Abstract
Multilayer Fuzzy Cognitive Maps (MFCM) represents an approach for analyzing situations, which allows the simulation, inference, theorem proving of tendencies, and verification of theories, among other things. This paper reviews the promise of this method in a novelty case study of management of professional sports clubs. Professional sports clubs have the possibility of making their management profitable through the proper management of their commercial product portfolio. This possibility is conditioned by the adequate configuration of each component of the commercial product portfolio, namely: Brand licensing, sponsorship, television and media rights, sporting and training rights, and hospitality. Each component of the commercial portfolio must maximize its attractiveness and desirability for each target customer segment. For these purposes, tools that contribute to manage the sports products will be vital to guarantee their commercial success. This article proposes a model based on MFCMs for supporting the management of products in professional sports – an intelligent decision-making system –, conceptually based on the “par conditio” principle. The model considers different aspects related to the “par conditio” principle, such as the socioeconomic environment where the sports activity is carried out, the legal bases of the professional competence, and other sporting aspects (stadium, fans, etc.), which are organized in layers, to analyze the behavior of the different components of the commercial portfolio. It is tested for the two most common sports in Latin America, football and baseball, considering countries of this region where these sports have good economic performance, both to analyze and understand the current situation of the sports products, and infer more appropriate configurations. Several specific case studies are carried out with encouraging results. The paper successfully shows the potentialities of MFCM for diverse purposes, particularly those named above.
Keywords

Introduction
The managers of professional sports clubs have the possibility of doing this through the proper management of their sports product portfolio. The sports product portfolio describes the different options available to professional clubs to generate income and make their operation a profitable business. They require a sports product management system to properly configure each component of the commercial portfolio: Brand licensing, sponsorship, television and media rights, sporting and training rights, and hospitality. The sports product management system must maximize the attractiveness of each sports product.
On the other hand, in the context of professional sports, there are big differences between the professional leagues and federated tournaments in European and North American countries, and those in Latin American countries. In Europe and North America, there are favorable effects in media coverage, television rights, recruitment of sponsors and strategic partners, brand exploitation, ticket and hospitality service sales, among other aspects. In Latin America the opposite happens, e.g., there are great losses of money, and commercial opportunities [1]. These differences are due to difficulties in decision-making, and the application of the “par conditio” Principle, among other reasons. Specifically, there is a need to develop an appropriate management system for commercial products of professional sports in Latin America that can respond to existing opportunities, and adapt to social, cultural, technological, demographic and natural characteristics of the region.
However, at present there are no previous studies about management systems for commercial sports products in professional sports clubs of Latin America, to support the conceptualization, design and implementation of such a management system. The few studies available consider the management of sports clubs rather than the management of commercial products. Zurita et al. [2] proposes a management model for professional soccer teams of Ecuador based on five principles, namely: Strategic planning, procedures manual, human talent management, marketing administration and financial administration. Similarly, there are other informal works about financial and administrative strategies for professional soccer clubs in Colombia.
As can be seen, the previous works of the Latin American case consider the general management of sports clubs, but not their commercial products. This article seeks to mix the use of the “par conditio” principle with the management of sports products for the Latin American case. The principle of “par conditio” looks for the competitive equilibrium, the equality of conditions among the participants of a league to guarantee the uncertainty in the result. In this way, the attractiveness of the sport for fans is maintained as a guarantee of commercial success [3].
Particularly, this article proposes a system for the intelligent management of commercial sports products in professional sports, based on the “par conditio” principle and multi-layer Fuzzy Cognitive Maps (FCMs). FCM allows us to elaborate a careful analysis of the “par conditio” principle in professional sport. With this case, we will show some outstanding characteristics of FCM. In our model, the theoretical description of the system considers the socioeconomic characteristics of the environment where the sport activity is carried out, the legal framework of the sports competition, as well as other features of professional sports (stadium, brand, etc.). With these characteristics, the FCM on the one hand is able to analyze the current situation of the different forms of commercial products in a given context, and on the other hand, to predict what will happen to each of the commercial sports products in another possible situation or scenario.
