Beyond crowd judgments: Data-driven estimation of market value in association football

European Journal of Operational Research 263 (2017) 611–624

Contents lists available at ScienceDirect

European Journal of Operational Research

journal homepage: www.elsevier.com/locate/ejor

Innovative Applications of O.R.

Beyond crowd judgments: Data-driven estimation of market value in

association football

Oliver Müller

a , ∗, 1

, Alexander Simons

b , 1

, Markus Weinmann

b , 1

IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark

University of Liechtenstein, Fuerst-Franz-Josef-Strasse 21, 9490 Vaduz, Liechtenstein

a r t i c l e i n f o

Article history:

Received 5 May 2016

Accepted 4 May 2017

Available online 11 May 2017

Keywords:

OR in Sports

Football

Soccer

Market value

Crowdsourcing

a b s t r a c t

Association football is a popular sport, but it is also a big business. From a managerial perspective, the

most important decisions that team managers make concern player transfers, so issues related to player

valuation, especially the determination of transfer fees and market values, are of major concern. Market

values can be understood as estimates of transfer fees—that is, prices that could be paid for a player

on the football market—so they play an important role in transfer negotiations. These values have tradi-

tionally been estimated by football experts, but crowdsourcing has emerged as an increasingly popular

approach to estimating market value. While researchers have found high correlations between crowd-

sourced market values and actual transfer fees, the process behind crowd judgments is not transparent,

crowd estimates are not replicable, and they are updated infrequently because they require the partici-

pation of many users. Data analytics may thus provide a sound alternative or a complementary approach

to crowd-based estimations of market value. Based on a unique data set that is comprised of 4217 play-

ers from the top ﬁve European leagues and a period of six playing seasons, we estimate players’ market

values using multilevel regression analysis. The regression results suggest that data-driven estimates of

market value can overcome several of the crowd’s practical limitations while producing comparably accu-

rate numbers. Our results have important implications for football managers and scouts, as data analytics

facilitates precise, objective, and reliable estimates of market value that can be updated at any time.

This is an open access article under the CC BY-NC-ND license.

( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Introduction

With millions of players and billions of fans, association foot-

ball (“football” hereafter) is the world’s most popular sport. Be-

cause of its popularity, professional football teams generate enor-

mous revenues; they are no longer just clubs but companies with

shareholders and managers, sales and proﬁts, and customers rather

than fans. From a managerial perspective, the most important de-

cisions that these “football companies” ( Amir & Livne, 2005 ) have

to make concern which players to employ. As player transfers have

a tremendous impact on a club’s chances for success ( Pawlowski,

Breuer, & Hovemann, 2010 ), researchers from various disciplines

have long studied the factors that impact transfer fees ( Frick,

2007 ).

∗

Corresponding author.

E-mail addresses: oliver[email protected] (O. Müller), alexander[email protected]

(A. Simons), [email protected] (M. Weinmann).

Authors are listed in alphabetical order to reﬂect equal contribution to this re-

search.

More recently, though, researchers have begun to pay particu-

lar attention to players’ market values. 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 ).

While transfer fees represent actual prices paid on the market,

market values provide estimates of transfer fees, so they play

an important role in transfer negotiations. Market values have

long been estimated by football experts like team managers and

sports journalists, while crowdsourcing websites like Transfermarkt

( www.transfermarkt.com ) have proved their usefulness in estimat-

ing market value during the past few years. However, data-driven

approaches to estimating market value have not yet caught on in

professional football.

Football has long lagged behind other major sports in the use

of data analytics. In 2010, the New York Times still called football

the “least statistical” of all major sports ( Kaplan, 2010 ), in large

part because the pool of data available at that time was com-

paratively weak. Today, however, sports-data companies like Opta

( www.optasports.com ) collect prodigious amounts of detailed per-

formance data that could be used for player valuation in profes-

http://dx.doi.org/10.1016/j.ejor.2017.05.005

( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

612 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

sional football (see, e.g., Brandes & Franck, 2012 ). While some foot-

ball clubs have started to analyze that data for training purposes

and decisions about line-ups, only a few have realized the data’s

economic potential. They still ignore the “Moneyball” idea of using

statistics to guide player scouting and recruitment ( Zhu, Lakhani,

Schmidt, & Herman, 2015 ).

In this paper, we evaluate the applicability of data analytics for

estimating players’ market values in professional football; in doing

so, we make four primary contributions: 1) we identify the short-

comings of crowd-based estimations of market value, which jus-

tify the exploration of data-driven approaches to estimating market

value; 2) we synthesize the academic literature on player valuation

to identify the factors that determine players’ market values; 3) we

use a large sample of publicly available data on the ﬁve biggest

professional football leagues in Europe over a period of six playing

seasons to train a multilevel regression model for data-driven es-

timation of market value; and 4) we evaluate the accuracy of our

model based on a comparison with actual transfer fees and crowd

estimates and deﬁne the potential of data analytics in overcoming

the crowd’s limitations.

2. Background

2.1. Market values in professional football

Players are the most important investments in professional

football from both a sporting perspective and a business perspec-

tive. While in the United States (U.S.), professional athletes are

often traded for other athletes or for future draft picks (e.g., in

American football or baseball), European football players are usu-

ally traded for cash settlements, which are referred to as “trans-

fer fees” ( Frick, 2007 ). Players’ market values are estimates of the

transfer fees that are most likely to be paid for them. Although

there are conceptual differences, market values and transfer fees

are comparable ( He, Cachucho, & Knobbe, 2015 ). Accordingly, a

player’s market value can be deﬁned as “an estimate of the amount

of money a club would be willing to pay in order to make [an] ath-

lete sign a contract, independent of an actual transaction” ( Herm

et al., 2014 , p. 484). As such, market values inform selling clubs and

buying clubs about football players’ monetary value—even those

whose contracts have not been sold recently—so they are impor-

tant in transfer negotiations. Market values have traditionally been

estimated by the clubs themselves or by sports journalists, but as

football fans have developed an interest in market values, websites

have emerged that provide estimates of players’ market values. In

particular, crowdsourcing has proved its usefulness in estimating

market values.

2.2. Crowd-based estimation of market value

Transfermarkt is the leading website on the football transfer

market. The site offers general football-related data, such as scores

and results, football news, transfer rumors, and estimations of mar-

ket value at the individual and team levels for most professional

football leagues. Once a user has registered at Transfermarkt, he

or she can follow discussion threads about players’ market val-

ues, propose personal estimations based on players’ current value

and performance, and discuss their proposals with other commu-

nity members. The ﬁnal market values are then determined by ag-

gregating the individual estimates. Launched in Germany in 2001,

where it now ranks among the most frequently visited websites

( Alexa , n.d.), Transfermarkt released an English-language version in

2009, and versions of the site have since been made available in

Austria, Italy, Poland, Portugal, Spain, Switzerland, Turkey, and the

Netherlands.

Transfermarkt’s idea is that users can build an estimate of mar-

ket value together as well as or better than a few football experts

can, a style of judgment for which Surowiecki (2005) coined the

term “wisdom of crowds.” Some of the most inﬂuential newspa-

pers and magazines in Europe regularly quote Transfermarkt’s mar-

ket values for football players ( Bryson, Frick, & Simmons, 2012;

Herm et al., 2014 ), which have been found to correlate closely

with experts’ estimates and player salaries ( Franck & Nüesch, 2011;

Torgler & Schmidt, 2007 ). Accordingly, Transfermarkt’s market val-

ues have provided the foundation for several studies of the foot-

ball transfer market (e.g., Franck & Nüesch, 2012; He et al . , 2015 ).

Transfermarkt’s accuracy in estimating market value is remarkable,

as crowdsourcing is generally associated with challenges like so-

cial inﬂuence, manipulation attempts, and lack of experience and

knowledge (e.g., Lorenz, Rauhut, Schweitzer, & Helbing, 2011 ) that

may bias estimations of players’ market value. As Herm et al.

(2014) explained, Transfermarkt has dealt with these challenges by

implementing the “judge principle,” a selective approach to infor-

mation aggregation.

