Exploring soccer transfers in Spanish League– The hidden role of strategic differences among teams

RESEARCH ARTICLE Exploring soccer transfers in Spanish League– The hidden role of strategic differences among teams Paulo Reis Mourao 1 , Jesyca Salgado-BarandelaID 2 * 1Deparment of Economics & NIPE, University of Minho, Braga, Portugal, 2Deparment of Business Organization and Marketing, University of Santiago de Compostela, Santiago de Compostela, Galicia, España *[email protected] Abstract Transfers in the football world have become a hot topic in academic studies in recent years. Spanish league (La Liga) is one of the men’s professional football leagues that have driven some of the most notorious transfers. In this way, we test determinants for the transfer relationships of football players in the Spanish League in the most expensive seasons with records (2018/2019 and 2019/2020 seasons). Furthermore, we identify determinants for the values of the observed transfers. The empirical analysis shows relevant findings. We recognize two implications. First, Spanish soccer transfers are not random and this evidence reflects the environment of imperfect competition characterizing La Liga. Second, the nonrandomness of the transfer process can be associated with an increasing inequality among teams and with a threat to the competitive balance in professional sports. 1. Introduction When a player moves from one club to another, his registration is transferred to that club, normally for a fee agreed between the two parties. This is the definition of football transfer, which involves two aspects: the transfer of the player from one team to another and the amount of money agreed between both teams. Transfers in the football world have become a hot topic in academic studies in recent years. The monetary resources involved as well as the growing trend helped in this highlight. The works focused on soccer transfers allow the identification of several lines of development. With no pretensions of exhaustion, we highlight three common lines of these publications. In a first line, there is the discussion of determinants for such flows, therefore determinants for transfers, either in number of players involved or in the associated amount [1–7]. In a second line, there are works like Mourao [2,8] that seek to assess the efficiency of transfers considering their own restrictions on the part of the involved determinants. Finally, in a third line, the specificity of the transfers is evaluated in the consideration of certain realities, such as the places occupied by some athletes, the nature of the national championships involved or the relationship with certain observed periods [9–11]. PLOS ONE PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 1 / 20 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Reis Mourao P, Salgado-Barandela J (2024) Exploring soccer transfers in Spanish League–The hidden role of strategic differences among teams. PLoS ONE 19(4): e0299853. https:// doi.org/10.1371/journal.pone.0299853 Editor: Ricardo Limongi, Federal University of Goias: Universidade Federal de Goias, BRAZIL Received: May 26, 2023 Accepted: February 18, 2024 Published: April 9, 2024 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0299853 Copyright: ©2024 Reis Mourao, Salgado- Barandela. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files. In a special way, the study of the determinants of transfers has achieved an important dimension in professional soccer. As Mourao [2] explains, the provisions of Financial fair play have pushed clubs to adopt transfer market strategies to save on relevant expenses and amortize transfers. At the same time, this strategy has increased the level of relevant income in terms of capital gains on player disposals and this effect is stronger for clubs from professional soccer leagues [12]. On the other hand, there are professional soccer leagues that show a notable increase in the monetary resources of player´s tranfers. This situation represents an opportunity to analyse the factors that influence transfers. Furthermore, scientific studies have evolved towards the consideration of new statistical tools in the study of determinants in this topic, such as network analysis [13]. One of the men’s professional football leagues that have driven some of the most notorious transfers is the Spanish league (La Liga). In the last decade the average value per club in question has grown from €15.23 million (from the season 2010/2011) to €74 million in 2019/2020 [14]. If the nature of the Spanish league contributes to this value (we remember that it is traditionally considered one of the 3 most valued professional football leagues in world), other specific reasons contribute to this notoriety. Being a league that traditionally places clubs in the final stages of the main European club competitions creates a special attractiveness in its clubs for receiving the best players in