FCMs represent knowledge from a qualitative perspective, allowing to create models of complex systems where an exact mathematical model cannot be used [4, 5]. FCMs have been applied in different domains to represent systems based on a set of concepts that describe them (states, variables, or characteristics of the system) and the causal relationships among them, which can be static or dynamic, fuzzy or not fuzzy [6, 7, 8, 9, 10, 11, 12]. Specifically, in this paper, a Multilevel FCM (MFCM) is used, which is an extension of FCM, with a higher and more flexible capability to represent complex situations [13].
In general, the main contributions of this paper are: i) the definition of a Management system for sports products using MFCMs; ii) the definition of a marketing strategy for the sports product based on the “par Conditio” principle; iii) the specification of a Smart Decision Support System based on MFCMs for the marketing of professional leagues “sports product” in Latin America.
The article is structured as follows. Section 2 offers the literature review. To complete the conceptual support of the paper, Section 3 gives a theoretical basis for the model to be developed. Additionally, this section reviews the main characteristics of MFCMs, while describing their advantages and potential for modeling, simulation, and analysis of scenarios. Then, Section 4 presents the design of the sports product management system and its layers based on the MFCM. Afterward, the experimentation phase is described in Section 5. Following, Section 6 analyzes the results and compares them with other models and previous research. Finally, Section 7 offers some conclusions.
Literature review
Previous studies have presented models regarding sports and competitive equilibrium, the basis of the “par conditio” principle, such as the work of Bahram et al. [14]. Here, the authors analyze the relationship between competitive equilibrium and attendance of sports spectators in the professional league of the first division of Iranian football. They use Pearson correlation to establish the characteristics of this league, concluding that there is no significant relationship between competitive equilibrium and attendance at stadiums. Therefore, they propose a system that seeks to help in making decisions about what products to offer their fans to maintain their attachment to the activity. On the other hand, Levin and McDonald [15] analyze competitive equilibrium as a predictor of attendance at sporting events, in the US and Canada. This research evaluates the relationship of five variables: Competitive imbalance, market potential, average market income, unemployment in the market, and equipment exchange rate to average attendance. Unlike a previous study, they show the link between competitive equilibrium and attendance of fans at sporting events. The model serves as a guide for decisions related to pricing and sponsorship. These authors use the model for describing the decision-making processes to manage the stock of players in a professional club. Johnston et al. [16] present a review of the literature studying the efficacy of the draft for professional North American sports leagues. They carry out a systematic review of four databases using the PRISMA methodology. This review highlights several aspects of the draft process and concludes in the need for more research about the draft process. Liam et al. [17] propose a draft-pick allocation such that the draft-pick order rule shall give the top pick to the team eliminated first, and the remainder in order of elimination. In their experiments, their policy produced an estimated 21.7% improvement in an already-eliminated team’s probability of winning late-season matches.
With regards to sports product management, several works propose the comparison of results achieved by professionally managed clubs, with respect to those without professionalized management, considering both, economic and financial aspects, as well as the types of sports, to establish whether professionalization in management leads to better performance. The main conclusions is that clubs with professional management have achieved a balance in terms of economic and financial assets, compared to clubs without professional management. For example, Rani [18] presents different aspects of professions integrated into the sports world, and their relationship with sports management. Management procedures used in sports are extremely varied, ranging from those focused on a specific segment of business operations, such as marketing and financial management, to holistic management models, where diverse aspects of sports management are integrally applied. This paper considers the most important aspects of sports management, with a focus on the opportunities for professional development in this field. Mackreth and Bond [19] present a theoretical contribution to sports management, specifically barriers to strategic marketing practices within professional sports organizations. Mills [20] outlines the centrality of market structures in sports management. He proposes to frame this discipline in the context of policy and market power, for a more legitimized and inclusive area of social science that does not sacrifice its managerial roots.