According to Herm et al. (2014) , the judge principle of infor-

mation aggregation works as follows. Transfermarkt does not esti-

mate market values in a democratic way, such that all user esti-

mates have equal value, but uses a hierarchical approach. There-

fore, Transfermarkt does not calculate the ﬁnal market values as

the mean or median of all individual estimates but gives a few

empowered community members, whom Herm et al. called the

“judges,” the ﬁnal say. Accordingly, judges review other users’ es-

timates and select and weigh them when making their decisions,

so they can decrease or increase the inﬂuence of users they con-

sider to be less or more qualiﬁed. Although the ﬁnal market val-

ues are not calculated democratically, there is reason to believe

that the selective-judge principle works better than purely demo-

cratic approaches to information aggregation would. For example,

when little-known players receive only a few votes, user estimates

that are clearly too high or too low would signiﬁcantly bias the

results–either because of manipulation attempts (e.g., by oppor-

tunistic sports agents) or because of a lack of knowledge (e.g., by

inexperienced fans). Judges can exclude such estimates from the

aggregation, which decreases the risk of bias. (For a more detailed

description of how Transfermarkt works see Herm et al. (2014) ).

However, despite its arguable beneﬁts and its demonstrated ac-

curacy, the crowdsourcing approach to estimating market value

comes with several limitations. First, community members base

their estimates on arbitrary indicators, which may happen even

unconsciously, so they lack objectivity. (Transfermarkt suggests a

list of evaluation criteria, but these are not mandatory.) Second,

judges can independently determine the ﬁnal market values based

on personal evaluations of user estimates and other indicators, so

they are not reproducible. (As Transfermarkt does not calculate

the ﬁnal values in a formal way, the question arises concerning

who judges the judges.). Third, as crowd estimations require the

participation of many users, market values are not updated on a

match-by-match basis and may no longer be accurate after a few

games, so crowd estimations are generally not eﬃcient. (Transfer-

markt usually estimates market values every six to twelve months.)

Fourth, crowd estimates tend to be more accurate for players who

are well known to a suﬃciently large audience, so they often do

not support player scouting in minor leagues. (The number of

Transfermarkt’s forum posts is rather low in some countries and

leagues.) Fifth, crowd-estimated market values are public, so they

do not offer a competitive advantage to clubs in transfer negoti-

ations. (Transfermarkt’s market values increasingly affect contract

and wage negotiations on the football market.) As the next section

explains, a data-driven approach to estimating market value would

address these limitations.

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 613

Fig. 1. Conceptualization of market-value estimation at Transfermarkt

(adapted from Herm et al., 2014 , p. 486)

2.3. Data-driven estimation of market value

Major League Baseball (MLB) was the ﬁrst sport to make serious

use of data analytics in player recruitment ( Steinberg, 2015 ). At the

end of the 1990s, Billy Beane, General Manager of the Oakland Ath-

letics, began using statistical data for player scouting and decisions

about the team roster, a story probably best known through the

bestseller, “Moneyball,” and its ﬁlm adaptation by the same name

( Lewis, 2004 ). Insights generated from player statistics helped the

team’s management to identify undervalued but talented players

and overvalued players who had passed their zenith ( Zhu et al.,

2015 ). In the following two decades, the Athletics’ innovative ap-

proach to player recruitment helped the team reach the playoffs

roughly every second season, although they had one of the low-

est budgets of all of the MLB teams, many of which later adopted

Beane’s ideas.

Professional football has long lagged behind sports like baseball

and basketball in the use of quantitative data, so football clubs es-

chewed the Moneyball idea. For example, in 2010 the U.S.’s Major

League Soccer (MLS) website displayed only six metrics per player,

while the MLB website featured twenty-nine batting metrics alone

( Kaplan, 2010 ). “Contrary to the situation in most American team

sports, few individual performance measures are recorded in foot-

ball” ( Frick, 2011 , p. 113). However, sports-data companies like

Opta have begun collecting exhaustive and detailed data about

football players, and some clubs have even begun to collect their

own data during training and games. For example, during the 2014

FIFA world cup in Brazil, the German Football Association (DFB)

used one of SAP’s big-data solutions to analyze player performance

( SAP, 2014 ). The software company estimated that only ten min-

utes of training with ten players and three balls produced more

than seven million data points (also see Bojanova, 2014 ).

However, most clubs use the newly available data to adjust

training plans and support decisions about line-ups, while the

data’s potential for supporting managerial decisions is ignored.

Only a few clubs are known to use data analytics systematically

for player valuation, but most of them are small or medium-sized

clubs for which buying expensive superstars is not a viable strat-

egy. For example, Danish Superliga club FC Midtjylland has begun

to use statistical models to evaluate teams and players ( Murtagh,

2015 ), and Dietmar Hopp, owner of German Bundesliga club TSG

Hoffenheim and co-founder of SAP, has pushed the use of statis-

tical analysis at Hoffenheim. After Hoffenheim received from FC

Liverpool an all-time-high transfer fee of €41 million in 2015 for

Roberto Firmino, who had cost Hoffenheim only €4 million four

years earlier, Hopp identiﬁed two success factors for running the

team in the future: being an early adopter of innovative technolo-

gies and identifying talented players early in their careers and de-

veloping them so they contributed on both the pitch and the bal-

ance sheet ( Zhu et al., 2015 ). While data analytics is an innovative

technology, its applicability to estimating market value and recruit-

ing talented young players remains to be assessed.

Research on judgment and decision-making provides strong

empirical and theoretical arguments that favor statistical estimates

over human (heuristic) judgments ( Dawes, Faust, & Meehl, 1989 ),

particularly when it comes to complex decisions ( Evans, 2006;

Tversky & Kahneman, 1974 ) like estimating a football player’s mar-

ket value. A meta-analysis of 136 empirical studies that compared

statistical predictions and human judgments in ﬁelds from clinical

decision-making to economics showed that statistical techniques

are, on average, 10 percent more accurate than human judgments

are ( Grove, Zald, Lebow, Snitz, & Nelson, 20 0 0 ). The superiority

of statistical methods over human judgments holds for trained,

untrained, experienced, and inexperienced judges alike ( Grove &

Meehl, 1996 ). Therefore, our approach to data-driven estimation of

market value uses a statistical model.

Brunswik’s (1952) lens model, which Herm et al. (2014) used

to conceptualize how the Transfermarkt crowd estimates market

value, can also be used to explain our approach to data-driven es-

timation of market value ( Fig. 1 ). On the Transfermarkt website,

community members j make subjective estimations

of a foot-

ball player’s true, unobservable market value y based on arbitrary

indicators x

and subjective weightings a

i,j

. A Transfermarkt judge

then creates a ﬁnal estimation of market value

y based on selected

user evaluations

and other indicators x

, to both of which he or

she assigns subjective weightings b

and a

. Accordingly, the crowd-

based approach to estimating market values uses divergent indica-

tors and weightings. In contrast, a data-driven approach to estimat-

ing market value uses a statistical model with consistent indicators

and empirically derived weightings a

to estimate players’ mar-

ket values, so it overcomes the limitations of the crowd: Because

the model uses the same indicators and weightings for all players,

it is transparent and replicable; it is eﬃcient, so market values can

be updated on a match-by-match basis; it produces unbiased esti-

mates for well-known and lesser known players alike, so it can be

used for player scouting; and its use does not require public an-

614 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

Table 1

Indicators of market value.