the world [15]. Additionally, La Liga has become a league with millions of worldwide followers, with a growing number since 2000. Finally, the values of the brands associated with La Liga’s clubs have reached record numbers over the last few seasons, with the Spanish championships having some of the teams with the highest value in the international market, regardless of the sport [16]. These reasons are strong reasons for an increasing interest in an analysis of the costliest seasons in terms of transfers. Thus, contributions can be made to the topic of study of the determinants of transfers in relation to the upward tendency of transfers in professional soccer leagues. In this way, the main objective of this work is testing determinants for the transfer relationships of football players in the Spanish League in the most expensive times with records. For it, we use network analysis and we test the hypothesis about dominant teams create hierarchical structures in which they move more players to lower-ranked teams rather than to other highly ranked teams. We use random graph models (ERGM) confronted with Paneldata Logit models to teste the determinants of the relationships. Thus, we will observe if certain teams’ characteristics enhance the creation of ties with other teams in terms of players’ transfers. Furthermore, we identify determinants for the values of the transfers observed and we use Ordinary Least Squares with Random Effects to estimate this model. The main knowledge gap covered by this work is to study the dimensions responsible for the value of transfers from an approach of intense dynamics between clubs using network analysis. This work adds to the high-potential area of social network analysis in sports organizations [1,9,13,17]. In this way, empirical analysis shows relevant findings. First, Spanish soccer transfers are not random and this evidence reflects the environment of imperfect competition characterizing La Liga. Second, the non-randomness of the transfer process can be associated with an increasing inequality among teams and with a threat to the competitive balance in professional sports. Additionally, we identify that larger point differences, as well as age of the team, balances of transfers and attendances throughout the seasons increase the value of the transfers observed. The remaining structure of this paper is as follows. Section 2 reviews the literature in relation to attributes and determinants analysis to explain football transfers. Section 3 describes the data and explains the used methodology. Section 4 shows our empirical efforts regarding testing determinants of transfer networks and identify determinants for the values of the transfers observed. Section 5 concludes and provides opportunities for further research. PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 2 / 20 Funding: The author(s) received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist 2. Literature review: Determinants of transfers and the importance of implementing network analysis Previous literature has investigated the main drivers of transfer fees paid by clubs. The evidences indicate that, the level of a transfer fee is linked to the player’s characteristics and performance features [6,7,14,15]. Franceschi et al. [16] identifies in his systematic review study that age and age squared are the most often tested variables, consistently associated with significant. In addition to age, variables such as usage of the player (minutes played or number of appearances) and international status and decisiveness (goals and assists) are frequently included in the studies and positively and consistently influence the valuation of the football player. On the other hand, Franceschi et al. [16] explains that this positive relationship can be explained by the low-score nature of football. When the usage variables are studied together with the performance variables, the significant results are low. Furthermore, these indicators are probably correlated, thus they may weaken each other’s influence on the dependent variable. Previous studies also consider the economic-financial dimension in the analyzed determinants. In a specific way, economic variables are defined such as wage rate, relevant incentives, and the remaining duration of the contract, play a role in determining the transfer fee for player registration [5,17]. In relation to the financial dimension, variables such as the values of past transfers and the respective balances, in addition to the financial indicators observed from the Account Reports of the Clubs [2,7]. Campa [5] explains that they reflect the influence of factors related to neither players’ skills nor to other economic features, for example: the race of a player or the number of Google searches associated with the player. In relation to the dependent variable, most of the works in extant literature propose at least one model specification where the dependent