On the other hand, sports marketers must monitor their marketing strategies to ensure that they communicate honest images and messages about their products, which must be consistent with the core values of their organizations. Fullerton and Russell [21] present a conceptual paper addressing what is meant by the term “sports marketing”, by developing a framework based on two dimensions: Type of product and level of sports integration. They categorize goods and services as either sports products or non-sports products, and differentiate between traditional strategies and sponsorship-based strategies, in four sports marketing domains. The categories are represented by theme-based, product-based, alignment-based, and sports-based strategic domains. Many examples for each strategic domain are provided as a means of illustrating their conceptual differences and forms of implementation. Shabani, Gharehkhani and Naderi [22] investigate the role of the sports marketing mix (strategic combination of product, price, place and promotion elements) in generating revenue for football clubs. The results show that each element of the sports marketing mix, apart from price, has a positive and significant impact on generating revenue for football clubs. They conclude by recommending club managers to strive to choose an appropriate marketing mix. Ratten [23] proposes a marketing planning process that reflects the overall plans for the organization. The purpose of Mihai [24] is to introduce the sports marketing area, linking academic research, marketing practitioners, and public policy planners. They analyze the role of marketing intelligence and planning for the sports sector. This paper also discusses the main sports marketing issues and suggests directions for future research. The purpose of Pharr and Lough [25] is focused on cause-related sports marketing (CRM). For this study, the qualitative content of each website is analyzed in relation to the outreach programs of the NBA, NFL, NHL, and MLB. The offered content analysis allows the categorization of the outreach programs in one of the following categorical positions: CRM, social marketing, and other community outreach. Forty-three programs were evaluated, of which twenty-two (51.2%) were categorized as social marketing, eight (18.6%) as CRM, and 13 (30.2%) were considered as other community outreach. Significantly, more social marketing programs, than CRM, were identified. The findings demonstrate that major leagues have embraced the use of social marketing strategies to show its corporate social responsibility. Chard, Mallen and Bradish [26] carry out a content analysis of the marketing-ES literature, to develop a sports marketing-ES research agenda. They review 49 journals published from 1999 to 2019. Key findings include 63 marketing-ES manuscripts, characterizing their conceptual approaches, themes and sub-themes, which were used to construct 30 questions to develop a sports marketing-ES research agenda. Finally, Oshiro et al. [27] describe an experiential learning for sports management courses to enhance students’ understanding of building a personal brand. This is for a course focused on sports marketing and consists of three components: 1) Individual brand video, 2) Personal Brand Audit, 3) Project Critical Assessment.
In [28], Demir and Söderman proposed a framework for strategic sponsorship of sports. The multilevel framework uses the sponsorship theory and provides practitioner clues for rethinking their sponsorship programs. They consider the concept of regime as the key principle for strategic sponsorship activities. Then, they define six different regimes: Cause regime, loyalty regime, appropriability regime, value-differential regime, heuristics-based regime, and associational regime. Each one of these regime types is further related to the classic sponsorship activities. Liao, Chen and Hsu [29] propose the utilization of the Apriori algorithm of association rules, and clustering analysis, which has an ontology-based data mining approach for mining customer knowledge. Knowledge extracted is used to propose strategies regarding product promotions and sports marketing and solutions to Taiwan Adidas. This approach facilitates marketing segmentation, helps to know the sports market (customer profile, client segment), and builds the pattern of marketing activities. Schilhaneck [30] proposes a conceptual framework that comprises both strategic and operative brand management options for professional sports clubs. They identify the club branding options and use these findings to design a special brand management model for the professional sports club setting, which provides information about how to build and maintain strong club brands. Eagleman [31] examines the role that social media plays within National Governing Bodies (NGBs) in the United States, including employees’ acceptance of social media, motivations to use social media, and the organization’s current usage of social media. The results reveal that, contrary to studies on other sports organizations, NGB employees report high levels of acceptance and motivation to use social media regardless of demographic factors. Additionally, NGBs use social media as a communication tool to a greater degree than as a marketing tool. They conclude that it must be used as an alternative method to mainstream media and traditional marketing, in order to increase brand awareness, and reach fans and stakeholders. Witkemper, Lim and Waldburger [32] examines what motivates and constraints the utilization of Twitter in sports. The proposed model consists of items to measure the motivation (information, entertainment, pass time, and fanship), and items to measure the constraints (accessibility, economic, skills, social). Motivation for the utilization of Twitter among the respondents were positive, whereas constraints were negative. These results and their implications for sports marketing are also discussed. Chmait and Westerbeek [33] present an overview of machine learning for enhancing sports (performance and business) analytics. They summarize relevant research literature on the areas in which artificial intelligence and machine learning have been applied to the sports industry and in sports research. The paper of Faganel et at. [34] discusses the impact of technology in the sport management field, from the perspective of key stakeholders in journalism, education, tourism, sport economy, leisure, performance analysis, talent identification, and high-performance sports.
