
(Number of goals scored from penalty before scoring a game from the game)
Initially, we have also added a few more ratios underlying the frequencies of the players’
substitutions both on and oﬀ the pitch, but the ratios contained a lot of inﬁnity values due
to often cases of 0 being the divisor. All of the performance metrics were used at the time
of the transfer, so for example the age of the player was identiﬁed by substituting the date
of birth of the player from the date of the transfers. In addition to the seasonal metrics of
performance, the cumulative measures of the player were used at the time of the transfer. The
operation used to accumulate the performance metrics were summation for all performance
measures except points per game for which the running mean operation was used(Each two
year’s ppg were summed up and divided by two until the year of the transfer). The same
operation was used for calculating the cumulative ratios.
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g Number of goals scored
a Number of assists recorded
gc Number of conceded goals(GK)
cs Number of clean sheets(GK)
(games with no conceded goals)
yc Number of yellow cards
rc Number of red cards
syc Number of second yellow cards
son Number of substitutions on to the pitch
soﬀ Number of substitutions oﬀ from the pitch
s Number of selections into team squad
app Number of appearances
mp Minutes played on the pitch
ppg Points per game the team
earned when the player was on the ﬁeld
mpg Minutes per goals
pg Number of goals scored from penalties
og Number of own goals scored
Table 2: Abbreviations for seasonal perfomance variables.
The variables deﬁned in Table 2, were available in Transfermarkt for all the play-
ers. The website contained historical seasonal performance data for each of the described
performance measures for the players since the beginning of their career 3.
3The abbreviations for cumulative perfomance metrics were the same with cum at the beginning
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fmpct Percentage of time spent on the ﬁeld playing
(mp)/(s * 96).
fwpct Winning percentage of the team when the
player was on the ﬁeld (fmpct * ppg) / 3.
mpson Per how many minutes the player was
substituted on to the pitch (mp / son).
mpsoﬀ Per how many minutes the player was
substituted oﬀ from the pitch (mp / soﬀ).
apps Per how many squad selections was
the player playing on the pitch (s / app).
Per how many minutes the goalkeeper
had a game (90minutes), during which
he didn’t concede any goals (mp / cs).
mpgc Per how many minutes does the goalkeeper
allow a goal (mp / gc).
How many goals the goalkeeper
has conceded per a game of not
conceding any goals (gc / cs).
Per how many minutes does the player record
an assist(pass after which a goal is scored)
(mp / a).
mpyc Per how many minutes does the player receive
a yellow card (mp / yc).
mprc Per how many minutes does the player receive
a red card (mp / rc).
mprc Per how many minutes does the player receive
a red card (mp / rc).
ycprc Per how many yellow cards
the player has got a red card.(rc /yc )
gppg How many penalty goals the player
has scored per goal. (g / pg)
Table 3: Abbreviations for ratio variables.
The variables deﬁned in Table 3 were all calculated using the variables in Table 2.
The calculations required for calculating each ratio are described in Table 3. The minutes
were chosen as a base metric as the number of games are strongly correlated with minutes
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played, also the average length of a game is calculated using 96 minutes in order to take into
account average delays in-game time due to extra-times and over-times 4.
Figure 1: Entity Relationship Diagram
Figure 1 Shows the structure and relationships of the database. As no new records
were added and all of the dataframes had a relationship only with Players’ dataframe, we
did not use any SQL framework. All of the entities were stored in a pandas dataframe and
later the attributes that were relevant to the output variable were merged together into one
dataframe for each position. The historical statistical data of the players was initially stored
in a long format and later transformed into a wide format for analysis and modeling.
4The abbreviations for cumulative ratio metrics were the same with cum at the beginning
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2.2 Data Analysis
2.2.1 Exploratory Analysis
To identify the main characteristics of the players’ that contribute or do not contribute
to their transfer values and market values accordingly we have mostly used heatmaps, scatter
plots, histograms, and boxplots each used with corresponding categorical and numerical
variables. As there are 4 main positions for footballers, we have analyzed each position for
ﬁnding the most relevant attributes speciﬁc to each position, that contribute to the transfer
fee and market value of the players. However, while analyzing the performance ratios we
have paid attention only to the ratios that make sense for the position in order to avoid
missing values, as for example, the attackers receive yellow or red cards rarely thus they
need more minutes for receiving a warning, which will lead to having a high number for the
minutes per red or yellow card ratio for the player, thus having a correlation to the transfer
price, and similar scenarios are present for each position. In order to avoid redundancy in
data and missing values, only the ratios that are relevant to the position of the player were
considered during the analysis. Also the early stages of the analysis showed that the player’s
injury history was not contributing to his transfer fee, so the information about the injury
history was not later used.
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Figure 2: Price and statistics heatmap(Goalkeepers)
As we can see the market value of the player has the highest contribution to his
transfer fee, and the statistical measures are not highly correlated with the transfer fee. The
statistical measures of goalkeepers that have the highest correlation to their transfer price are
the number of clean sheets the player made during the season of the transfers, the number of
squad appearances, minutes played, the number of points per game the team earned when
the player was on the ﬁeld, and the number of goals conceded. When we take a look at the
cumulative statistical measures at the time of the transfers we can see that most contributed
ones to the transfer fee are the cumulative number of clean sheets, the cumulative value of
points per game, minutes played, and appearances. However most of the statistical measures
for the players are highly correlated to each other, as for example if the number of player’s
appearances on the ﬁeld increase the number of minutes he played on the ﬁeld increases
correspondingly, and also we should take into account the ratios of some statistical measures
as in general most of the measures are correlated to the number of appearances or minutes
played for the players (Figure 2).
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Figure 3: Price and ratios heatmap(Goalkeepers)
The statistical ratios that have the highest correlation to the player’s transfer price
are the cumulative and season based number of games per substitution on and oﬀ from the
ﬁeld, however, these metrics are not relevant to the goalkeepers as most of the time they are
not often substituted oﬀ or on from the ﬁeld. The ratios that are relevant to goalkeepers and
have some contribution to the transfer price are the cumulative ratios of the ﬁeld winning
and playing percentage and minutes per conceded goal (Figure 3).
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Figure 4: Transfer price vs market value(Goalkeepers)
Figure 5: Transfer price vs clean sheets(Goalkeepers)
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We can see that most of the time the transfer fee of the goalkeepers was lower than
their estimated market values and there are only a few extreme cases when the diﬀerence
between the transfer price and market values is signiﬁcantly diﬀerent, which happens mostly
during transfers of young players or expensive players who have a few years left on the
expiring contract (Figure 4). Also, the number of clean sheets tends to contribute to the
transfer price, but the connection is not very strong as players as a goalkeeper may have
conceded a lot of goals thus having a lower number of clean sheets, but also have many good
save which can contribute to high transfer value (Figure 5).