variable is the transfer fee. It is necessary to consider that transfer fee it is not available for every player at any time but rather only when a transfer eventually occurs [12,16]. For this reason, studies of transfer determinants usually use crowdsourced estimates of players value, retrieved from the website Transfermarkt [16]. It is possible to find differences in relation to the use of transfer fee as a dependent variable. Matesanz et al. [18] use three variables to construct transfer data: transfer spending (transfer spending is the amount of money each club has spent in transfers in each season), transfer earnings (represent the amount of money each club has generated from transfers in each season) and transfer fee volume (transfer spending + transfer earnings). On the other hand, Liu et al. [19] and Rosseti and Caproni [20] detail transfers by type of transaction: free / payed transfer, and loans. In the case of Coates et al. [21] they treat loans also as a connection between clubs. In the literature, only a small number of papers have analyzed football transfers using network analysis. Liu et al. [19] studied the relationship between the success of a club and player transfers on a dataset of transfer records from 2011 to 2015 of 410 professional clubs in 24 world-wide top class leagues. They show “that clubs’ match performance and profitability from the transfer market are strongly associated with the coreness and brokerage properties of their corresponding nodes in the player transfer network” [19]. Moreover, Matesanz et al. [18] explore the evolution of the football players’ transfer network among 21 European first leagues between the seasons 1996/1997 and 2015/2016. They get findings similar to Liu et al. [19]. Rosseti and Caproni [20] also studied the impact of club transfer strategies on team performance, but with a different database. In this case, they worked with data covering 25 years of trading among clubs of the 6 FIFA federations. Unlike Liu et al. [19], Rosseti and Caproni [20] found support for a nonlinear relationship between network characteristics and roster changes. On the other hand, Coates et al. [21] extend the work previously done using a massive dataset on transfers and club characteristics to study the relation between transfer strategy and PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 3 / 20 performance. They use data on 23220 clubs from 189 countries from 1996 through 2016 and they found that a wide transfer network is harmful for a club’s sport performance, and the best strategy is to have the lowest number of connections inside the league. As Coates et al. [21] explains “for financial performance, it is better to have a high number of international connections with clubs that have widespread transfer networks, whereas connections inside domestic league are not important”. More recently, Clemente y Cornaro [13] have applied network analysis to study number of transfers and the related costs for football players in the world market. They use all transfers between football clubs regarding the season 2020–2021, taking into account both winter and summer sessions, 44,481 transfers in total. They find that clubs of top football leagues tend to behave in a similar way in the network and to trade players each other and highlighted the role of several European countries that represent top leagues in the soccer market and are also involved as central countries in the economic trades. In relation to those studies [13,18–21] it is identified that the number of points is a variable commonly used as an independent or control variable. Liu et al. [19] use Kendall’s Tau coefficient to analyze the relationship between club functionalities versus network properties in international and domestic transfer networks, node properties in transfer network and loan network, and node properties in money leagues and farm leagues. These authors consider two variables in relation to the number of points, which are: average league points (domestic league) and IFFHS Club World Ranking points (The IFFHS Club World Ranking points are composed by the International Federation of Football History & Statistics (IFFHS) based on a set of rules composing both domestic and international match results). While, Matesanz et al. [18] include domestic rank and UEFA points to study the football player transfer market activities among European first leagues from 21 countries. Rosseti and Caproni [20] and Coates et al. [21] only consider points per game like a dimension to represent number of points. In this same line, previous papers also consider characteristics of the players in the selection of independent or control variables. Matesanz et al. [18] and Rosseti and Caproni [20] include various characteristics in relation to the transferred players. In the case of Matesanz et al. [18] variables are: age, nationality, field position. Matesanz et al. [18] find that “the connection