We have indicated that research work related to Latin American sports management considers the management of sports clubs, but not their commercial products (see Section 1). In addition, the previous review of related research regarding sports and competitive equilibrium based on the “par conditio” paradigm, sports marketing, and utilization of social media in the sports world is not associated with the issue of sports product management. Research related to the management of sports products is linked to economic and financial issues, and activity planning. However, this research does not take into account the different dimensions (socio-economic context, sporting environment, etc.) of the management of sports products. This article aims at integrating the use of the paradigm “par conditio” with conceptual elements of the management of commercial sports products, in order to develop a holistic model of sports management in Latin America. In addition to this integration, a smart decision-making system based on MFCMs is proposed, which allows the marketing management process of the sports product to be carried out.
Theoretical aspects
“Par conditio” principle and sports commercial products
In several contexts, the “par conditio” principle or competitive equilibrium can apply to professional sports. The competitive equilibrium is defined as the balance that must be maintained in all sports competitions, in order to keep the uncertainty in the results of sporting events as much as possible [3]. So, the “par condition” alludes to the condition of equality or pairing between two or more things, which in the case of sports refers to two or more competitors.
The “par conditio” principle seeks to ensure a general balance in the competition, generating equal conditions among the participants of a league, maintaining the attractiveness of the sports product in the eyes of the fans. To do this, the “par conditio” principle guides the equitable distribution of sports talent, to maintain the balance of strength between clubs, and carefully considers the distribution of income of the clubs of the league, looking for equality of conditions in all aspects, trying to guarantee competitive parity, to maintain the attractiveness of the competition. In this way, this principle has an impact on the next concepts related to professional sport:
Operating rules: They establish the conditions by which the sports competition will be governed: Calendars, schedules, minimum conditions of participation, general regulations of competition, promotions and discounts, concessions of franchises, among other conditions. It is not only a kind of contract between the league and the clubs, but it also defines the structure and functioning of the competition.
Salary caps: These are constraints that establish the minimum and the maximum amount that a club can pay to its players. The salary cap policy provides for the existence of a luxury tax that must be paid by clubs that exceed the established salary caps, in order to promote a balance among all the players in the league.
On the other hand, the sports commercial products are:
Sport and training rights: Professional sport has the athlete as one of its main players. It can generate economic benefits for those clubs that form the athlete or own their sports rights. In some sports such as football, when an athlete is formed by a club A and this has the opportunity to transfer it to another club B, club A has the right to receive economic compensation from club B for each year of training, if the new condition assumed by the athlete after being formed by A is that of “Professional”. Similarly, when the athlete becomes a professional, s/he owns sports rights that may be his/her property, or belong to the club that acquired the athlete. The transfer conditions describe the policies and rules that clubs must respect when selling or interchanging their athletes to other clubs.
Television and media rights: They represent one of the most important options in terms of economic income that a sports show has. It consists of the cession or transfer of commercial exploitation rights of the sporting event to third parties, who, using the media, especially television, radio and social media, make their operations profitable, marketing them to other interested parties, usually audiences interested in the sport as a means of entertainment. In sports spectacle, television and media rights are usually the main income generator for their owners.
Brand licensing: This represents the exploitation of a brand through products, services and promotions. These three components must be managed from a commercial, marketing and communication perspective. In general, trademark licensing refers to the possibility of using or assigning the rights of commercial exploitation of a trademark.
Marketing and sponsorship: Marketing usually has a duality of policies that occurs between participants in leagues or tournaments in professional sports. The first establishes that the league as an organizing entity assumes the responsibility of managing marketing in a centralized manner, with benefits for all parties involved. The second gives authority to each participating club to apply its own marketing policies, so it is decentralized. Sponsorship refers to a communication strategy that pursues commercial and/or institutional objectives, exploiting the direct association between, on one side, an organization, a brand or a product; and on the other side, another organization, event or personality, which implies a commercial transaction between the different participating subjects [43]. For the sponsored party, the sponsorship functions as revenue generating a commercial mechanism. For the sponsor, it is an effective way to gain notoriety and positioning, in addition to increasing sales revenue.