Figure 6: Price and statistics heatmap(Defenders)
The main attribute contributing to the transfer fee of defenders is also his market
value, and the statistical measures have a very low correlation with the transfer fee of the
player. The only season based performance metrics for the defenders that have a relatively
higher contribution to their transfer fee in comparison with other metrics are points per
game the team earned when the player was on the ﬁeld, the number of appearances and
the number of times the players was involved in the team’s squad either as a starting eleven
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player or substitute player. None of the cumulative statistical measures have even a relatively
high contribution (Figure 6).
Figure 7: Price and ratios heatmap(Defenders)
For defenders, we can see that the highest correlation with the transfer fee is the
minutes per red card statistic of the player, which shows on average how many minutes does
the player does not a receive a red card after receiving one. As defender is a very aggressive
position in soccer, it is excepted that defenders can receive many red or yellow cars, so a good
indicator of a defender can be the interval of receiving red cards in minutes, and generally
expensive players receive a red card more rarely. The ratio of yellow cards and red cards is
a good indicator to ﬁnd out, how many not so dangerous fouls does a player commit before
committing a very dangerous foul, worth a red card. However, this ratio is not strongly
correlated. Almost the same correlation value to the transfer fee has the winning percentage
of the player when he is on the ﬁeld. This is a little bit biased variable as the team’s points
are not dependent only on the defenders, they alongside the goalkeepers are responsible for
the teams defending qualities and attacking attributes of the team is independent of the
defenders’ quality. (Figure 7)
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Figure 8: Transfer price vs market value(Defenders)
Figure 9: Transfer price vs minutes per red card(Defenders)
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The number of defenders who were sold for a price higher or lower their estimated
market value is pretty much the same (Figure 8).Also, we can see that the defenders who
receive red cards not very often thus having a very high metric for minutes per red card
are generally valued higher than those with a lower metric for minutes per red card who
correspondingly receive more red cards on average (Figure 9).
Figure 10: Price and statistics heatmap(Midﬁelders)
The seasonal statistical measures having the highest contribution to the transfer price
are the number of appearances, squad selections, assists, minutes played, goals scored, and
the average number of points gained by the team when the player was on the ﬁeld. None of
the cumulative statistical metrics have any contribution to the transfer fee of the midﬁelders
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Figure 12: Transfer price vs market values(Midﬁelders)
Figure 13: Transfer price vs number of appearances(Midﬁelders)
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Most of the midﬁelders are sold for a price close to their expected market value,
except some midﬁelders who were sold for a signiﬁcantly higher or lower price than their
market value at the time of the transfer (Figure 12).The correlation between the number
of appearances and transfer fees of midﬁelders is not very high, but in general, the players
with a higher number of seasonal appearances during the transfer’s season are priced higher
Figure 14: Price and statistics heatmap(Attackers)
The most contributed metrics to the transfer price of attackers are the number of
assists, goals, the number of points earned by the team when the player was on the ﬁeld,
and also the number of squad selections and appearances. None of the cumulative metrics
are connected to the players’ transfer price (Figure 14).
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Figure 15: Price and ratios(Attackers)
The ratios are again not signiﬁcantly contributing to the transfer price. The ratio
that is related to the attacker’s position and have a relative contribution to the price are
player’s ﬁeld playing percentage(What proportion of time being elected in the squad of the
team does the player spend on the ﬁeld) (Figure 15).
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Figure 16: Transfer price vs market value(Attackers)
Figure 17: Transfer price vs number of goals(Attackers)
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In general, the attacker’s transfer price is more likely to be higher than his estimated
market value rather than being lower, and only a few attackers were bought for a price
signiﬁcantly lower than their estimated market value (Figure 16). The number of goals the
attacker scored during his transfer’s season has a little correlation to his transfer price as in
general the higher the number of goals the higher the price, but the connection is not strong
as some players with a huge amount of goals were sold very cheap and some players with a
few amount of goals were sold very expensive (Figure 17).
As a result of analyzing each position’s attributes to the transfer price, we found out
that the market value of the player had the highest contribution to his transfer price in each
position. Market value is a very close attribute to the transfer price, however, the market
value of the player is not always a valid estimate for the player’s price. Market value is also
dependent on many attributes of the player. As we already analyzed the player’s performance
metrics contribution to their transfer price, and the contribution was also identical to the
market value, we analyzed some other attributes of the players that had some correlation to
their market value. We have analyzed the market value of the selected players during the
2019/2020 season to identify the currently important non-performance variables(Metrics that
are independent or not highly correlated to the player’s performance) that are contributing
to the player’s market value.
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Figure 18: Market Value vs age
Figure 19: Market value by years on contract left
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As we can see the correlation between the age and market value is not explicit.
Starting from some moment the market value of the player decreases with the age increasing.
Most of the expensive players are in the age period of 20-26 as in these years their market
value increases alongside the age, as for this age period the players don’t lose their physical
attributes but gain more experience so their market value increases too. As we can see most
of the players’ market value is less than 100 million, and only a few players have higher
market value. Most of these players are young superstars. For example, K.Mbappe who is
the most expensive player in our dataset has market value of 200 million at the age of 20.
According to his age, he has not reached his peak of performance yet but already has a very
high market value. Most of the other expensive players are at their peak level of performance
or very close to it, as they are in the 25-28 age period. Examples are Kevin De Bruyne or
Antuan Griezmen. The market value of the players drastically drops after they turn 30,
except some superstars and legends of the game such as Messi and Ronaldo who are aged 32
and 35 have market values of 140 million and 75 million accordingly. There are also other
aged players who have pretty decent market value for their age such as Karim Benzema(35
million, 32 years old) or Angel Di Maria(40 million, 32 years old), but their market value does
not overcome 40 million. Most of the expensive players are either attackers or midﬁelders.
Only a few goalkeepers and defenders have signiﬁcantly high market values. Also, in general,
almost all the positions have the same age period where the players have their highest market
values (Figure 18).
The players whose contract expires at the end of the season have the lowest market
value, as at the end of the season if they do not expand their contract, other teams can sign
them for free. A similar situation is for players who have one more year according to their
contract. Those players are valued higher as their teams still have the chance of negotiating
the player’s contract or sell them by a relatively high price. The players who have 2 years
remaining to their contract are usually those who can be sold by a very high price as if
the team fails to agree on terms with the player, they can sell him on a very good deal.
The players who have 3 or more years on their contract most of the time joined the team
recently(1 or 2 years ago as based on age the teams mostly sign new players for averagely 5
years) or have recently extended their contract at the club (Figure 19).