between transfer spending and sportive performance, especially in UEFA competitions, is extremely strong particularly for clubs from the top cluster, which might further limit the overall level of uncertainty of outcome”. While, Rosseti and Caproni [20] include role, age and market value to players transferred, and they identify among other findings that roster stability plays a crucial role on the obtained results and more you change more unpredictable your future results will be. Coates et al. [21] include player´s rating in its methodological model. Also, it is the only work that also measures the performance of the coach using fixed effects for its measurement. Finally, the attendance variable is only included by Coates et al. [21], the rest of previous works do not consider it in its measurement. 3. Data and methodology 3.1 Data The seasons studied here– 2018/2019 and 2019/2020 –were the most notorious Spanish seasons in terms of transfer values. The data proves that there have never been such high values in terms of transfers paid by Spanish club; also this period has allowed Spanish clubs the highest values received from transfer moves. In this way, we collected a database with transfers of the Spanish League (La Liga) for 63 weeks, between 1/July/2018 and 1/September/2019. The information to build the database has been obtained from the website transfermarkt.es. The descriptive analysis of the database shows that in the 63 weeks between 1/July/2018 and 1/ PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 4 / 20 September/2019 a total of 503 transfers had been reported, with a total value of €3,471.94 million. In the case of the 2018/2019 season, 265 transfers occurred, with a total value of €1,630.67 million. On the other hand, during the first two months of the 2019/2020 season (July and August), 238 transfers occurred, with a total value of €1,841.27 million. Just for illustrative purposes, we constructed Fig 1, which highlights these flows. Let us remark that the node “Otros” include all the other teams (of all championships in the globe) having had transfers with Spanish teams. Thus, three reasons emerge for us to focus our study on these times, without neglecting to extend to more remote times. These three reasons are: the maximum achieved in relation to sports transfers in Spain, the emerging role of network analysis to study competitive phenomena, and the importance of observing the dimensions of oligopolies that exist in sport. First, the maximums observed during the transfer windows listed here, due to the current pandemic, have not yet been exceeded in the most recent transfer windows. It is important to understand what happens in these seasons because this provides relevant findings to explain a scenario of upward tendency in transfers. This situation is not exclusive to the Spanish Soccer League; other leagues also have high transfer costs. Thus, the understanding of a general situation of the transfer market can be improved. Second, the transfer market has not considered so far either the role of the networks involved or the importance of more likely transfers due to imbalances in characteristics between clubs. Thirdly, behaviors induced in oligopolistic environments, such as that observed in professional soccer championships, induce asset transfers between companies that compete for different market shares, a central hypothesis in our study. Our dependent variable for the model proposed in this study is the value of transfers from club A to club B at the observed seasons. The independent variables are the variables shown in Table 1, which follow the quoted literature from Section 2. In addition to the variables in Table 1, certain attributes are added to the model to explain the properties of the network. These attributes are: number of points obtained at the end of season, transfer balance value (millions of euros), average age of the team squad for the seasons and total attendance at the team’s stadium for the seasons. Fig 1. Spanish transfer network—All transfers included (1 st September 2019). https://doi.org/10.1371/journal.pone.0299853.g001 PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 5 / 20 The explanatory variables of our model were inspired by the literature presented in the previous section. Still, we recall the underlying reason as well as the supporting literature below. The number of points in previous seasons is a variable associated with the value of the team’s budget as well as the ability to generate transfers around the club. The use of values from several epochs allows for a more robust associated reading [18,19]. The average value of the number of points allows you to control possible fluctuations outside the predictable performance of each team. The variable focused on the transfer balance is a variable that shows the difference between the amount received from transfers made and the amount paid due to transfers that