Hospitality: In the case of professional sports, stadiums are used to provide a series of services and products aimed at captive audiences attending shows, audiences that wish to receive something more than sports. Services, such as restaurants, hotels, shops, shows and museums are the most employed options. To do this, ticket revenues at each game, as well as parking, among other commercial elements, are added. These commercial elements are commercially used by the organizer of the show. In this regard, a hospitality zone must be designed to accommodate all aspects directly involved with the activity.
Conceptualization of an MFCM
A cognitive map is a modeling method to describe a domain using concepts (variables, states, inputs, outputs) and the relationships between them, based on knowledge and experience in the domain [4, 5]. A cognitive map is defined like a directed graph, where the arcs are causal connections between nodes (representing concepts). An arc with a positive sign between node A and node B, means that A (causally) increases B; alternatively, if the arc has a negative sign, then A decrements B. The FCMs are an extension of the cognitive maps [4, 5], such that the definition and dynamic of the concepts and relationships are based on the theory of fuzzy sets. Thus, the concepts and relations can be represented as fuzzy variables (expressed in linguistic terms), like, “Almost Always”, “Always”, “Normally”, “Some”, to describe the concepts and their relationships.
In general, the actual value of a concept depends on its values on previous iterations, according to the following Eq. (1):
Here,
An extension of the FCM is the Multilayer Fuzzy Cognitive Map (or MFCM), which is an FCM with several layers, where each layer represents a set of concepts that describe a specific subsystem component of a system. In an MFCM, the Eq. (1) is modified, to describe the relationships between different layers [13]:
Where
The multilayer approach enriches the modeled system with a flow of information between layers, in order to favor the holistic study of a process. With this extension, it is possible to have several FCMs for the same problem, where each one expresses a different level of knowledge of the system under study, or a subsystem. In this extension, the variables in one level can depend on those in other levels.
In this paper, we use the FCM Designer Tool [7], in order to define an MFCM representing the sports product management system. The FCM Designer Tool allows defining FCMs with concepts and relationships that can change during the execution time. This tool has been extended to allow the creation of MFCMs. In the multilayer approach, the relationships between the cognitive maps in different layers are defined by weights, but they could be described in other ways [13]: by using fuzzy rules, or mathematical equations. The FCMs and MFCMs have been used in diverse areas of research [4, 5, 8, 9, 10, 11, 12, 35, 36].
In order to compare MFCMs with other modelling tools and examine its novelty, we should briefly assess what they are and their potential usage. MFCMs allow us to model any kind of well-conceptualized system, defining a situation, which can be represented as a network of interlinked concepts. Each possible configuration of the network, from which a stable state can be determined/calculated, represents a scenario of the situation, offering a set of final values of: i) the concepts, and 2) the relationships between them. Each simulated scenario can be used as follows:
To analyze the final state and evolution of the network, in order to comprehend better the system and situation it represents (either hypothetical or real), and then explain it better, allowing the observers (researchers or stakeholders of the real situation) to learn from the experience; To infer certain concepts or a whole layer of the scenario; To predict certain elements (concepts and relationships) of hypothetical future scenarios (these elements are inferred);
Beyond exploring a single scenario, we can perform a scenario analysis, exploring a set of scenarios defined in accordance with a certain interest. Finally, by developing a scenario analysis, we could perform different kinds of evaluations related to either the whole situation the MFCM represents or a subspace of it. For instance, checking for the consistency of the conceptual formulation of the whole situation represented by the MFCM, or for a set of propositions (e.g., “beliefs”) related to a subspace of the conceptualization of the problem [37, 38]. This can be applied for the verification of a theory (like in this paper, the “Par conditio”), or the proving of a certain set of affirmations constituting a theorem, among others, regarding the modelled situation or part of it [10].
Because of all this, an MFCM is useful to evaluate an appropriately conceptualized situation in various ways, via a qualitative or quantitative model. The conceptualization can pertain to any ambit, e.g., related to Physical Theory or Control System [9], or an ideal one such as the Utopia of Tomas Moro, which has been previously modeled [36, 39]. Therefore, we basically need an appropriate conceptual formulation to develop an MFCM model. Several examples show this versatility [11, 12]. The models can be used for diverse purposes, including theoretical ones, or for applications, such as policy analysis.