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Figure 20: Market value vs instagram followers
Correlation Goalkeepers Defenders Midﬁelders Attackers
Corr(Market Value, Followers) 0.47 0.28 0.40 0.47
Table 4: Correlation table of followers and market value
Nowadays soccer is a very proﬁtable business with lots of attractive contracts from
huge companies, for both the players and the clubs. Taking that into account the famous
soccer teams consider the player’s popularity too when buying him, as if the player has good
performance metrics and is also popular outside soccer then they can make huge proﬁts from
the contracts of the player. Taking this into account let’s check the correlation between the
number of player’s Instagram followers and his market value. As we can see the correlation
is positive meaning that in general the more popular(more followers Instagram) the player
is the higher his market value. In this case, the age of the player is not a key factor as the
number of the player’s followers is mostly not dependent on his playing attributes. There
only a few players who have a signiﬁcantly high amount of followers. Most of these players
Analyzing soccer’s transfers and predicting footballers’ transfer price Page 31
are from famous soccer clubs and have huge sponsorship contracts. Cristiano Ronaldo is
actually the person with the highest number of followers on Instagram. We can see that
the most popular position is attackers as players having an attacking position enjoy the
highest popularity among social media users. The situation is very similar for defenders and
midﬁelders as both positions players have more or less the same ratio of market value and
followers. However, we can see that the goalkeepers are not that popular among social media
users as for example one of the most expensive players of the dataset Yan Oblak who has a
market value of 100 million euros has only about 1 million followers,(Table 4) whereas the
attackers who have approximately the same market value enjoy double triple and even more
number of followers (Figure 20).
Players’ physical and racial attributes
Figure 21: Market Value over continents
As we can see the players from European countries are valued the highest, as most
of them play in European leagues. Players from South America and Africa are also highly
Analyzing soccer’s transfers and predicting footballers’ transfer price Page 32
valued, as the South Americans are mostly very talented and have good technique and the
African players have great physical conditions. The other continents are in general similar
in terms of the market value of their players. Only a few Asian or North American players
have high market values and the others are no diﬀerent based on the continent (Figure 21).
Figure 22: Player’s height over positions
Another attribute that can be important for the player based on his position is
height.As we can see high height is very important for the goalkeepers as the players with
the highest height are goalkeepers and only a minority of the goalkeepers have a height of
lower than 180 cm.Most of the defenders and attackers also have high heights but not as
high as the goalkeepers and some of the players from these positions have heights lower or
equal to 160 cm.According to the visualization, the height of the player is least important
for midﬁelders (Figure 22).
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Figure 23: Player’s age by positions
The positions where there are more players with generally older age are goalkeepers and
defenders. These two positions in soccer require good experience in the game and some times
the player’s ability to understand the opponent, which is usually high among experienced
players is valued even more than his physical attributes as the player can compensate those
with his experience. Good examples are Italian goalkeepers and defenders who sometimes
play up to 40 and do not lose their quality. The midﬁelders and attackers are usually younger
as they do a lot of physical work on the ﬁeld and old players mostly fail to keep their high
level in these positions due to physical attributes that get worse by their age (Figure 23).
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2.2.2 Time Series Analysis
In order to identify the overall patterns of the economic valuations of players in
soccer, we have analyzed the transfer fees and market values of the player’s over the years
and over their age. We have also taken into account the eﬀects of the categorical variables
and other factors such as worldwide events taken place during the moment of the peaks of
transfer prices and market values of the players. In order to summarize the overall prices
of the players, we used diﬀerent summarizers such as mean, median, maximum to identify
the patterns for the players in each price category. The time period analyzed for transfers is
around 20 years, starting from the late 1990s and early 2000s transfers. The market value
of the players was available only starting from 2007, so the historical data of market value
contains around 13 years and around 17,000 players.
Players’ transfer fee over time
Figure 24: Transfer price and Market value correlation over years
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As we can see the highest correlations between the transfer fees and market values
were before 2010. Also, we can notice that after each world cup year(2006, 2010, ..., 2018),
the correlation between the variables decreased as most of the time the players who played
well in the tournament were sold for a price higher than their real value. And also we can
see multiple cases, where the correlation decreased signiﬁcantly the following year. Those
are 2009, 2005, 2013, and 2016, 2019. Here again, We noticed a pattern. During the years
2009,2013, and 2016 transfer records were broken. So after a new expensive transfer, the
fees for players became higher and thus less correlated to their market value (Figure 24).
Figure 25: Transfer price over years(mean)
If we take mean as a summarizer for transfer fee over years, the highest point appears
in the early years, as during those years transfers were not common things and in case of
expensive transfers, the mean transfer fee became very high. We can see that the highest
point was in 2001 for goalkeepers, as in that year the transfer record for goalkeepers was
beaten when Buﬀon was bought for around 53m euros. Over time the high points seem to
become less common as more expensive transfers happen (Figure 25).
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Figure 26: Transfer price over years(median)
After taking the median as a summarizer we can see the position for the highest
point changed becoming midﬁelders and attackers in the 2000s. The goalkeepers do not
have high value, taken median as a summarizer as the median is sensitive to extreme values
and expensive goalkeeper transfers are a very rare phenomenon in soccer (Figure 26).
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Figure 27: Transfer price over years(median)
Taking maximum as a summarizer we can see the transfer fee record-breaking years
for each position. In this aspect, the goalkeepers are the most stable position as there were
only 2 cases of goalkeeper transfers when the fee was record-breaking. Defenders are also
mostly stable in this aspect with a few record-breaking transfers in this period. Midﬁelders
also have only a few occurrences of record-breaking transfers and the periods between two
record-breaking transfers were very long before 2014, after which the record was beaten twice
in 4 years. Attackers have the highest transfer fee records and have the shortest periods
among the record-breaking transfers. Also, the diﬀerence between two record transfers price
was highest among attackers (Figure 27). That transfer took place in 2018 and the fee paid
was two times expensive than the previous transfer record’s fee. More details about Transfer
5Link to historical transfer fee records
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Figure 28: Transfer price over years by transfer window type(mean)
The most expensive transfers mostly happen during the summer transfer window, as
the teams have more time to make the transfers. There are also some years when relatively
expensive transfers happened during the middle of the season. But most of the time transfers
in the middle of the season are rare events (Figure 28).
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Figure 29: Transfer price over years by transfer window type and position(max)
Taking max as a summarizer we can see that almost all the records were beaten
during summer transfers’ window, except for midﬁelders, for which the transfer record for
that position was beaten during a winter transfer window. Also, one of the records for
attackers was beaten in 2013’s midseason as Gareth Bale’s transfer happened on September
2 (Figure 29).