entered the club. In line with the literature consulted [18], higher transfer balances produce a leverage effect on the club’s future operations. Once again, the presence of a variable associated with the average value (in this case, the balance of transfers) aims to provide greater robustness to the model. The average age of the team shows the need to renew the squad in future exercises. As suggested by Samur [22], aging teams increase the probability of incoming transfers in the future. The total number of spectators reported for each team’s home games is a variable that controls the number of points as well as the balance of transfers. Teams with good home game attendances show significant support from the surrounding community. The inclusion of the average attendance at home aims to control possible imbalances that consecutive fluctuations in attendance may suffer [23]. 3.2 Methodology Recalling the literature on network analysis, specifically Mariotti and Haider [24] and Pardalos and Zamalaev [25], we want to observe the selectivity of these transfers, testing the claim that certain teams make the moving of their players to other teams easier. Therefore, we want to observe if certain teams’ characteristics enhance the creation of ties with other teams in terms of players’ moves (or if these characteristics make these ties more difficult). We are particularly concerned with team budgets, points/ranks usual in championship or centrality positions [26, 27]. Therefore, the empirical development is divided into three stages. In the first place (section 3.2.1), we want to test the hypothesis about “Dominant teams” creating hierarchical structures in which they move more players to lower-ranked teams rather than to other highly ranked teams [28]. Our empirical section will test this hypothesis following the works of Table 1. Descriptive statistics of the La Liga teams’ attributes (2017–2018 and 2018–2019). Mean Std Dev Max Min number of points got at the end of season 2015/2016 55,12 17,489 91 32 number of points got at the end of season 2016/2017 55,56 19,894 93 20 number of points got at the end of season 2017/2018 55,72 17,516 93 20 average number of points for the seasons 2015/2016, 2016/2017, and 2017/2018 55,47 14,068 91,3 35 TrfBalan value (millions of Euros) at the end of season 2015/2016 -1,115 26,861 78,9 -90,95 TrfBalan value (millions of Euros) at the end of season 2016/2017 -0,453 37,797 88 -142 TrfBalan value (millions of Euros) at the end of season 2017/2018 -4,135 27,132 47,1 -95,6 average TrfBalan value (millions of Euros) for the seasons 2015/2016, 2016/2017, and 2017/2018 -1,901 20,636 26,7 -76 Average Age of the team squad for the seasons 2015/2016, 2016/2017, and 2017/2018 26,023 0,923 28,11 24,54 Total Attendance at team’s stadium for the seasons 2015/2016, 2016/2017, and 2017/2018 466.313 337.168,495 1.342.982 100.544 Average Attendance per match at team’s stadium for the seasons 2015/2016, 2016/2017, and 2017/2018 24.458 18.129,9161 73.159 5.292 Source: Author´s elaboration https://doi.org/10.1371/journal.pone.0299853.t001 PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 6 / 20 Hanneman and Riddle [29], Holland and Leinhardt [30], and Shumate and Palazzolo [31]. We start the empirical analysis using network analysis. The main empirical outcomes from this first stage will be summarized in Table 2. Afterwards, we will also want to test the robustness of these outcomes consider panel data logit models (check the theoretical motivation at sub-section 3.2.2 and the empirical outcomes at sub-section 4.2). Finally, taking advantage of the panel data, we will test determinants for the different values of the transfers by recurring to Panel-data linear models (check Table 4 at the empirical sub-section 4.3 and the theoretical motivation at Sub-section 3.2.3). 3.2.1 Exponential random graph models (ERGM). As Morris [32] states, “[actors/teams] may come and go, the links form and dissolve, but the structural pattern remains.” Thus, it is relevant to study the probability of observing a graph (i.e., a set of relationships) y on a fixed set of nodes. In our case, we keep the motivation to explain the existence of the observed structure of players’ moves because of dimensions such as the existence of arcs, the simultaneous presence of bidirected moves (i.e., players coming from a team and going to another team and the reverse), or even the effects of certain exogenous variables, such as the points of each team or its budget value. Table 2. ERGM estimates for La Liga players’ transfers (2018–2019 and 2019–2020). Parameters Posterior Mean Estimate -2018 (Std Deviation) [Acceptance Rate] Posterior Mean Estimate -2019 (Std Deviation) [Acceptance Rate] Model 1: Arc Baseline Arc -5.291*(0.247) [0.50] -3.402*(0.095) [0.44] Model 2: Structural Parameters Arc -5.891*(0.277) [0.52] -3.245*(0.102) [0.42] Reciprocity 0.666*(0.288) [0.52) 0.684*(0.249) [0.42] Model 3: Attributes