Indicator Description Selected references

Player characteristics

Age Age reﬂects players’ experience and potential. (1)–(19)

Height Height reﬂects heading ability, which can inﬂuence the probability of scoring or preventing goals. (2), (4), (11), (18)

Position Position reﬂects players’ ﬂexibility on the pitch and their crowd-pulling capacity. (1)–(19)

Footedness Two-footedness is an advantageous footballing ability that also

reﬂects players’ ﬂexibility. (2), (12), (18)

Nationality Nationality refers to a player’s country or continent of birth. (2), (6), (8), (9), (14), (16), (17)

Player performance

Playing time Playing time refers to the number of games or minutes played at the national and international levels. (1)–(13), (15)–(19)

Goals Goals refers

to the number of goals a player has scored. (2)–(5), (7), (8), (10)–(19)

Assists Assists refers to the number of a player’s assists that helped other players score goals. (7), (11)–(16)

Passing Passing refers to the number of passes to other players or the accuracy of passing. (7), (12), (16)

Dribbling

Dribbling refers to the number and success rate of a player’s ball maneuvers. (7), (11), (16)

Dueling Dueling refers to the number and success rate of a player’s tackles, clearances, blocks, and interceptions. (7), (12), (14), (16)

Fouls Fouls refers to the number of fouls committed or the number of

times a player has been fouled. (7), (11), (13)

Cards Cards refers to the number of yellow, yellow/red, and red cards received by a player. (7), (8), (13), (18)

Player popularity

News A player’s news-worthiness is reﬂected in press citations. (7), (13), (14)

Internet links Popularity is reﬂected in the number

of links reported by web search engines like Google. (9), (12), (13)

References: (1) Brandes and Franck (2012) ; (2) Bryson et al. (2012) ; (3) Carmichael and Thomas (1993) ; (4) Carmichael et al. (1999) ; (5) Dobson et al. (20 0 0) ; (6) Feess

et al. (2004) ; (7) Franck and Nüesch (2012) ; (8) Frick (2011) ; (9) Garcia-del-Barrio

and Pujol (2007) ; (10) Gerrard and Dobson (20 0 0) ; (11) He et al. (2015) ; (12) Herm

et al. (2014) ; (13) Kiefer (2014) ; (14) Lehmann and Schulze (2008) ; (15) Lucifora and Simmons (2003) ; (16) Medcalfe (2008) ; (17) Reilly and Witt (1995) ;

(18) Ruijg and

van Ophem (2014) ; (19) Speight and Thomas (1997)

nouncement, so it can offer the club that uses it an advantage in

transfer negotiations.

The next section’s literature review identiﬁes indicators of mar-

ket value in order to provide a conceptual background for develop-

ing such a model.

3. Indicators of market value

3.1. Overview

Research has identiﬁed several factors that can be used to es-

timate market values and these factors are similar to those the

Transfermarkt crowd uses (see Herm et al., 2014 ). Table 1 or-

ganizes the most common indicators of market value into three

categories—player characteristics , player performance , and player

popularity —and shows selected studies that have used these indi-

cators.

While researchers have studied indicators of transfer fees (e.g.,

Carmichael & Thomas, 1993; Carmichael, Forrest, & Simmons,

1999; Dobson, Gerrard, & Howe, 20 0 0; Gerrard & Dobson, 20 0 0;

Medcalfe, 2008; Ruijg & van Ophem, 2014; Speight & Thomas,

1997 ) and market values (e.g., Franck & Nüesch, 2012; Garcia-del-

Barrio & Pujol, 2007; He et al., 2015; Herm et al., 2014; Kiefer,

2014 ), studies on players’ remuneration (e.g., Brandes & Franck,

2012; Bryson et al . , 2012; Feess, Frick, & Muehlheusser, 2004;

Frick, 2011; Lehmann & Schulze, 2008; Lucifora & Simmons, 2003 )

can also be used to identify indicators of market value. In fact,

players’ salaries are inﬂuenced by the same—or at least similar—

factors

as those that inﬂuence market values and transfer fees

(see, e.g., Brandes & Franck, 2012; Bryson et al., 2012; Frick, 2007 ).

Therefore, we explain the three indicator categories of market

value by reviewing research on player valuation, payment, and

transfer. (Text references to the indicators listed in Table 1 are

italicized.)

3.2. Player characteristics

We conceptualize player characteristics as players’ physical and

demographic attributes. Age is an important indicator of market

value, as it reﬂects both experience and potential (e.g., Carmichael

& Thomas, 1993 ). Most studies on player valuation have used

quadratic age terms to allow for non-linear relationships, consid-

ering that players’ values usually increase into their mid-twenties

and decline thereafter (e.g., Bryson et al., 2012 ). Age (age squared)

has frequently been found to inﬂuence pay and value positively

(negatively) (e.g., Lehmann & Schulze, 2008 ). In addition, a player’s

height has been found to signiﬁcantly increase salary returns

( Bryson et al., 2012 ) because it indicates good heading ability that

may increase the probability of scoring or preventing a goal ( Fry,

Galanos, & Posso, 2014 ).

Another player characteristic that has been studied in player-

valuation research is footedness . For example, Bryson et al.

(2012) concluded that two-footed ability raises players’ salaries,

and Herm et al. (2014) found that it positively impacts their

market values. Two-footedness is a generally advantageous foot-

ball skill, but it also reﬂects ﬂexibility because players who are

adept with both feet can be used in various positions on the

pitch ( Bryson et al., 2012 ). Like the other player characteristics,

footedness is a talent-related indicator of market value, but re-

searchers have also studied whether players’ nationalities inﬂu-

ence their value and pay because of discrimination ( Frick, 2007 ).

For example, in their study of the Spanish professional football

league, Garcia-del-Barrio and Pujol (2007) found that non-Spanish

European players were systematically overrated, while non-

European players were systematically underrated. However, Reilly

and Witt (1995) found no evidence of discrimination of players

in professional football, which was more recently conﬁrmed by

Medcalfe (2008) .

Finally, a player’s position —goalkeeper, defender, midﬁelder, or

forward—is important in estimating market value. Several re-

searchers have found that players’ positions impact salaries and

transfer fees, as they reﬂect players’ degrees of specialization and

crowd-pulling capacity. For example, Frick (2007) found that goal-

keepers earn signiﬁcantly less than midﬁelders because goalkeep-

ers can be used less ﬂexibly on the pitch. Garcia-del-Barrio and

Pujol (2007) concluded that attackers receive much higher atten-

tion and rewards than goalkeepers, as attackers are more visible to

the audience and so have higher crowd-pulling power ( He et al.,

2015 ).

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 615

3.3. Player performance

Player performance reﬂects how well players function on the

pitch. Playing time has consistently been used in player-valuation

research. For example, appearances in domestic leagues, in the Eu-

ropean leagues, and on the national team have a positive impact

on transfer fees and market values (e.g., Carmichael & Thomas,

1993; Garcia-del-Barrio & Pujol, 2007; Gerrard & Dobson, 20 0 0 ).

Researchers have distinguished between appearances during play-

ing seasons and appearances during players’ careers (e.g., Franck

& Nüesch, 2012 ), and they have considered substitute appearances

(e.g., Bryson et al., 2012 ) and minutes played (e.g., Ruijg & van

Ophem, 2014 ) to account for the actual time spent on the ﬁeld.

Several other performance measures can be used to estimate

market values. Goals , including ﬁeld goals, headers, and penal-

ties, indicate players’ scoring ability, so they are a largely unam-

biguous performance measure ( Carmichael et al., 1999 ). Accord-

ingly, the total and average number of goals, each across play-

ing seasons and players’ careers, have often been used in player-

valuation research (e.g., Bryson et al., 2012; Carmichael & Thomas,

1993; Frick, 2011; Gerrard & Dobson, 20 0 0 ). Assists refer to players’

contributions that help others score goals, so they are also com-

mon indicators of player value. For example, Lucifora and Simmons

(2003) provided evidence from Italian football that forwards’ as-

sist rates can increase their salaries, a ﬁnding that Lehmann and

Schulze (2008) and Franck and Nüesch (2012) reinforced for Ger-

man Bundesliga players.

Because of the protracted unavailability of detailed performance

data in professional football, only a few researchers have used per-

formance measures other than goals and assists to explain value

and pay. Infrequently used are passing (e.g., Herm et al., 2014 );

dueling in the form of clearances, blocks, and interceptions (e.g.,

Franck & Nüesch, 2012 ); dribbles (e.g., Medcalfe, 2008 ); commit-

ted fouls (e.g., He et al., 2015 ); and yellow and red cards (e.g.,

Kiefer, 2014 ). Because the signiﬁcance of performance indicators

varies by position, researchers have also included interaction ef-

fects in their models of player value (e.g., Dobson et al., 20 0 0;

Gerrard & Dobson, 20 0 0 ). For example, while forwards are sup-

posed to score goals, defenders should win tackles, and midﬁeld-

ers are expected to defend and attack equally well. To account for

the variety of performance indicators, some researchers have also

replaced them with aggregated indices and expert estimations as

proxies for player performance (e.g., Brandes & Franck, 2012; Feess

et al., 2004; Garcia-del-Barrio & Pujol, 2007 ).