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Figure 30: Transfer price over age(max)
As we can see most of the expensive transfers take place with players aged from 20 to
25 for all positions. Players belonging to this age category are the ones with huge potential,
that increases over time till they reach their peak age, which is for most of the player’s
around 29-32 years old based on the position on the ﬁeld. We can also see a huge increase
for 33 years old attackers, but this peak happened because of Cristiano Ronaldo’s transfer
to Juventus for around 100m when he was aged 33. This is an exception rather than a
general behavior as a player at his age are valued low, and top transfers of players in this
age category is a very rare event (Figure 30). More details on the player’s based on age can
be found on transfermarkt’s most valuable players page 6.
6Link to the most valuable players
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Players’ Market value over time
Figure 31: Market value over years(mean)
We have ﬁrstly analyzed the players who have a very high market value, which most of
the time means that they play in the top championships and most probably for good national
teams. Almost all the positions started to have a rise in market value starting from 2007.
Goalkeepers and defenders did not lose track and increased in value most of the time up to
2020. However, there is a noticeable pattern. As we can see in general almost every two
years the player’s market value rises compared to the previous year. The increase happens
due to International tournaments. Most of the major international tournaments take place
every 4 years, so every 2 years, there is either a world cup or a continental cup. During the
tournaments, most of the player’s who play good earn high market value increases, and we
can see that in 2014 when the world cup in Brazil took place, the midﬁelders had an increase
in their market value compared to 2013 and then a decrease in 2015. The same pattern
is repeated for attackers in 2010. However, after 2016 all the players started to have an
increase in their market value in general, with only once having a decrease(for goalkeepers
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in 2018). The goalkeepers were mostly stable in terms of rising their market value, having
a notable drop in 2015(again after world cup).The reason for the drop in the market value
of goalkeepers is that the world cups that took place during the analyzed years were the
ones with the highest number of goals scored on average in our dataset, so in general, the
goalkeepers allowed many goals during those tournaments and as a result had decrease in
their market value after the tournaments (Figure 31).The average goals statistics over the
world cups 7.
Figure 32: Market value over years(mean)
As we can see if we include all the players from the dataset, the international cup
eﬀect is not very often anymore, as most of the players are playing for teams from not
popular leagues and weak countries which play in international or continental tournaments
very rarely. In general players from all the positions had their peak value in 2009, (during
that year a record-breaking transfer of Cristiano Ronaldo took place), after which the values
7Link to an infographic about the world cups
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seemed to be stable and started to rise dramatically from 2018 when Neymar’s record-
breaking transfer took place (Figure 32).
Figure 33: Market value over age(mean)
As we can see the players have the lowest market values at the beginning and at the
end of their career and most of them reach their peak value at the age of 27-31(based on the
player’s position. The goalkeepers are able to have the least amount of decrease in market
value as they get older compared to the other positions. Also, we can see that the market
values of the players started to increase dramatically from the late teens and early twenties
of the player up to his peak (Figure 33).
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Figure 34: Market value over age by continents(mean)
If we take mean as a summarizer for market values, we can see that the African players
have the highest market value in comparison to players from other continents. Asian players
have the lowest values as the majority of them play in their domestic championships. The
players from North America and Oceania do not have a high market either, as they also
mostly play in their domestic leagues. North American players are the youngest to retire in
comparison with other leagues, whereas Asians are the oldest to retire, our dataset contains
a Japanese player who is 53 years old. The market value’s behavior is very similar for South
American and European players, except the fact that young players from South America are
valued more expensive than the European players of the same age (Figure 34).
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Figure 35: Market value over age in top leagues(mean)
If we take a look at the market value change over player’s age in the most popular
leagues, we can see that players in League 1(French league) have the highest market value at
the youngest age(mean taken as summarizer). However, players older than 18 do not have
a higher market value than their agemates from other leagues. The young players also have
a good starting point in Liga NOS and Serie A.(Portuguese and Brazilian). These leagues
are famous to the whole world for exporting the youngsters to top European leagues. Old
players have no value in any league. We can see that players have a signiﬁcant increase in
their market value only in the top 5 soccer leagues. The top 5 league player’s market value
has almost the same path in terms of increasing and decreasing along with age, and the most
expensive players are in LaLiga and Premier League. The situation in other leagues does
not change almost at all as the mean values of the players reach only about 2-3 million in
the best cases (Figure 35).
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Figure 36: Market value vs cumulative market value over years)
As we can see before the middle 2010s the correlation between the player’s seasonal
market value and the cumulative mean of his market value at the time of the transfer was
very high, meaning that seasonal based increases or decreases in the players’ market value
were rare. However, we can see that after around 2011, the seasonal market values of the
players started to have a little deviation from their cumulative market value meaning that
over time more seasonal based overvalued or undervalued players occurred (Figure 36).
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Figure 37: Market value correlation with cumulative market value over years
As we can see the correlation between the variables is solid and there were only a few
peaks , and we can see that the current trend is decreasing in the correlation between the
variables as currently more and more one season wonderers appear, who get attached high
market value to them, having no signiﬁcant market value history. The decrease in the rate of
correlation emerged in 2017, nevertheless the decrease rate is not signiﬁcant yet. (Figure 37).
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Figure 38: Market value vs previous year’s market value over years
As we can see the players’ previous year market value is strongly correlated to their
current market value. The correlation seems to be higher in the early years and started to
get lower after the early 2010s late 2000s, similar to the case of market value and cumulative
market value correlation(Figure 38).
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Figure 39: Market value correlation with previous year market value over years
As we can see the correlation between a player’s market value and his previous year’s
market value was the highest in the early years and started to drop drastically starting from
2018. This behavior is explained by the fact that in the early years it was easier to value
the players and mostly their valuation was done using trusted approaches build over time,
but over time more factors inﬂuence the market value of the player so the correlation with
previous years value gets lower and lower. Again we can see breakouts in some international
competition years and after Neymar’s transfer (Figure 39).
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2.2.3 Network Analysis
In order to identify the main ruling clubs and countries of the transfer market, we have
analyzed the transfers’ network by visualizing and interpreting diﬀerent network statistics.
We have used each transfer of the dataset as an edge, taking the team from which the player
was bought and the team the player was sold to as nodes. The same approach was used for
analyzing the loan network and winter transfers. As, in soccer transfer between two same
clubs can happen many times, so as a result the network’s type is directed multigraph. We
have also used the Node2Vec algorithm for ﬁnding the similar clubs in the network.