For generating the simulation or calculation of a scenario, the initial values of the network can be determined from diverse sources, including consult to experts, historical data, and data mining. Similarly, the results can be validated by using a variety of forms (again, expert domain knowledge, historical data, and data mining). Consequently, our approach has a high versatility in this respect, for data feeding and model validation [8, 13].
Then it can be used in parallel and as an alternative for diverse modelling and simulation purposes where multiple approaches are used, for instance, Systems Dynamics (SD), Cellular Automata (CA), Agent-based Simulation (ABS), and Event Driven Simulation. Consequently, MFCMs can be used either as the main approach, or as a complementary method to create parallel models to existing ones, with numerous purposes, including model replication and model docking [40].
Summarizing, MFCM is highly flexible in relation to the sources of data either for initialization or for validation, and can be used with very diverse purposes, ranging from very specific ones (e.g., taking a very specific decision associated with a single scenario) to very general ones (related to, e.g., inference, prediction, model replication, model docking, verification of theories, theorem proving of facts or tendencies).
Accordingly, MFCMs capabilities clearly surpass those of decision-making tools, such as Analytic Network Analysis (ANP) [41] and Influence Diagrams (ID [39]. ANP and ID are strongly limited devices. These tools offer a very constrained modelling mark and are useful only to take single and specific decisions, in well-structured and defined situations, where a contextual analysis is not needed. Compared with MFCMs, those tools have a limited range of applications, and can be used neither in all the range of situations in which MFCMs can be employed, nor for the diverse purposes for which MFCM is useful. In particular, the analysis developed in this paper can be performed in an MFCM but not in ANPs in IDs, since it requires a careful analysis of a situation.
On the other hand, MFCMs combine qualitative and quantitative elements during the modelling process, facilitating the use of qualitative data (e.g., experts domain narratives, historical narratives, or narratives taken from the internet) for building the model, and for validating it, an advantage beyond the reach of most simulation approaches and tools [12]. Difficulties to combine qualitative and qualitative data in a simulation are well known, and efforts to find appropriate methods to combine these two kinds of data are currently made by diverse communities of researchers. One of the difficulties is how to go from narratives (qualitative facts) to simulation models (usually quantitative) [37, 38]. MFCMs offers a potential alternative to simulation languages, since it closely rests on conceptualizations, and the determination of the concepts and the relations can naturally come from narratives [12]. Also, for the scenarios generated in the simulation, both qualitative and quantitative interpretations can be made. All this indicates that MFCMs have a wide and promising arena of applications in the near future.
The “par conditio” principle seeks to generate equality conditions between clubs that participate or integrate a professional sports league, so that the competition is balanced, strengthening, as a consequence, the attractiveness of sports for the fans. This attractiveness arises due to uncertainty in the sporting result: The greater the uncertainty, the more attractive the show will be. On the other hand, the FCM alike any decision-making system for product management in professional sports, includes all elements of the commercial portfolio of a professional sports league, in order to contribute to the integral business management, and consequently, to the success of the sports activity. By producing a greater amount of income due to a correct business management, more resources will be available to distribute equitably among the participating clubs, as stated in the parity principle. Each result generated by the FCM responds to a specific context, indicating which components of the commercial portfolio should be emphasized to increase the income, and thus, in accordance with the previous principle, effectively distributes the resources to their members, contributing to maintain the attractiveness of the competition. Our FCM becomes a management guide that establishes the direction of the commercial strategy of a league, so that the “par condition” principle can be fulfilled.
In order to accomplish that, the concepts are distributed in four levels in our MFCM (see Fig. 1), based on the “par conditio” principle. The first three levels describe each of the aspects/dimensions to be considered for the management of the commercial sports products in professional sports, while the last one permits the analysis of each commercial sports product. Each level of the MFCM comprises the concepts corresponding to one dimension, as follows (see Fig. 1): layer 1 contains the concepts related to the competition bases of a professional league. The involved concepts are norms, salary caps and transfers. These concepts exert causality on layer 2, which is identified as the source of sports products, and is constituted by the following concepts: Brand, promotion of talent, the stadium and the show or game. The bases of the competition regulate or determine the sources of sports products, because they establish parameters, norms and policies for each one. Layer 3, entitled commercial sports products, contains the concepts: Hospitality, licensing, sponsorship, television and media rights, and sports and training rights. These concepts are generated from the sources of sports product; i.e., they are determined by layer 2. Finally, layer 4, called environment, is comprised of the concepts: Fans, business executives, and economic, demographic, political, social and legal environment. These concepts have a direct influence on all concepts of the rest of the layers.