3.4. Player popularity

Theories on the emergence of “superstars” like actors and

singers suggest that not only talent ( Rosen, 1981 ) but also the ex-

ternalities of popularity ( Adler, 1985 ) can explain demand for foot-

ball players ( Franck & Nüesch, 2012 ). Therefore, players’ market

values also depend on their crowd-pulling power, independent of

what they show on the pitch, as this power can sell their clubs’

jerseys and seats. Accordingly, studies of the football transfer mar-

ket have investigated popularity-related factors. While early studies

left popularity to the error term (e.g., Carmichael & Thomas, 1993 ),

the Internet has provided new ways to measure player popularity

by, for example, analyzing online news and web links . For exam-

ple, Lehmann and Schulze (2008) concluded that media presence,

measured as the number of times a player’s name is mentioned

in the online version of the German sports magazine Kicker, re-

lates to salary. Likewise, Franck and Nüesch (2012) found that non-

performance-related press citations in the LexisNexis database are

positively related to market value, and Brandes, Franck, and Nüesch

(2008) counted how often German Bundesliga players’ names were

mentioned in newspapers and magazines to determine whether

superstars boost attendance at home and away matches. Herm

et al. (2014) and Garcia-del-Barrio and Pujol (2007) measured

public attention as the total number of Google search hits and

found it to be a signiﬁcant factor in player valuation, while Kiefer

(2014) measured popularity using Facebook “likes” and mentions

on the UEFA website.

In summary, research has identiﬁed several indicators of market

value, including player characteristics, performance, and popularity,

with most of the extant studies relying on similar factors. The next

section explains how we operationalized these factors and how we

collected and analyzed data to train a statistical market-value esti-

mation model.

4. Data collection and description

We gathered season-level data about players’ characteristics,

performance, and popularity from several Internet sources, in-

cluding Google, Reddit, Transfermarkt, WhoScored, Wikipedia, and

YouTube. We collected data for six playing seasons, from the

2009/10 season to the 2014/15 season, for players from the ﬁve

top European leagues, that is, England’s Premier League, Spain’s La

Liga, Germany’s Bundesliga, Italy’s Serie A, and France’s Ligue 1.

To increase the reliability of the performance data, and in line

with previous research, we considered only those players who ap-

peared on the pitch for at least ninety minutes in a given season

( Brandes & Franck, 2012 ) and excluded goalkeepers from our sam-

ple ( Bryson et al., 2012; Lucifora & Simmons, 2003 ), as their per-

formance is measured in a considerably different way than that

of outﬁeld players. The resulting data set consisted of 10,350 ob-

servations from 4217 players on 146 teams. Table 2 provides an

overview.

Our data-driven approach to estimating market value is concep-

tually similar to how the crowd estimates market values. To es-

timate a player’s market value after a given season, we use his

estimation of market value from the end of the previous sea-

son as a baseline and add data about his characteristics, perfor-

mance, and popularity from that season. As the accuracy of Trans-

fermarkt’s estimations of market value has been repeatedly con-

ﬁrmed by researchers, and because of the unavailability of other

credible sources that provide historical data, we used Transfer-

markt’s estimations of market value to train our model. We ﬁrst

collected the estimations that were made at the end of the six sea-

sons (as per June 30) for all players in our sample. The average

player across all leagues and seasons was worth around €5.6 mil-

lion at Transfermarkt; players’ market values ranged from €50,0 0 0

to €120 million with a standard deviation of around €8.2 million.

( Appendix A provides a more detailed overview of the transfer

market.)

To conduct our own estimation of players’ market values, we

collected data about their characteristics, performance, and popu-

larity. We operationalized the player characteristics by means of

a player’s Age (years), Height (centimeters), Footedness (two-footed

ability or not), Nationality (continent of origin), and Position on

the pitch (defender, midﬁelder, forward). The average player in our

data set was 26.5 years old and 181.5 centimeters (nearly six feet)

tall. Eight percent of all players were adept with both feet, 41 per-

cent of them were midﬁelders (21% forwards, 38% defenders), and

76 percent were from Europe (12% from South America, 10% from

Africa, 2% from other continents). (Categorical variables are not dis-

played in Table 2 .)

We measured player performance by means of the number of

Minutes played , Goals , Assists , and Yellow or Red cards per season;

the number and success ratio of Passes , Dribbles , Aerial duels , and

Tackles per game; and the number of Interceptions , Clearances , and

committed Fouls per game. The average player in our sample was

on the pitch for 1612 minutes per season, during which he scored

616 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

Table 2

Descriptive statistics.

Variable Measurement Mean Median St. Dev. Min. Max.

Player valuation

Transfermarkt’s market value EUR 5588,529 30 0 0,0 0 0 8208,470 50,0 0 0 120,0 0 0,0 0 0

Player characteristics

Age Years 26.51 26.00 4.08 17.0 0 40.00

Height Centimeters 181.49 182.00 6.15 161.00 203.00

Player performance

Minutes played total p.s. 1612.39 1612.00 884.85 90.00 3420.00

Goals total p.s.

2.39 1.00 3.85 .00 50.00

Assists total p.s. 1.64 1. 0 0 2.25 .00 20.00

Passes total p.g. 29.45 28.48 13.36 1.55 110.03

Successful passes percent p.g. .78 .78 .07 .43 1.0 0

Dribbles total p.g. 1.21 .90 1.12 .00 9.58

Successful dribbles percent p.g. .51 .50 .24 .00 1.0 0

Aerial duels total

p.g. 2.22 1.79 1.71 .00 15.50

Successful aerial duels percent p.g. .47 .48 .18 .00 1.00

Tackles total p.g. 2.21 2.09 1.21 .00 9.00

Successful tackles percent p.g. .71 .72 .14 .00 1.0 0

Interceptions total p.g. 1.35 1.25 .92 .00 7.13

Clearances total p.g. 2.09 1.07 2.35 .00 13.44

Fouls total

p.g. 1.10 1.03 .53 .00 4.27

Yellow cards total p.s. 3.48 3.00 2.89 .00 18.00

Red cards total p.s. .20 .00 .46 .00 3.00

Player popularity

Wikipedia page views total p.s. 104,509.30 23,944.00 319,022.80 .00 8786,701.00

Google Trends search index average index p.s. 13.36 13.21 12.38 .00 91.83

Reddit posts

total p.s. 15.42 2.00 38.79 .00 789.00

YouTube videos total p.s. 36,075.46 918.50 141,882.30 .00 10 0 0,0 0 0.0 0

Notes: p.s. = per season; p.g. = per game; N = 10,350

2.4 goals, gave 1.6 assists, and received 3.5 yellow and .2 red cards.

In an average game, he made 29 passes (at a success rate of 78%),

did 1.2 dribbles (51% successfully), and committed 1.1 fouls. He

conducted 2.2 aerial duels (47% won) and made 2.2 tackles (71%

successfully), 1.4 interceptions, and 2.1 clearances per game.

We used four Internet metrics to measure player popularity: the

number of times a player’s Wikipedia page was viewed, how often

a player’s name was searched on Google , the number of times a

player’s name appeared in the “soccer” forum on Reddit , and how

many videos about a player were shared on YouTube . The average

player had more than 10 0,0 0 0 Wikipedia page views and more

than 35,0 0 0 YouTube videos. His name appeared in 15.4 forum

posts on Reddit, and his average Google Trends search index was

13.4. (The data Google provides is scaled from 0 to 100 for a given

time frame, so it refers to total searches for a term relative to the

total number of searches over time.)