Node2Vec is a feature learning algorithm for networks that transforms the network’s
information into vectorized form using random walks and a combination of tree-based BFS
and DFS (Grover & Leskovec, 2016). In order to visualize the similarity scores of the nodes
we have used PCA dimensionality reduction algorithm (Qu, Ostrouchov, Samatova, & Geist,
The framework used for building the networks was networkx and as the networks
contained a lot of nodes, and interactive visualizations tool bokeh was used. In most of the
visualizations, the color of the node represents the content of the club, the size of the node
represents the node’s degree(number of incoming and outcoming edges), the color of the edge
represents the transfer window type, the width of the edges represents the fee of the transfer
and the opacity of the edges represents the age of the players involved in the transfer.
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Soccer’s Transfers Network by teams
Figure 40: Transfers network using teams as nodes
As the networks contain a lot of nodes, we cannot get much information from the
visualization. However, we can see that the European teams(node color blue) dominate in
the market, with the majority of them connected with each other, also the majority of the
transfers happen during the summer transfer window(edge color orange), except for most of
the Asian teams, which make most of their deals during the winter transfer window(edge
color black) as the primary pre-season transfer window for most of the Asian leagues takes
place during January-February. We can also see that the young players(low opacity of the
edge) tend to be transferred to big teams from small teams for high transfer fees(high width
of the edge) (Figure 40).
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Soccer’s Loan Network by teams
Figure 41: Loans network using teams as nodes
The main players of the market are again the European teams(node color green) and
most of the loans again take place during the summer transfer window. We can see that
there are only a few teams with many connections(big node size) and most of the other
teams have similar levels of connections. We can see that most of the players loaned are
young(low opacity) as most of the time big teams cannot provide enough gaming practice
for their youngsters so they send them to loans to teams where they can gain enough gaming
practice and develop their skills (Figure 41).
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Statistic Transfers Loans
Network’s density 0.08 0.12
Network’s reciprocity 0.64 0.95
Network’s assortavity based on continent 0.627 0.76
Network’s assortavity based on league class 0.379 0.417
Network’s assortavity based on country 0.563 0.593
Network’s assortavity based on degrees 0.270 0.15
Table 5: Networks Statistics on transfers and loans networks
Let’s ﬁrst analyze the transfers network. As we can see the network’s density is very
low, which is logical as we have many teams, and not all of them have connections between
each other. However, the reciprocity of the network is relatively high, as most of the teams
that make deals with each other have transferred in opposite directions too. The main
attributes for the assortativity of the teams are their continent and country, as it is easier
for players to move to another team that is in the same continent where they play, and even
more when it happens in the same country. The metric is around 0.5, as most of the talented
players from other continents and non-EU countries tend to move to European soccer clubs,
as there they have higher chances of succeeding. League’s class has the lowest eﬀect on
the assortativity as most of the time players from leagues with lower-ranking tend to move
to higher-ranked leagues. The degree of the node also has a relatively low connection to
the assortativity of the nodes, as teams with a low number of connections not always are
connected to teams with a lot of connections (Table 5).
If we investigate the networks statistics for the loans network we can see almost the
same metrics as for transfers network, except almost maximal value for reciprocity, which is
logical as in most of the cases player who is loaned to another club comes back to his club,
and only in some cases the club that loaned the player buys him.
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Figure 42: Communities in the transfers network
Girvan Newman’s community detection algorithm was used to identify the commu-
nities of the transfer network (Girvan & Newman, 2002). The algorithm’s generator was
iterated 5 times and as a result, it found 7 communities. In the ﬁgure above the node color
attribute is the community of the team. We can see that there is a very big community with
most of the teams involved in it. If we compare this visualization of the network with the
one using the content of the team as the node color, we can see that many teams from South
America migrated into a community with most of the European clubs. We can clearly see
the young talent suppliers of the European teams. (Small nodes in green with wide edges
and low opacity). With the help of the graph’s interactivity on IPython, we were able to
ﬁnd out that the Asian clubs have two communities, which contain the Japanese and South
Korean teams accordingly. The other 4 communities detected by the algorithm were very
small and not visible on the visualization (Figure 42).
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Figure 43: Similar teams according to Node2Vec
Node2Vec identiﬁed the team’s similarity mostly based on the country of the teams,
frequency of transfers between the clubs, and similarity in terms of making transfers. We
can see that one of the most proﬁtable making teams of the network, Benﬁca is similar to
many Portugues teams and also some famous teams as the club is famous for providing the
top leagues with high-level youngsters. Another famous youngster provider Porto has almost
the same situation as Benﬁca. Porto is very similar to some Portuguese teams and also some
teams from outside Portugal (Figure 43).
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Through exploratory data analysis we have identiﬁed that the most signiﬁcant variable
to the reponse was the player’s market value. We have also identiﬁed that the categorical
variables also make impact on the player’s market value which in its turn impacts the po-
tential transfer fee. Also we have found out that the perfomance metrics and ratios were not
strongly connected to the output variable.
Time Series Analysis insights
As a result of analyzing the historical data of transfer fees and market values of the
player over the years and their age, we have found out the periods of the players’ peak
valuation and also identiﬁed that external events, such as world or continental tournaments
taking place during the transfers’ years make an impact on the fee.
Network Analysis insights
The analysis of the transfers and loan networks gave general information about the
main active participants of the transfer market and showed the main communities of the
network. The implementation of Node2Vec showed an overall criterion for the similarity
amongst the teams and the results were pretty similar to the community detection algorithm’s
ﬁndings, as most of the similar teams were part of the same community.
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2.3 Data Preparation
2.3.1 Data Transformation
After analyzing the data in various aspects, we have started the process of preparing
our data for the modeling stage. In order to gain most of our data without losing too many
observations and information, we have made some changes to our dataset. The transforma-
tions were made on both the output variable and on some input variables.
Output variable transformation
Figure 44: Histogram and probabilty plot of transfer fee(original scale)
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Figure 45: Histogram and probabilty plot of transfer fee(logarithmic scale)
As the output variable was highly skewed and we were losing a lot of observations
when removing the outliers, we have decided to scale the output variable to logarithmic
scale in order to normalize the output’s distribution (Figure 44). We used log (1 + x) to
scale the output variable from millions scale to log scale, the same transformation was also
applied to players’ seasonal and cumulative market values at the time of the transfer as those
variables were also from the same scale as the output variable (Figure 45). After applying
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the transformation we have removed the observations for which the output variable was an
outlier using the z-score approach.
One hot encoding of categorical variables
As the dataset contained some categorical variables that had contribution to the
output variable we have encoded those using one hot encoder as some of them contained
more than two levels and we did not want to use one variables for deﬁning each as in that
case we would have to assign levels of importance for each group for each categorical variable,
we rather wanted the model to identify the importance of each group for each categorical
variable. The categorical variables used were
•The continent of the player(6 groups)
•The strong foot of the player (Right,Left,Both or unknown)
•The window of the transfer(Summer, Winter, Mid-Season)
•The type of the year of the transfer(Tournament year or non-tournament year)
•The tactical position of the player on the ﬁeld. (This variable was not used for goal-
keepers, and had from to 3-5 levels depending on the position.)