Model Arc -5.804*(0.139) [0.40] -3.632*(0.127) [0.39] Points16_DifferenceA -3.310*(0.181) [0.40] -4.118*(0.174) [0.39] Points17_DifferenceA -6.581*(0.407) [0.40] -5.487*(0.218) [0.39] Points18_DifferenceA -0.438 (0.469) [0.40] -0.088 (0.188) [0.39] TrfBalan16_DifferenceA 37.54*(0.160) [0.40] 37.70*(0.199) [0.39] TrfBalan17_DifferenceA 27.22*(0.421) [0.40] 28.12*(0.287) [0.39] TrfBalan18_DifferenceA 23.91*(0.248) [0.40] 23.17*(0.472) [0.39] Team_age_DifferenceA -0.574*(0.213) [0.40] -2.627*(0.222) [0.39] Assistance_DifferenceA -0.117*(0.007) [0.40] -0.133*(0.052) [0.39] Model 4: Combined Model Arc -5.704*(0.139) [0.50] -2.911*(0.271) [0.40] Reciprocity 0.671*(0.362) [0.50] 0.644*(0.352) [0.40] Points16_DifferenceA -3.300*(0.181) [0.50] -4.108*(0.174) [0.40] Points17_DifferenceA -6.582*(0.407) [0.50] -5.488*(0.218) [0.40] Points18_DifferenceA -0.338 (0.469) [0.50] -0.088 (0.188) [0.40] TrfBalan16_DifferenceA 37.44*(0.160) [0.50] 37.70*(0.199) [0.40] TrfBalan17_DifferenceA 27.21*(0.421) [0.50] 28.09*(0.287) [0.40] TrfBalan18_DifferenceA 22.91*(0.249) [0.50] 22.47*(0.411) [0.40] Team_age_DifferenceA -0.584*(0.214) [0.50] -2.697*(0.232) [0.40] Assistance_DifferenceA -0.217*(0.107) [0.50] -0.133*(0.051) [0.40] *means convergence statistics lower than 0.1. Note: for each attribute, we have also estimated the following dimensions: Value of Sender; Value of Receiver; Sum of both values; Product of both values. As the related estimates revealed themselves to be non-significant, we omitted them (although they are available upon request). https://doi.org/10.1371/journal.pone.0299853.t002 PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 7 / 20 Following Holland and Leinhardt [30] and their original models, we will use exponential random graph models (ERGM). As these authors demonstrated, there are properties of ERGM that must be noted, as these types of models “can easily accommodate other relations, attributes, and structural estimates as predictors of a given network” [33]. Additionally, and still quoting Snijders et al. [33], ERGM can differentiate “the senders of relations, the receiver of relations, or that actors with the greatest differences in valued attributes are likely to have relations.” Following the notation of Shumate and Palazzolo [31] and Mourao [34], we can enunciate the ERGM model as follows: P X ¼xð Þ ¼ expfy0zðxÞg kðyÞðEq 1:1Þ According to Eqs 1.1,1.2, we are modeling the probability of a given network P(x) depending on the estimation of a vector of model parameters ɵ. z(x) refers to a vector of network statistics, and k is a normalizing function. The role of this normalizing function is to guarantee a certain probability distribution across the random networks. For the estimation of Eqs 1.1,1.2, we have to use maximum pseudo likelihood estimations. This method fits a logistic regression for the vector of network statistics. Therefore, we will work with the following maximum pseudo likelihood estimation: PLðyÞ ¼ Yi6¼jYr m¼1PðXijm ¼1jXC ijmÞXijm PðXijm ¼0jXC ijmÞ1Xijm ðEq 1:2Þ Following Shumate and Palazzolo [31], the maximum pseudo likelihood estimation for each parameter is computed as a product of the log-odds ratio of the following two probabilities: the probability for each observed tie, P(X = 1) and the probability of not observing that tie in the network, P(X = 0). Additional features–such as the use of pseudo likelihood ratio statistics, the discussion of the independence assumptions, and robustness in small samples–are discussed by authors including Shumate and Palazzolo [31] and Robins, Pattison and Wasserman [35]. Given the nature of our sample [36], we opted for estimating Eqs 1.1,1.2 by Bayesian procedures. We follow Caimo and Friel [36] who state that “Instead of obtaining the point estimates [. . .], the Bayesian estimation generates the posterior distributions of the model parameters. In lieu of MLEs and standard errors, point estimates and measures of uncertainty are calculated as averages and standards errors of this distribution, respectively”. 3.2.2 Panel data logit model for robustness. In order to explore the robustness of the results obtained by ERGM, we intend to estimate the following “Panel-data logit Model” (Eq 2.1) which will explain the probability of a transfer happening between each pair of La Liga’s teams. Generically, this model has the following specification, for n periods and i observations [37]: Pr Yi1;...;YinijXi1;. . . ;Xini ð Þ ¼ Z1  1 ev2 i=2s2 v ffiffiffiffiffiffiffiffiffiffi 2psv pnYni t¼1Fðyit;XitbþViÞodviðEq 2:1Þ In Eq 2.1, we model the probability of a given pair of teams I at a given season n having had a transfer of players. The random effect v i follows a Normal Distribution N (0, Sigma^2_v). PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 8 / 20 The following specification is also observed. f y;zð Þ ¼ 1 1þexpð zÞif y 6¼ 0 1 1þexpðzÞotherwise ðEq 2:2Þ 8 > > < > > : Finally, the panel-data likelihood l_i is