General view of our MFCM.
Layer 3 contains the concepts to be inferred, which determine the behavior of commercial sports products in professional sport, based on the “par conditio” principle. They depend on the values of the variables of the other layers, such as the environment, bases of competition and sources of commercial sports products. Each of these concepts is described below. In this model, only direct and positive relationships of causality are defined (see Fig. 2). Finally, it is assumed that the values of the concepts are between 0 and 1, and can be located in three zones: a concept has a high value (between 2/3 and 1) when it (what it represents) is clearly present in the modelled case, and has a good state in the current scenario; it has an average value (between 1/3 and 2/3) when it is only sometimes (with a medium probability) present in the system; and, finally, it has a low state (between 0 and 1/3) when it is almost not present in the system.
The concepts corresponding to the competition bases of a professional league, founded on the “par conditio” principle belong to this level. These concepts define regulations, rules, and agreements among clubs, describing the sports activity. The concepts are defined as follows:
Salary caps: They establish a minimum and a maximum amount of money that a club can pay to its players.
Transfers: They describe the policies and rules by which clubs can transfer their athletes to other clubs, under favorable conditions for those involved, including the athlete himself.
Rules: They establish the conditions by which the sports competition will be governed, highlighting general regulations of competition, concessions of franchises, among other aspects.
Our FCM. The arrows indicate the influence among the concepts.
The high values of these concepts mean that the rules, the conditions that govern the different aspects of the sports activity, etc., are clearly defined. If any of such concepts has low values, it means that there are deficiencies in the ambit they represent. For example, in the case of salary caps, a low value would mean that there is little, or no agreement, among the clubs, and the professional league has not been able to establish applicable regulations.
The concepts that describe the sources for the generation of commercial sports products, which determine them, belong to this level. These concepts are:
Brand: In professional sport, clubs and their leagues make their names, brands of high economic value, with recognition in the local, national and international context.
Promotion of talent: Professional sports clubs invest large amounts of money in the training of their sports talents. Academies are dedicated to the formation, at an early age, of their own athletes, under the premise that each club must form its stars, and stock up on these when they reach maturity, in order to incorporate them into a high competition.
Stadium: Every spectacle of professional sport requires a physical infrastructure to execute its fundamental activity. The stadiums fulfill this role.
Game(Show): It is the configuration of all the elements associated with the sports product, which make it a rewarding experience for fans, as well as turning it into an event that exceeds the proposal of a simple game between rivals playing a sport, but rather pursuing the championship as an end.
The high values of these concepts mean that the sources of the sports activity are working very well. Conversely, the low values of these concepts indicate problems with the specific source. For example, a high value for the concept “Stadium” means that it has good conditions in all its aspects (ground, stands, spaces for services, such as restaurants, bathrooms, etc.).
At this level are the concepts linked to the different commercial sports products. Particularly, our model considers the following sports products [42]:
Hospitality: Availability of services, such as restaurants, hotels, shops and museums. Also, this concept includes various income sources, such as ticket sales, preferential boxes, and parking.
Sponsorship: Sponsorship exploits the commercial relationship between an organization, brand or product, with another organization, event or personality.
Brand licensing: It refers to the possibility of using or assigning the rights of commercial exploitation of a brand, which guarantees a reasonable share in the performance of the business for those involved in it.
TV and media rights: They consist of the cession or transfer of commercial exploitation rights of the sporting event to third parties, which, using different media (e.g., television, radio and social media), monetize their operations, marketing them to other interested parties.
Sports and training rights: A club that has formed a player, and has the opportunity to transfer him/her to another club, has the right to receive economic compensation for each year of training, if the athlete achieves a new position: The condition of “Professional”. Similarly, when the athlete becomes a professional, he/she owns sports rights that are his/her property, or may belong to the club that acquires him/her.