2.3.2 Missing Value Imputation
After selecting the most signiﬁcant variables based on the insights from the data
analysis stage, we have imputed the missing values for each position. Most of the missing
values were in ratios as the ratios were calculating using divisions of diﬀerent statistical
measures and sometimes the divisor was 0 leading to na values. Before applying an imputer
algorithm we have identiﬁed the variables which we were going to drop. The criterion
for keeping a variable with missing values was that it should have no more than around
30$ missing values. After identifying the variables missing data of which can be imputed
according to our criterion, we have proceeded with the imputation algorithm.
Missing values imputation with KNNImputer
We have used the KNNImputer algorithm on the selected input features (Garc´ıa-Laencina,
Sancho-G´omez, Figueiras-Vidal, & Verleysen, 2008). KNNImputer ﬁlls the missing values
in the dataset by taking the mean of the knearest neighbors of the observation, where kis
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the parameter for how many neighbors to look for. The neighbors are identiﬁed based on
the similarity of the non-missing features of the observation with other observations.
2.3.3 Feature Selection
There were a few stages of feature selection. We have deﬁned a general pipeline that
was used for all the datasets and there were two approaches to choosing the features inputted
to the models. Firstly we have identiﬁed the most signiﬁcant variables to the output variable
using the insights gained during the analysis stage. As most of the features were strongly
correlated with each other we later removed correlated input variables by keeping only one
of them. Later we imputed the missing values. After these stages, the observations where
the input variables were outliers using z-score were removed. After accomplishing all of these
stages we have used 2 approaches for selecting the ﬁnal input variables that were used for
training the models and predicting. The two approaches of feature selection for the models
were applied for each position and the one with the best results was kept.
Feature selection using p-value
We have used an iterative approach of keeping all the variables that have a signiﬁcance
for the output variable lying in a conﬁdence interval of higher or equal than 95%, thus picking
the variables that have p-value lower than equal to 0.05. The algorithm iterates over all the
input variables each time removing the variable with the highest p-value and keeps the
variables that meet the threshold criteria for the p-value calculated by ﬁtting the input
variables to the output variables using Ordinary Least Squares method. While using this
approach we have given only the numerical features of the dataset as an input, without
calculating the signiﬁcance of the categorical variables in order to not face miscalculations
during the p-value calculation process, as the columns with encoded categorical features take
values of either 1 or 0.
Feature selection using RFR’s feature importance
The second approach was using Random Forest Regressor’s feature importance pa-
rameter. Random Forest Regressor shuﬄes each column while predicting and if as a result the
predictive power decreases the variables’ importance increases. We have inserted the dataset
including the categorical variables and have chosen ncolumns sorted by their importance,
where nwas the number of desired input variables to use for the models
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Data preparation and exploratory descriptive analysis helped us to gain some crucial
insights about the data. At this moment, we will implement commonly used machine learning
and deep learning algorithms to predict footballers’ transfer price. Since the characteristics
of the football players may diﬀer for each position, we decided to implement same set of
models on each position separately (goalkeepers, defenders, midﬁelders, attackers). Since
the transfer price is a continuous variable, we can conﬁdently state that we need to solve a
To start the analysis, ﬁrstly we should deﬁne the success metric for this particular
problem, which will eventually help us to compare diﬀerent models and analyse their perfor-
mance. Understanding interpretation and diﬀerences between several regression metrics, we
decided to use root mean squared error to evaluate diﬀerent models. RMSE stands for the
square root of the average of squared diﬀerences between the actual and predicted values.
Since RMSE squares the diﬀerence between actual and predicted values, it may eventually
give huge weight to large errors, which will help us to choose model that predicts the output
as precise as possible. After training the models, we have predicted the output using the
test dataset and calculated the RMSE for the outputs converted back to the original scale
in millions in order to compare the models’ prediction powers.
2.4.1 Machine Learning
Before starting to implement machine learning models, ﬁrst we need to split our
data into training and testing sets. Each dataframe will use 80 percent of observations to
perform training and 20 percent of observations to validate models. At the end, we will also
implement 5-fold cross validation in order to check how models will work on diﬀerent splits
of the data. Now let us see the set of machine learning models that were used to solve the
1. Multiple Linear Regression.
•No transformations were made on the training set.
2. Polynomial Regression.
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•Training set was transformed by including diﬀerent interactions of variables with
the degree of 2.
3. Elastic-Net Regression.
•The algorithm is used to perform regularization of features.
•The penalty parameter alpha was tuned with cross validation from 500 diﬀerent
4. Decision Tree Regression.
•The parameters like maximum depth of the tree, minimum number of samples
required to split internal node and maximum number of features were tuned using
5. Random Forest Regression.
•The number of trees and maximum depth parameters were tuned using cross
6. Voting Regression.
•Voting regression combines all models by taking the mean of all predicted values
as a ﬁnal output.
Above mentioned 6 models were implemented on all positions. To summarize the perfor-
mance of the models, we calculated RMSE using 5-fold cross validation and took the mean
of all folds to ﬁnalize the performance of the models. At the end, we can state that the
model that outputs the minimum cross validated score can be considered as a best model
for the following problem.
2.4.2 Deep Learning
After applying various machine learning algorithms using the structured representa-
tion of the data, we applied deep neural networks regression in order to identify whether the
predictions can get any better when using unstructured data and diﬀerent neural networks.
We again applied the neural networks to each position using the same metric for success
as in machine learning models. The only signiﬁcant diﬀerence between the applications of
the models on each position is that we used a simple neural network for the goalkeepers, as
the number of observations was the fewest in this position and the experiments with more
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ﬂexible neural network structures did not improve the accuracy over the simple network.
The structure of the network for the other positions was more ﬂexible in comparison to
the network used for goalkeepers and contained 4 layers. As the training process of neural
networks is very costly, we did not implement cross-validation for the models, and in order
to estimate the generalization of the models, we have used validation datasets. As the goal-
keepers contained the least amount of observations we have used the test dataset in order
to evaluate the performance of the model on unseen data during the training process. As
for the other positions the number of observations was signiﬁcantly higher we have used a
20 percent split of the training data as a validation data. In order to prevent overﬁtting, we
have implemented early stopping callback on the training process, which will stop training
if the loss of the model on the validation data does not have signiﬁcant improvements over
n/10 epochs, where nis the number of epochs used in the training and will restore the
weights from the epoch with the best validation loss. We have also added L1regularizations
on the kernel weights, activity function outputs, and on the bias.