None of the independent variables were highly correlated, but

an exploratory data analysis revealed that the distributions of the

players’ market values were highly right-skewed, which was also

the case for the popularity variables. ( Appendix B shows how the

market values were distributed across seasons, leagues, and po-

sitions, and how the independent variables were correlated.) We

log-transformed these variables to avoid violating the linearity as-

sumption of linear regression. “Eyeballing” the associations be-

tween the players’ market values that we collected from Transfer-

markt and the numerical independent variables with scatterplots

showed that all variables except age had reasonably linear relation-

ships with market value. Therefore, we squared the age variable to

get a more linear relationship with market value.

5. Results

5.1. Model speciﬁcation

In order to build a statistical model with which to estimate

players’ market values, we ﬁtted a series of regression models,

which included as predictors the players’ previous market values,

and the players’ characteristics, performance measures, and pop-

ularity metrics. As our data structure is hierarchical (players are

nested within teams, and teams are nested within leagues) and

longitudinal (players played multiple seasons), the model’s resid-

uals are likely not independent, which would violate a central as-

sumption of linear regression. Therefore, we used multilevel mod-

els that we speciﬁed to include player, team, league, position, con-

tinent of origin, and season as random factors, and for which

we allowed the intercepts to vary (notation adapted from Lee,

1975 ):

Market value

i(t(l)

∗

c)[s]

= α

i(t(l)

∗

c)[s]

+ β · Market value

i(t(l)

∗

c)[s-1]

+ χ’ · Player characteristics

i(t(l)

∗

c)[s]

+ δ’ · Player performance

i(t(l)

∗

c)[

]

+ γ ’ · Player popularity

i(t(l)

∗

c)[

]

+ u

i(t(l)

∗

c)[s]

+ u

t(l)

+ u

+ ε

i(t(l)

∗

c)[

]

where i(t(l)

∗

c)[s] indexes a player i , who is nested within each

of three factors that are crossed with each other—a team t (which

is further nested in a league l ), a position p , and the conti-

nent of origin c —corresponding to season observations s . Market

value

i(t(l)

∗

c)[s]

is the market value to be estimated; α

i(t(l)

∗

c)[s]

rep-

resents an individual intercept; Market value

i(t(l)

∗

c)[s-1]

is the mar-

ket value from the preceding season; Player characteristics

i(t(l)

∗

c)[s]

consists of the predictors Age

, Height , and Footedness ; Player

performance

i(t(l)

∗

c)[s]

consists of the predictors Minutes played ,

Goals , Assists , (Successful) Passes , (Successful) Dribbles , (Successful)

Aerial duels , (Successful) Tackles , Interceptions , Clearances , Fouls , Yel-

low cards , and Red cards ; and, Player popularity

i(t(l)

∗

c)[s]

consists

of the predictors Wikipedia page views , Google Trends search in-

dex , Reddit posts , and YouTube videos . u

i(t(l)

∗

c)[s]

, u

t(l)

, u

and u

are random effects that are designed to capture the non-

independence between 1) market values observed for the same

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 617

player i over time s ( u

i(t(l)

∗

c)[s]

), 2) market values observed for

players on the same team ( u

t(l)

), 3) market values observed for

teams in the same league ( u

), 4) market values observed for play-

ers who play the same position ( u

), 5) market values observed

for players from the same continent of origin ( u

), and 6) market

values observed for players in the same season ( u

), respectively.

i(t(l)

∗

c)[s]

captures the remaining error. The random effects and

the error term are assumed to be independently and identically

distributed and follow a normal distribution with mean zero and

standard deviation σ

5.2. Regression results

Table 3 shows the estimated coeﬃcients, standard errors, and

p -values of the ﬁxed effects as well as the standard deviations of

the random effects. Model 1 serves as a baseline model and con-

tains only an intercept and the Previous market value . Model 2 adds

player characteristics, Model 3 adds the player-performance vari-

ables, and Model 4 adds the player-popularity metrics. The good-

ness of ﬁt, measured by the Akaike Information Criterion (AIC) and

the Bayesian Information Criterion (BIC), improves with each block

of variables added; likelihood ratio tests conﬁrm that these im-

provements are signiﬁcant (from Model 1 to 2: χ2 (3) = 2439.00,

p = .0 0 0; from Model 2 to 3: χ2 (16) = 4843.20, p = .0 0 0; from

Model 3 to 4: χ 2 (4) = 144.12, p = .0 0 0).

As our dependent variable is measured on the logarithmic scale,

the models’ coeﬃcients can be interpreted roughly as percent

changes. The coeﬃcients of the log-transformed independent vari-

ables have to be interpreted as elasticities. For example, an addi-

tional Goal (Assist) per season increases a player’s Market value by

2.4 (1.5) percent in Model 4, holding all other variables constant,

and a 1 percent increase in the number of Wikipedia page views is

associated with a .02 percent increase in Market value .

In Model 1, the baseline model, the Previous market value (.543;

p < .001) is signiﬁcant. The signiﬁcant variables in Model 2 are

Previous market value (.610; p < .001) and Age

( −.002; p < .001).

AIC drops from 17,416.2 to 14,983.2, indicating an improvement in

goodness of ﬁt. In Model 3, the signiﬁcant variables from Model

2—that is, Previous market value (.495; p < .001) and Age

( −.002;

p < .001)—are still signiﬁcant, and from the set of performance

variables, Minutes played , Goals , Assists , Passes , Successful passes ,

Dribbles , Aerial duels , Tackles , and Yellow cards are also signiﬁcant.

With every minute a footballer plays, his market value increases

by .03 percent ( p < .001), each goal increases it by 2.60 percent

( p < .001), and each assist increases it by 1.58 percent ( p < .001).

Passes (0.57%; p < .001), the ratio of Successful passes (30.05%; p <

.001), Dribbles (3.02%; p < .001), and Aerial duels (1.33%; p < .001)

further increase a player’s market value, whereas Tackles ( −2.08%;

p < .001) and Yellow cards ( −0.41%; p < .05) decrease it. The

model’s goodness of ﬁt increases compared to Model 2, as AIC

drops from 14,983.2 to 10,172.0.

Model 4 adds popularity data. The variables from Model 3

remain largely stable when Wikipedia page views , Google Trends

search index , Reddit posts , and YouTube videos are added. Three of

the four popularity variables are signiﬁcantly related to a player’s

market value, with a .02 percent increase for each 1 percent in-

crease in Wikipedia page views ( p < .001), a .03 percent increase for

each 1 percent increase in Reddit posts ( p < .001), and a .01 per-

cent increase for each 1 percent increase in YouTube videos ( p <

.01). The model’s goodness of ﬁt increases compared to the previ-

ous models, as AIC drops from 10,172.0 to 10,035.9.

The parameter estimates for the random effects (i.e., the stan-

dard deviations) remain largely stable across models ( σ

to σ

However, unexplained player-speciﬁc variability ( σ

, the standard

deviation for Players nested in Teams nested in Leagues ) is com-

paratively large in Model 1 (.4 4 4) but decreases when additional

Table 3

Multilevel regression models.

Dependent variable: Log of market value

Model 1 Model 2 Model 3 Model 4

Fixed effects

Intercept 6.789

∗∗∗

6.492

∗∗∗

7.432

∗∗∗

7.272

∗∗∗

(.132) (.219) (.203) (.200)

Log of previous market value .543

∗∗∗

.610

∗∗∗

.495

∗∗∗

.486

∗∗∗

(.006) (.005) (.005) (.005)

Age

−.002

∗∗∗

−.002

∗∗∗

−.002

∗∗∗

(.0 0 0) (.0 0 0) (.0 0 0)

Height .002 .001 .001

(.001) (.001) (.001)

Footedness −.003 −.006 −.007

(.022) (.017) (.017)

Minutes played .0 0 0

∗∗∗

.0 0 0

∗∗∗

(.0 0 0) (.0 0 0)

Goals .026

∗∗∗

.024

∗∗∗

(.002) (.002)

Assists .016

∗∗∗

.015

∗∗∗

(.002) (.002)

Passes .006

∗∗∗

.005

∗∗∗

(.001) (.001)

Successful passes .301

∗∗∗

.286

∗∗∗

(.083) (.083)

Dribbles .030

∗∗∗

.028

∗∗∗

(.005) (.005)