specified as li¼Z1  1 ev2 i=2s2 v ffiffiffiffiffiffiffiffiffiffi 2psv pnYni t¼1Fðyit;XitbþViÞodvi�Z1  1 gðyit;xit;vitÞdviðEq 2:3Þ 3.2.3 Panel data linear models for transfers´values. After these steps, we will also test determinants for the values of transfers observed (at subsection 4.3). Our dependent variable is thus, for this model, the value of transfers from club A to club B at the observed seasons. To estimate the model relating to the value of transfers made between club A and a different destination, and as we are dealing with panel data, we used two estimation methods: Ordinary Least Squares with Fixed Effects and Ordinary Least Squares with Random Effects. To choose between the two methods, we performed the Hausman test. The result of the Hausman test always had a p-value greater than 10%. This value suggests that random effects should be used, revealing that each club and each season have introduced significant effects of their own. More detailed results will be displayed upon request. 4. Empirical analysis 4.1 Hypotheses for determinants of transfer networks When we intend to analyze network structures, studies are based on the need to explore not only the dimensions that explain the values observed in flows but also on the need to explore dimensions that explain the existence and meaning of flows in the network. Thus, we have two groups of hypotheses for the design observed in a network: • structure hypotheses, where arcs/connection pairs are evaluated, among other more complex structures; • and the hypotheses of the determinants of values, closer to linear estimation analysis. Within the second group, we cite the literature that had already been discussed before—[2, 28,29,34]. Therefore, for player transfers in the Spanish League, we will analyze sporting performance (measured by the team’s number of points in previous seasons) but also the financial performance of that period (evaluated by two variables–the team’s budget and the balance of transfers). But we will also evaluate, for each pair of teams, the respective differential of these variables, as is common in the literature on network analysis. Within the first group, the structure hypotheses, network analysis suggests the assessment of the existence of arcs as well as reciprocal flows [31,32]. First, we show the result obtained from the ERGM model. Following Shumate and Palazzolo [21], if the estimated posterior mean parameters have significant values, i.e., higher than twice the estimated standard deviation, then this is an indication of a good fit. Additionally, the acceptance rate must be as high as possible. In empirical terms, posterior distributions are a ‘compromise’ between two sources of information–the likelihood estimation and the prior distributions of the parameters–which has been found empirically adequate for studying social networks [25]. We included the most-frequently cited indices for goodness-of-fit of ERGM PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 9 / 20 between sports clubs [18–21]. Other works had focused on some dimensions of footballer transfers in Spain [1]. However, our work has shown how analyzing the network structure is essential to understanding the phenomenon under analysis, especially the differentiation of values involved. We emphasize that these results converge with some authors but advance the current state of the art. They converge with [2,4,18] in the sense that there is a strategic behavior of clubs in transfers. Players are transferred as an important source of revenue for the club’s financial cycle, but they are also transferred so that the expected sporting objectives are guaranteed. This strategic behavior of oligopolistic agents had already been detected in previous works: [2, 4,18]. However, our study went further–it demonstrated that the greater the differences between the values of a financial or sporting variable observed for two teams, the greater the probability of a player transfer between these two teams in the Spanish championship. We also observed that the greater the differences between these teams (in financial or sporting variables) the greater the values involved in the observed transfers. These results surpass existing literature as in [5]. Specifically, our results have important implications–the use of transfers as an instrument for the strategic management of clubs cannot be neglected as an important cause for existing imbalances, particularly in terms of competitive balance. Secondly, the observed flow could compromise the financial and sporting viability of smaller teams, which are much more dependent on the surplus resources of larger teams. Thirdly, the structure of the network designed by transfers clearly shows the dependence of the same network on a small group of clubs. This dependence is a serious threat to the integrated objectives of the entire industry, requiring reflection in favour of a more sustainable structure. 