L1(x, y) =
The neural network built for goalkeepers also contains a dropout before the ﬁrst hidden
layer. The optimization algorithm used for both networks was Adam and the loss function
was mean squared error.(Kingma & Ba, 2014) The activation function used for all the layers
in both networks was relu. The networks for each position were trained on 2000 epochs.
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Figure 46: Neural Networks structure for goalkeepers
The neural network used for goalkeepers, contains 1 input layer, 1 hidden layer, and
an output layer. The input layer contains 25 neurons, the hidden layer contains 10 neurons
and the output layer contains 1 neuron (Figure 46)
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Figure 47: Neural Networks structure for other positions
The structure of the network used for other positions was more ﬂexible containing
one input layer with 100 neurons, 3 hidden layers with 50,25 and 10 neurons accordingly,
and an output layer containing 1 neuron (Figure 47).
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Figure 48: Models’ loss for all positions
As we can see all of the models have generalization power and the validation loss
decreases alongside training loss. Also, we can see that Early Stopping prevented the training
at some point before the full number of iterations which was 2000 for each position, after
seeing no considerable improvements on the model’s loss on validation data (Figure 48)
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2.5.1 Predictive Power and Interpretations
Machine Learning Results
Figure 49: Cross validated RMSE for each position and model
After performing machine learning models we can see that the best performing models
are Linear Regression on goalkeepers and Random Forest on other positions.
Due to the small number of observations in the goalkeepers’ dataset, we can clearly
see that the results are more biased compared to the other positions. Here we can also see
that the best performing model Random Forest works best for defenders and midﬁelders
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Figure 50: Actual vs predicted values of the test set
Correlation Goalkeepers Defenders Midﬁelders Attackers
Corr(ytest , ypredicted ) 0.75 0.84 0.80 0.79
Table 6: Correlation table for actual vs predicted price (Machine Learning)
We can see that the predicted values and actual values of the test set have a strong cor-
relation, which indicates the strong predictive power of the models (Table 6). The correlation
coeﬃcients between predicted and actual values were bigger than 0.7 (Figure 50).
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Deep Learning Results
Figure 51: RMSE on each position(Neural Networks)
As we can see only the predictions for the goalkeepers have a noticeably smaller
score of RMSE in comparison to the best model from Machine Learning algorithms in
each position. The RMSE score for defenders is also very similar to the results of the
best Machine Learning model for that position. The RM SE scores for attackers is a little
higher than the same score obtained using RFR. However, the RMSE score for midﬁelders
using deep neural networks regression is signiﬁcantly higher compared to RFR for midﬁelders
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Figure 52: Actual vs predicted transfer price(Neural Networks)
Correlation Goalkeepers Defenders Midﬁelders Attackers
Corr(ytest , ypredicted ) 0.77 0.87 0.91 0.91
Table 7: Correlation table for actual vs predicted price (Deep Learning)
As we can see the predictions made using the neural networks regression have a
higher correlation with the actual output, and the variance amongst the predictions is lower
in comparison with the predictions made by the best machine learning algorithm for each
position (Table 7). However, we can also see that the model generally tends to undervalue
the players, and most of the time the predicted price for the players using neural networks
regression was lower than their actual price (Figure 52).
The correlation score of predicted and actual variable increased for all the positions.
The improvements in the correlation score were signiﬁcant only for midﬁelders and attackers
in comparison with the correlation score obtained by the best machine learning approaches
used for each position.
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2.5.2 Comparisons and best model selection
Before comparing and interpreting the results of the Machine Learning and Deep
Learning approaches, let’s ﬁrst identify the main diﬀerences in the way we implemented
One of the key diﬀerences between the Deep Learning and Machine Learning ap-
proaches was the pipeline used for preparing the data for inputting to the models. The com-
mon parts of the pipeline amongst the approaches were the process of removing multi-colinear
variables, removing the outliers observations amongst the input features using z-score. In
contrast to Machine Learning algorithms, Deep Neural Networks did not use categorical data
as the results seemed unchangeable in the case of both using and not using those, whereas
the categorical variables made a huge impact on Machine Learning models. Another key dif-
ference between the pipelines of data preparation amongst the approaches was the process
of ﬁnal feature selection for the model.The 5 most important features according to RFR’s
feature importance criteria were selected and later transformed into z−score for all posi-
tions in neural networks regression approaches. The approach of the ﬁnal stage of the data
preparation pipeline,which was the process of selecting the features for the training and test
datasets was diﬀerent amongst the positions in Machine Learning approaches.
•Goalkeepers (p-value based signiﬁcance) + ppg
•Defenders (p-value based signiﬁcance)
•Midﬁelders (10 most important variables according to RFR)
•Attackers (10 most important variables according to RFR)
The described approaches were a result of various experiments and the best results in
terms of lower RMSE score are represented. For goalkeepers the attribute of points per
game was also added to the 95% signiﬁcant variables as the initial p-value score for this
attribute was very close to the threshold, and the model had noticable improvements after
adding this variable. The input variables were not transformed in the training and testing
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Interpretations and best model selection
We can see that in general, the Machine Learning algorithms have given better results
in terms of lower RMSE. The only position for which the Deep Neural Networks regression
usage leads to lower RMSE was goalkeepers. The scores were also similar for Attackers and
Defenders. So, overall the Deep Neural Networks regression approach worked considerably
well for the positions for which the relationship was very close to linear. If we check the
cross-validated RMSE scores in Machine Learning Results we can see that for the mentioned
positions the obtained RM SE(CV) score in Multiple Linear Regression algorithm was close
to the best model’s score and for goalkeepers, the Multiple Linear Regression usage leads to
the lowest RMSE(CV) score. Taking those facts into account we can conclude that for this
problem, the deep neural networks do not work particularly well, and had closer predictions
to Machine Learning algorithms only for positions for which the relationships between the
input variables and output variable were close to linear.
According to our main criteria for selecting the best models, the Random Forest Re-
gressor algorithm works best for all the positions except Goalkeepers. For goalkeepers the
lowest RMSE score was obtained using deep neural networks, so according to our criteria it
is the best model for this position, but if take into account that the diﬀerences amongst the
RMSE scores obtained by the Multiple Linear Regression approach and Deep Neural Net-
works approach were around 1million, but the cost of training the neural networks is much
much higher than the cost of training the Multiple Linear Regression model, we choose the
Multiple Linear Regression as the best model for goalkeepers, as it is much more simple
and the predictive power is not very signiﬁcantly lower compared to Deep Neural Networks
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Figure 53: Most important features according to RFR
We have used Random Forest Regressor’s feature importance for each position in
order to identify which of the features have the highest contribution to the fee according to
the trained model. As expected after the data analysis stage, the market value of the player
is the most important feature in all positions. We can also see that the points per game has
relative importance for each position, as this is mostly a team attribute and not speciﬁc to
any position, but rather its a combination of each positions’ players eﬀort on the pitch. The
importance of the other features is considerably lower. Let’s interpret the most signiﬁcant
variables except market value for each position according to RFR.