Successful dribbles .035 .034

(.019) (.018)

Aerial duels .013

∗∗∗

.014

∗∗∗

(.004) (.004)

Successful aerial duels −.005 −.006

(.028) (.027)

Tackles −.021

∗∗∗

−.018

∗∗∗

(.005) (.005)

Successful tackles .049 .050

(.030) (.030)

Interceptions −.013 −.010

(.008) (.008)

Clearances .003 .003

(.003) (.003)

Fouls .002 .004

(.010) (.010)

Yellow cards −.004

∗

−.004

∗

(.002) (.002)

Red cards .007 .007

(.009) (.008)

Log of Wikipedia page views .016

∗∗∗

(.002)

Log of Google Trends search index .006

(.004)

Log of Reddit posts .026

∗∗∗

(.005)

Log of YouTube videos .007

∗∗

(.002)

Random effects

(Player/Team/League) .4 4 4 .298 .179 .185

(Team/League) .280 .217 .237 .219

(League) .138 .137 .150 .120

(Position) .083 .052 .056 .050

(Continent of origin) .057 .053 .034 .029

(Season) .107 .089 .089 .098

(Residual) .409 .411 .347 .343

Log Likelihood −8699.1 −7479.6 −5058.0 −4986.0

AIC 17,416 .2 14,983.2 10,172.0 10,035.9

BIC 17,4 81.4 15,070.1 10,374.9 10,267.8

Notes:

∗

p < .05

∗∗

p < .01

∗∗∗

p < .001; standard errors are in parentheses.

Number of observations: 10,350. Number of groups: Players, 4217; Teams, 146; Con-

tinents of origin, 6; Seasons, 6; Leagues, 5; Positions, 3.

ﬁxed factors and covariates are added (Model 4: .185). In other

words, these variables explain additional variability between play-

ers. In what follows, we evaluate the accuracy of Model 4 in esti-

mating market value, as it is the model with the highest goodness

of ﬁt.

618 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

5.3. Model evaluation

Market values are unobservable, which made it diﬃcult to eval-

uate the accuracy of our statistical model. Still, market values are

proxies for transfer fees ( He et al . , 2015 ), so we compared the

model estimates with actual transfer fees. However, market val-

ues and transfer fees are not necessarily the same. For example,

players can switch clubs after their contracts have expired with-

out any transfer fee, but that does not mean that their market

value is zero, and clubs sometimes pay unreasonably high fees

for players, especially if they have to ﬁnd replacements for in-

jured players quickly or want to weaken competitors ( Herm et al.,

2014 ). Against this background, we also compared our model esti-

mates with the crowd estimates, which provided another bench-

mark for evaluating our model’s accuracy. We collected data on

publically announced transfer fees for all six playing seasons, ex-

cluding players from the evaluation sample whose transfer fees

were zero (because their contracts had expired or they were on

loan) and players other than those who had been sold by one of

the 146 clubs in our data set (because players they had bought

may have come from leagues other than the European top ﬁve,

so we would not have had their data). From this process we col-

lected 845 transfer fees with which we could evaluate our model’s

accuracy.

Because our sample spanned several playing seasons, we could

not use standard evaluation strategies for predictive models, such

as k-fold cross-validation (see, e.g., Hastie, Tibshirani, & Fried-

man, 2017 ), as these strategies would have introduced the risk of

leakage–that is, the use of data from the future to train a model in

the past ( Kaufman, Rosset, & Perlich, 2011 ). Therefore, we applied

a time-series-based evaluation approach to ensure that a player’s

market value after a given season was estimated based only on

data that was known at that point in time. For example, to esti-

mate players’ market values after the 2009/10 season, we trained

the model on data from the 2009/10 season, and to estimate play-

ers’ market values after the 2010/11 season, we trained the model

on data from the 2009/10 and 2010/11 seasons. After we had ob-

tained statistical estimates of market value for all 845 players in

our evaluation sample, we calculated the differences between the

model estimates and the transfer fees for each of them and, on

that basis, the Root Mean Squared Error (RMSE) and the Mean

Absolute Error (MAE) as aggregated measures. We calculated the

same two measures for the crowd’s estimates.

As Table 4 shows, the evaluation results indicate that the

crowd’s estimates are slightly more accurate in that they are closer

to actual transfer fees than the model’s estimates, with an RMSE

that is 3.4% lower and an MAE that is 3.6% lower. However, a

Diebold-Mariano test that compared the MAEs of the crowd’s es-

timates and the model’s estimates showed no statistically signiﬁ-

cant difference ( p < .340) ( Diebold & Mariano, 1995 ). On average,

the crowd estimates deviate by €3241,733 from the players’ trans-

fer fees and the model estimates by €3359,743.

However, as the exploratory data analysis revealed, the distri-

bution of players’ market values was highly skewed and character-

Table 4

Model evaluation.

RMSE MAE

Crowd estimates 5793,474 3241,733

Model estimates 5996,341 3359,743

Relative difference + 3.4% + 3.6%

Notes: A positive value for relative difference in-

dicates superiority of crowd. Actual transfer fees

were used as ground truth. N = 845

ized by extreme outliers ( Appendix B ), as was the case with their

transfer fees. Therefore, we evaluated the accuracy of both the

model estimates and the crowd estimates for various price ranges.

Fig. 2 shows the development of the difference in RMSE between

the model’s estimates and the crowd’s estimates when the data

set is ﬁltered at various cut-off points. While the differences be-

tween the two estimation approaches are generally not large, the

model tends to be more accurate for low- to medium-priced play-

ers, whereas the crowd tends to be more accurate for high-priced

players.

The crossover between the model’s estimates and the crowd’s

estimates occurs at a transfer fee of approximately €18 million,

which is at the 90th percentile of the distribution. ( Fig. 3 pro-

vides a transfer-fee histogram.) In other words, the model pro-

duced more accurate estimates on average than the crowd did for

the lower 90 percent of all transfers (i.e., for 769 out of 845 trans-

ferred players).

In contrast, the crowd produced more accurate estimates on

average for players with high transfer fees, such as superstars

like David Luiz and Edinson Cavani, who were both bought by

Paris Saint-Germain F.C. for fees of €49.5 million and €64.5 mil-

lion, respectively. ( Appendix C provides more detailed evaluation

results.)

6. Discussion

Overall, the results from the evaluation of our statistical model

conﬁrm the applicability of data analytics to estimating market

value, as the estimated market values did not deviate consider-

ably from actual transfer fees. The average deviation was around

€3.4 million, which is not much considering the high transfer

fees in today’s football. (The players’ transfer fees ranged from

€10 0 0 to €101,0 0 0,0 0 0 in our sample, with a standard devia-

tion of €9414,575.) Still, it is diﬃcult to draw conclusions from

a comparison with transfer fees alone, because they are concep-

tually different from market values. To have another benchmark,

we also compared our model estimates with Transfermarkt’s es-

timates of market value, which we found to be more closely re-

lated to actual transfer fees. However, the difference was relatively

small, with an RMSE that was only 3.4 percent lower and not

statistically signiﬁcant, so our evaluation results do not necessar-

ily indicate that crowds are more accurate in estimating market

value.

In fact, we found that the model tends to provide more ac-

curate estimations for low- to medium-priced players, while the

crowd tends to be more accurate for high-priced players. Specif-

ically, the model produced more accurate market-value estimates

on average for the lower 90 percent of the transfers we con-

sidered, even though the differences between crowd estimations

and model estimations were often not large. However, especially

for the smaller share of expensive players, the model estimations

were disproportionally inaccurate, which skewed the average so

the crowd was more accurate for the overall sample. There are at

least two possible explanations for this ﬁnding. First, the model

may not be able to value expensive players, especially superstars,

accurately because it may lack important intangible indicators (e.g.,

players’ potential to boost ticket or jersey sales). While the crowd

can consider such factors, which can range widely from player

to player, the statistical model uses the same set of predeﬁned

factors for all players. In other words, the crowd has more free-

dom in selecting relevant information for player valuation, which

may be an advantage when it comes to setting a value on a su-

perstar. Second, professional football clubs sometimes pay very

high transfer fees for players, which may not reﬂect their “true”

value,

so the model has diﬃculty in estimating their prices. In that

case, the crowd would be severely biased by these players’ tal-

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 619

Fig. 2. Comparison of the model’s and the crowd’s estimates

Notes: The x -axis is log-transformed and it represents the upper limits of transfer fees. The y -axis shows the difference in RMSE between the model and the crowd, calculated

based on a comparison with transfer fees. The dotted line separates

the lower 90% of all transfers from the higher 10% of all transfers.

ent and popularity, while the statistical model would allow to de-

tect disproportionate and unreasonable payments on the transfer

market.