5. Conclusion, implications and challenges This work studies in depth soccer transfers in the Spanish League in the most expensive seasons of its History (2018/2019 and 2019/2020 seasons). Following the literature on the topic, we have tested the hypothesis that dominant teams create hierarchical structures in which they move more players to lower-ranked teams rather than to other highly ranked teams. Also, we identify determinants for the values of the transfers observed. This work confirmed, through the originality of Network Analysis, the existence of an oligopolistic structure with strategic behavior in the professional football industry in Spain. Additionally, this work showed that transfers are a vital instrument of this strategy between oligopolists. However, we want to emphasize that this instrument is aimed at temporal consistency, reducing the possibility of mid-table teams being champion teams in Spain. This type of consequence is important for the discussion of the lack of sporting competitiveness in the championship, reduced to a competition whose biggest prize is only within the reach of a small group of teams. Table 4. (Continued) RE estimates Marginal effects Assistance_Buying team 0.311*(0.151) 0.602*(0.119) Seasons dummies No N 882 R2 (Overall) 0.614 Robust standard errors between parentheses. Significance level: 1%, ***; 5%, **; 10%, *. https://doi.org/10.1371/journal.pone.0299853.t004 PLOS ONE Exploring soccer transfers in Spanish League PLOS ONE | https://doi.org/10.1371/journal.pone.0299853 April 9, 2024 16 / 20 The review of the previous literature identified works which studied dimensions responsible for the value of transfers in the world of professional soccer. However, the approach of such intense dynamics between clubs has not yet been widely discussed using Network Analysis. In this way, we tested four models. We started with only one parameter and the results suggested that the existence of ties in the observed network is less likely to be explained by chance. Then, we explored a second model in which we included structural parameters (there we added reciprocity). Also, we included the possibility of certain attributes explaining the properties of the network in a third model. Finally, we have tested combined model with structural parameters and attributes. At last, we have been able to provide a more complete perspective of situation. In this way, we tested a larger set of characteristics involving each element of the dyad of teams involved in a transfer process for our Hypothesis. Considering this hypothesis, Spanish teams tend to transfer players with teams that are not competing for the same rank, which is a behavior fitting markets. Additionally, we used Ordinary Least Squares with Random Effects to identify determinants for the values of the transfers observed. We concluded that larger point differences, age of the team, balances of transfers and assists throughout the seasons increase the value of the transfers observed. We recognize two major implications from this empirical effort. The first implication is the identification of the Spanish Soccer League with an oligopolist market which deserves additional study to preserve and maintain the competitive balance, a structural factor for the financial sustainability of professional sports. Additionally, the non-randomness of the transfer process implies that resources such as information on players and teams or the role of players’ agents/’third-parties’ are elements that are able to generate rents, which can be associated with an increasing inequality among teams and with a threat to the already mentioned competitive balance in professional sports. These results stimulate further works. First, we suggest investigating not only the two most recent seasons but also a longer period and for other professional soccer leagues. This would enhance the robustness of these original achievements. Additionally, we also suggest enlarging the observed and tested attributes explaining the reported transfers, i.e., enlarging the analysis to other independent variables than those tested here for the exponential random graph models. We also consider relevant the possibility of detailing these results by considering the continents of the leagues which were the origins or the destinations of the observed players’ transfers. Finally, given the structure of time series easily perceived for the evolution of the indicators analyzed for the weekly and monthly networks of transfers, we also consider running a structural breaks test on these relevant series, as well testing Markov-Switching models for deepening the study of these observations. Supporting information S1 Data. (XLSX) Author Contributions Conceptualization: Jesyca Salgado-Barandela. Data curation: Jesyca Salgado-Barandela. Formal analysis: Jesyca Salgado-Barandela. Funding acquisition: Paulo Reis Mourao. 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