For goalkeepers, the most important attribute after the market value is their height,
as taller goalkeepers generally have better goalkeeping skills. The age also seems relatively
signiﬁcant. From the encoded categorical variables, only two have importance, and the
importance is very low. The variables are goalkeeper’s race(it is important whether the
player is European or not), and the transfer’s year type indicating whether a tournament
took place during the transfer’s year. (Figure 53, upper left ﬁgure)
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For defenders age, the cumulative number of won games and minutes per yellow card
and the number of appearances during the transfer’s year are the most important. The strong
foot of the player(left-footed defenders only) and European nationality are the important
categorical variables, alongside with the transfer speciﬁc variables, from which the important
ones for defender are whether or not the transfer’s year was a tournament year and whether
the transfer took place during the summer transfer window.As described in the analysis the
defenders usually gain many yellow cars, and the expensive ones gain yellow cards in a lower
frequency, thus having high numbers for mpyc.(Figure 53, upper right ﬁgure)
For midﬁelders the age, the cumulative number of won games, minutes per yellow
card during the transfer season, appearances, cumulative playing percentage, and minutes
per assists are the most important, alongside height and cumulative minutes per goal. The
relatively important positions for the price of midﬁelders are central defensive midﬁelder and
attacking midﬁelder and the other categorical variables’ importance is similar to defenders.
We can see that for midﬁelders both attacking and defending attributes have a contribution
to their price, as midﬁelders are generally the most balanced players. (Figure 53, lower left
For attackers, the important performance attributes are pretty similar to midﬁelders,
except defensive performance metrics not being important for attackers. We can also see
that for attackers most of the attributes are important on the cumulative basis, including the
player’s cumulative mean of his market value before the transfer. So attackers, in general,
are priced based on their whole career performance rather than season based performance.
(Figure 53, lower right ﬁgure)
As for goalkeepers the model with the lowest cross validate RMSE score was Linear
Regression let’s also interpret the coeﬃcients for each feature.
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Figure 54: Weights of each feature according to MLR(Goalkeepers)
As we can see only the height of the player, his market value’s log, and the type
of the transfer’s year have positive weights, and the other variables have negative weights.
The mid-season transfer window type has a very unsigniﬁcant negative coeﬃcient, as in
general transfers made during the Midseason are rare and especially for goalkeepers, for
which transfers, in general, happen rarely. We can also see that age, points per game and
the Europan nationality of the goalkeepers have negative coeﬃcients. Age’s relationships
to the fee were expected to be negative as in general old players are valued lower. We can
also see that the European nationality of the goalkeeper has a negative coeﬃcient, which is
explained by the fact that most of the European players play in EU leagues, and most of
the EU teams changed their goalkeepers very rarely, and for many teams, the goalkeepers
stay in the starting eleven for even around 10 years, and later as they get older they are sold
to other teams for low values, most of the European goalkeepers are also bought when they
are young, thus, in general, having a lower price. The negative weight for the points per
game variable indicates that if the team has ppg rates, thus a high winning percentage, the
goalkeepers probably are not the main players responsible for that (Figure 54).
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To conclude we can see that with the usage of the only performance-based variables,
the model mostly undervalues the players rather than overvalues them, meaning that accord-
ing to the models we have used the transfer fee of the player is not only dependent on his
performance-based statistics. We can see that the transfer speciﬁc categorical variables such
as tournament year and transfer window were important for each position. So, our ﬁndings
in the analysis can be conﬁrmed as in years during which a national tournament takes place
the prices of the transfers seem to get higher. Another common measure amongst all the
positions was the race of the player indicating the importance of only the European players,
which again shows that the players from other continents are generally undervalued and for
European players their nationality is an advantage. We can also see that the relationship
between the performance metrics and position gets more complex over positions, being very
close to linear for goalkeepers and defenders and getting more complex for midﬁelders and
attackers. A crucial insight from the analysis about the popularity can be related to this,
as the midﬁelders and attackers gain the most popular amongst social media, and taking
into account the current tendencies of soccer, their popularity can be a key factor for their
price. We did not include the player’s popularity rate as the data of Instagram followers was
missing for most of the players, and in order to be more precise about the player’s popularity
his contracts with brands and his desirability in the advertisement market should be taken
into account, but the data for those attributes was not available.
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3.1 Interactive Dashboard Application
As a visual representation of collected and analyzed data, we used plotly.dash to create
a simple dashboard. This dashboard contains table representations of dataframes we have
used, as well as the scatter plots and line charts of market value and transfer fees of the players
in relation to their age, current year, last year’s, and cumulative market values as well as
positions, continents and major leagues. The dashboard uses Dash Core Components (DCC)
and Plotly Express (PX) for converting the data frames to a more user-friendly appearance.
The dashboard is deployed using Heroku servers.
Although we saw deep analysis of the football players’ data, there is always a room
of improvement that can be done to improve projects results and further the studies. Here
you can ﬁnd some important points that may increase the value of the project in the future.
•Adding more features.
There exist wide variety of data that can be added to the main dataset, which
may eventually increase predictive power and quality of interpretations. This step is
heavily based on strong domain knowledge, as well as applying creativity in the feature
•Adding more observations.
As you can see at the beginning of the paper, we exclusively used publicly available
data to make the following analysis. There are numerous private and public data
sources, using which will greatly impact the analysis by adding more observations.
•More hyperparameter tuning.
Tuning the large set of hyperparameters may sometimes be limited by time and
computational resources. Thus, adding computational power will also help to tune
more hyperparameters, which may eventually lead to better performance of machine
learning and deep learning models.
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With this project, we aimed to fully analyze the data by implementing in-depth
exploratory descriptive analysis, which also included some crucial insights from network and
time series analysis. With the help of a large amount of information obtained about the
data, we tried to predict football players’ transfer fee, unlike other projects which were more
concentrated in predicting football players market value. Based on the domain knowledge
it was decided to apply algorithms separately based on positions (goalkeepers, defenders,
midﬁelders, attackers). As a result, diﬀerent models were selected for each position based
on cross-validation obtained RMSE score. The insights gained from the analysis stage and
the predictive power of the models used for each position can be used in order to identify
the undervalued and overvalued players based on their performance and to identify the best
conditions and time for selling the players to gain the maximal proﬁt.
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