Our ﬁndings have several implications for the practice of esti-

mating market value in professional football. We argued that data-

driven estimation of market value can overcome several limitations

that are associated with crowd-based estimates of market value.

The use of data analytics is arguably more transparent and re-

producible than crowd judgments are, as the estimated regression

coeﬃcients directly quantify the impact of several variables on a

player’s market value. Transparency about the relationships of mar-

ket values with player characteristics, performance, and popularity

can help managers to make predictions about future market-value

developments that can be repeated at minimal cost and with a

high level of reliability. Because data analytics is eﬃcient, it may

even allow players’ market values to be estimated on a match-

by-match basis, while the crowd can update market values only

infrequently. Based on a comparison with actual transfer fees, we

showed that formal models can provide accurate estimates of mar-

ket value that do not deviate much from crowd-based estimates,

even though the crowd’s estimates require considerably more time

and effort. Theref ore, our st atistical result s can f orm the basis f or

building real-time information systems that estimate and predict

players’ market values. In addition, our results may also be in-

teresting for operators of fantasy-football websites, where partic-

ipants slip into the role of club managers and choose their team

rosters by buying and selling players, as such games likewise use

performance data to determine players’ value, yet in a much sim-

pler way.

Furthermore, while crowdsourcing platforms like Transfermarkt

produce public numbers, data analytics allows football clubs to

evaluate players internally, so they can provide a competitive ad-

vantage to football clubs in transfer negotiations. In particular, data

analytics can support clubs in player scouting, while the crowd of-

620 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

Fig. 3. Distribution of transfer fees

Note: The dotted line separates the lower 90% of all transfers from the higher 10% of all transfers.

ten has diﬃculty evaluating lesser-known players (e.g., from less

popular leagues). Players who are largely unknown tend to receive

only a few votes from the crowd, which increases the risk of bi-

ased estimations. Formal models have the potential to identify tal-

ented young players early in their careers, when their value is still

unknown to the broader public. Against this background, our study

demonstrates the applicability of the “Moneyball” idea in associa-

tion football.

To the best of our knowledge, this study is grounded in the

largest data set in terms of both coverage (ﬁve leagues, six years)

and level of detail (more than twenty indicators) that has been

used for research on estimating market value in professional foot-

ball. Accordingly, our study can also inform future research in the

ﬁeld. In particular, we determined the signiﬁcance of various in-

dicators of market value that have guided related work, by which

we proposed a multilevel model for estimating market value. How-

ever, although our model incorporated a large number of market-

value indicators, commercial providers of sports data capture more

than two hundreds metrics per player per game to which we did

not have access. Therefore, future research is challenged to test the

applicability of alternative model speciﬁcations and to determine

the signiﬁcance of additional indicators of market value. For exam-

ple, it is likely that market values are a function of several other

variables at the league level (e.g., UEFA coeﬃcients), at the club

level (e.g., team popularity), and at the individual level (e.g., ap-

pearances and performance on the national team or in the Cham-

pions League or Europa League), which we did not include in our

model. Moreover, future research could investigate the added value

of not only considering the volume of news shared on Reddit or

keywords used on Google as indicators of market value, but also

their sentiment ( Pang & Lee, 2008 ). For example, research on the

applicability of social-media data to predict politicians’ popularity

has shown that combining information on volume and sentiment

can enhance the accuracy of predictive models (see, e.g., Gayo-

Avello, 2013 ).

Against this background, our study has several limitations. First,

we could not conﬁrm empirically the potential of data analyt-

ics in scouting young and/or unknown players. Because we used

data from the ﬁve largest European leagues, most of the play-

ers in our sample were already well known to the public and

crowd. Therefore, future research should conduct similar analy-

ses using minor-league data, which may be a challenge because

less data are available for the minor leagues. Second, we argued

that data analytics can make estimating changes in players’ mar-

ket value possible on a match-by-match basis, while crowd es-

timations require much more time and effort. However, this po-

tential also remains to be empirically conﬁrmed. Our model used

seasonal data, so future research is challenged to conduct simi-

lar analyses with match-day data. Third, because of the unavail-

ability of other credible sources that provide historical estima-

tions of market value, we trained our model based on Transfer-

markt’s estimates of market value–another reason why our eval-

uation results are diﬃcult to interpret. Therefore, data analytics

should not be viewed at this stage as an alternative but as a com-

plementary approach to crowd-based estimation. As our model in-

corporated human judgment, it can be considered a “model of

the judge” ( Baron, 2008 , pp. 366ff.)–that is, we used the subjec-

tive estimations by the Transfermarkt judges to train a statisti-

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 621

cal model based on objective market-value indicators. To evalu-

ate the superiority of purely formal models over crowd estimates,

or vice versa, future research should develop time-series based

approaches to data-driven estimation of market value that pre-

dict market values in the future based on their own past estima-

tions.

7. Conclusions

Based on an analysis of a unique data set of 4217 players on

146 teams from the top ﬁve European leagues and a period of six

playing seasons, we demonstrated the value of using multilevel re-

gression models to estimate players’ market values. Comparing our

results with crowd estimates shows that a data-driven approach to

estimating market value can overcome several of crowdsourcing’s

practical limitations while producing comparatively accurate esti-

mates. Given the increasing availability of data about football play-

ers in the form of data sets from commercial data providers and

user-generated content from the web, we expect that the football

industry will increasingly adopt data analytics to support player re-

cruitment and transfer negotiations.

Acknowledgments

This research did not receive any speciﬁc grant from funding

agencies in the public, commercial, or not-for-proﬁt sectors. We

thank Alin Secareanu for his assistance and support in collecting

and preparing the data.

Appendix A. Descriptive Overview of the European transfer

market

We collected Transfermarkt’s estimations of market value at the

end of the six seasons (as per June 30) for all players in our sam-

ple. Fig. A.1 shows how the players’ market values changed dur-

ing the six-year period for the various playing positions, and Fig.

A.2 shows how they changed during that time for the top ﬁve

Fig. A.1. Development of market value across positions

Note: The ﬁgure displays estimations of market value at the end of the six playing

seasons, as estimated on the Transfermarkt website.

Fig. A.2. Development of market value across leagues

Note: The ﬁgure displays estimations of market value at the end of the six playing

seasons, as estimated on the Transfermarkt website.

European leagues. For each of the ﬁve leagues, Fig. A.3 shows the

two teams with the highest average player values across all sea-

sons. Across all leagues, the average player was worth €5.4 mil-

lion in 2009/10 and €6.0 million by 2014/15, an 11 percent increase

in only six years, which illustrates how important player valuation

has become in recent years.

Market values have generally increased for all positions, but

the amount of the increase has differed considerably among them.

With an average market value of €4.4 million across all seasons,

defenders had the lowest market values, while midﬁelders’ and

forwards’ average market values were €5.9 million and €7.2 mil-

lion, respectively. From 2009/10 to 2014/15, forwards’ market val-

ues increased from €6.8 million to €7.6 million (11.8%), midﬁelders’

market values increased from €5.7 million to €6.5 million (14.0%),

and defenders’ market values increased from €4.4 million to €4.6

million (4.5%).

England’s Premier League had the highest average market value

in every season. In 2009/10, its average market value was €7.3 mil-

lion, and it increased to €8.5 million in 2014/15 (16.4%). The two

most valuable teams were Chelsea F.C. (with an average player

value of €19.3 million) and Manchester City (with an average

player value of €18.8 million). Both of these teams were much less

valuable than the two top teams from Spain, FC Barcelona (with

an average player value of €29.4 million) and Real Madrid (with

an average player value of €26.4 million), even though players in

the Spanish league overall had considerably lower average market

values (average of €6.8 million) across the six seasons.

German Bundesliga players’ average market values increased

from €4.3 million in 2009/10 to €5.8 million in 2014/15 (34.9%).

The two most valuable clubs were FC Bayern Munich (with an

622 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

Fig. A.3. Teams with the highest average player market values

Notes: The ﬁgure displays the average player values, not the total team values, at the end of the six playing seasons, as estimated on the Transfermarkt website. The two

teams with the highest average player values are shown for each of

the ﬁve leagues.

average player value of €17.8 million) and Borussia Dortmund (with

an average player value of €11. 3 million). In contrast, Italy’s Serie A

players lost value, with average market values decreasing from €5.5

million in 2009/10 to €5.0 million in 2014/15, so the Serie A lost

its place among the top three most valuable European leagues to

Germany. The two most valuable teams were Juventus Turin (with

an average player value of €12.6 million) and Inter Milan (with an

average player value of €10.2 million).

Finally, players’ market values in France’s Ligue 1 remained

largely stable over the six years under consideration, with an

average market value of €3.5 million in 2009/10 and €3.4 mil-

lion in 2014/15. The two most valuable teams were Paris Saint-

Germain F.C. (with an average player value of €12.0 million) and

Olympique de Marseille (with an average player value of €6.6

million).

Appendix B. Distribution and correlation of dependent and

independent variables

As we used Transfermarkt’s estimates of market value to train

our model, we investigated the distributions of the players’ market

values. Fig. B.1 provides box plots that show how the market values

were distributed across seasons, leagues, and positions. The distri-

bution of the players’ market values was highly right-skewed, with

means that were above the medians for all seasons, leagues, and

positions, which indicates that our sample contained a few players

with exceptionally high market values, as well as a large number

of players whose market values were below the average of around

€5.6 million.

We also investigated how the indicators of market value that

we used as independent variables in our regression model were

correlated ( Table B.1 ). All correlations were below the critical

threshold of 0.7; in addition, all variance inﬂation factors (VIF)

were below 4, well below the critical threshold of 10, so multi-

collinearity presented no problems.

Appendix C. Evaluation results

We used the sample of players who had transfer fees below €18

million to investigate our model’s accuracy by evaluating how the

estimates of market value differed from actual transfer fees across

seasons, positions, and leagues. Table C.1 shows the evaluation re-

sults.

In the ﬁrst four seasons, the crowd’s estimates were closer

to the actual transfer fees, especially in season 2012/13 (relative

difference in RMSE of + 20.0%), but in 2013/14 and 2014/15, the

model’s estimates were more accurate ( −13.2% and −3.1%, respec-

tively). While the model produced more accurate numbers for Ger-

many’s Bundesliga ( −6.4%) and England’s Premier League ( −5.2%),

the crowd provided more accurate estimates for Spain’s La Liga

( + 0.9%), France’s Ligue 1 ( + 2.1%), and Italy’s Serie A ( + 9.4%). Fi-

nally, the crowd’s estimates were closer to the actual transfer fees

for defenders ( + 4.6%) and forwards ( + 7.3%), while the model was

more accurate for midﬁelders ( −8.4%).

O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624 623

Fig. B.1. Distribution of market value across seasons, leagues, and positions

Notes: The ﬁgure displays box plots of market-value estimations at the end of the six playing seasons, as estimated on the Transfermarkt website. The y-axes are log-

transformed. The whiskers (i.e., the lines at the bottom and top of each

box) show the minimum and maximum values within 1.5 times the interquartile range; the bands

in the boxes represent the 25th, 50th (median), and 75th percentiles. The dotted lines that cross the box plots show the mean market value.

Table B.1

Correlation matrix.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22)

(1) Age 1

(2) Height 0.01 1

(3) Minutes played 0.10 0.02 1

(4) Goals 0.00 −0.01 0.37 1

(5) Assists −0.02 −0.20 0.42 0.51 1

(6) Passes 0.13 0.02 0.52 −0.03 0.20 1

(7) Successful passes 0.01 −0.13 0.07 −0.12 0.01 0.49 1

(8) Dribbles −0.22 −0.28 0.19 0.41 0.48 −0.02 −0.04 1

(9) Successful dribbles 0.03 0.10 0.18 −0.09 −0.04 0.32 0.21 −0.06 1

(10) Aerial duels 0.10 0.40 0.22 0.19 −0.04 0.06 −0.29 −0.09 0.07 1

(11) Successful aerial duels 0.14 0.41 0.13 −0.21 −0.23 0.29 0.04 −0.34 0.19 0.25 1

(12) Tackles −0.02 −0.05 0.33 −0.24 0.00 0.56 0.18 −0.02 0.22 0.00 0.24 1

(13) Successful tackles 0.00 0.09 0.10 −0.12 −0.11 0.13 0.09 −0.15 0.04 0.00 0.22 0.10 1

(14) Interceptions 0.07 0.12 0.33 −0.31 −0.16 0.53 0.17 −0.26 0.25 0.06 0.44 0.62 0.25 1

(15) Clearances 0.13 0.39 0.23 −0.27 −0.29 0.28 0.08 −0.42 0.25 0.29 0.53 0.22 0.28 0.55 1

(16) Fouls −0.02 0.10 0.26 0.10 0.05 0.21 −0.11 0.08 0.04 0.24 0.12 0.41 0.04 0.24 0.00 1

(17) Yellow cards 0.11 0.03 0.58 0.09 0.15 0.38 0.05 0.01 0.12 0.13 0.17 0.40 0.09 0.37 0.19 0.49 1

(18) Red cards 0.03 0.07 0.17 0.00 −0.01 0.11 0.00 −0.04 0.06 0.08 0.13 0.12 0.07 0.17 0.16 0.18 0.20 1

(19) Wikipedia page views 0.02 −0.01 0.13 0.27 0.24 0.15 0.16 0.16 0.03 0.01 −0.06 −0.07 −0.01 −0.13 −0.09 −0.08 −0.02 −0.03 1

(20) Google Trends search index −0.03 −0.02 0.03 0.10 0.08 0.04 0.08 0.04 −0.03 −0.03 −0.03 −0.03 0.04 −0.03 0.00 −0.04 −0.03 0.00 0.15 1

(21) Reddit posts 0.09 −0.03 0.13 0.17 0.17 0.18 0.18 0.11 0.09 0.18 −0.02 −0.02 −0.10 −0.11 −0.02 −0.14 0.04 −0.02 0.33 0.04 1

(22) YouTube videos 0.07 −0.06 0.14 0.21 0.20 0.15 0.12 0.15 0.03 0.08 −0.05 −0.05 −0.05 −0.08 −0.06 −0.09 0.08 0.00 0.26 0.08 0.63 1

624 O. Müller et al. / European Journal of Operational Research 263 (2017) 611–624

Table C.1

Model evaluation across seasons, positions, and leagues.

RMSE RMSE Relative N

Model’s estimates Crowd’s estimates difference

Seasons 2009/10 34 4 4,749 3382,450 + 1.8% 101

2010/11 3242,258 3217,317 + 0.8% 147

2011/12 4006,372 3808,920 + 5.1% 120

2012/13 3221,275 2635,404 + 20.0% 130

2013/14 3101,502 3541,482 −13.2% 129

2014/15 4241,699 4374,319 −3.1% 141

Positions Defender 3723,296 3556,600 + 4.6% 240

Midﬁelder 3175,083 3453,751 −8.4% 315

Forward 3932,515 3653,805 + 7.3% 213

Leagues Bundesliga 2743,188 2923,510 −6.4% 16 4

La Liga 3642,176 3610,105 + 0.9% 102

Ligue 1 3855,753 3775,886 + 2.1% 128

Premier League 4113,338 4332,412 −5.2% 144

Serie A 3532,511 3215,505 + 9.4% 230

Notes: The table shows RMSEs for transfer fees below €18 million. A positive value

for relative difference indicates superiority of crowd. N = 768.

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