A high value of these concepts means that the commercial sports products are a good condition. For example, a high value of Hospitality means that different services like restaurants or shops, among others, are available.
The concepts related to the context (social, cultural, economic, etc.), and additionally those associated with the sporting activity (fans, etc.) belong to this level. The involved concepts are:
Fans: They represent those persons towards whom the sports product is aimed. In general, they are the people who attend the show and consume all its benefits.
Business executives: Business executives use the show or sports product to integrate them into their products or services, as a promotion mechanism towards their own users.
Economic: This refers to the general state of the economy in the country where the professional league is held, measured mainly in terms of the behavior of its Gross Domestic Product.
Demographic: It describes the most relevant characteristics of the population where the league is held, in demographic terms (number of inhabitants, genders, ages, social classes, etc.).
Political: It is determined by the conditions of governance of the country where the professional league is held, measured in terms of respect for freedom, autonomy of public powers, citizen participation, etc.
Social: It denotes the degree of participation or adoption of the sport in the population; that is, the number of people who practice or follow the sport promoted by the league.
Legal: This mentions the degree of legal stability prevailing in the country where the league is held.
Cultural: It describes the level of rooting of the sporting discipline in the society where the league is held.
Alike the previous cases, a high value of these concepts means that the context has a good condition.
According to Aguilar [9], there are three ways to establish the causal relationships among concepts, based on: 1) opinion of experts (each expert provides his MFCM matrix according to his experience, then these matrixes are combined to form a new MFCM); 2) historical data, and 3) data mining. In this work option 1 is used, given that expert opinions were taken to shape the relationships between concepts.
To assign the weights in the relationships between concepts, values will be taken in the interval
For the determination of the concepts, a group of 42 Latin American experts was consulted, in both disciplines: Baseball and football. The chosen experts include coaches, athletes, journalists, sports leaders, among others. In Annex 1, these relationships are explained, as well as the final values of the arcs, based on the opinion of the consulted experts regarding the influence among concepts. Finally, the execution algorithm of the MFCM is as follows:
Define the initial values or states for each concept, according to the case study to be evaluated. Run the model in FCM Designer. As long as the system does not converge into a stable state (the convergence is reached when the values of the concepts do not change anymore and the system stabilizes), adjustments must be made in the values assigned to the concepts for the next iteration using Eq. (2).
This section is comprised of two sections. Firstly, a general analysis of the kinds of inferences that can be made through the proposed generic model is performed. Secondly, several case studies are offered, each one having some scenarios. The information about each of the professional sports leagues of the case studies has been recovered in the following way:
Official information available on the websites of the leagues, as well as their regulations and statutes. For example, Specialized newspaper articles, focused on the marketing area of the leagues under study, published between 2015 and 2019. Some examples of the newspaper articles consulted are:
“La ceguera del Futbol argentino”: “Qué mueve la industria del deporte en América Latina?”: “No todo es futbol en sports marketing, por qué apostar por otros deportes?”:
Understanding the state of the commercial sports products in a given context
The evolution of the concepts when the MFCM is trained indicates their influences on the state of the sports products. Thus, the dynamics of the concepts determine the behavior of commercial sports products. In general, the MFCM iterates until it reaches a state of equilibrium, which is a state of the system where each concept converges to a given value. The variation of a concept while the MFCM is trained, i.e., until this converges, can be analyzed as a time series that describes the behavior of the concept over time, in the context of a given situation. By analyzing the pattern of behavior of this time series, and the causal relationship of the considered concept with the other concepts, it is possible to determine the impact of the concept on the states of the sports products. In this way, by following the trail of the MFCM inference (how the concepts change over time), one can understand how the state of a commercial sports product changes, and identify the key elements that influence its state, which can be used to guide the sports product management actions. In this case, our model is helpful to characterize the behavior of the evolution process of a commercial sports product.
Initial values of the concepts for scenario 1
Initial values of the concepts for scenario 1
Final values of the concepts of layer 3 for scenario 1
The different concepts making up our model allow us to infer the state of the sports products, considering the different dimensions wholly: competition bases, product sources and environment. The suitability/quality of the sports products is determined by the final values of the concepts of the third layer. High values of the concepts hospitality, licensing, sponsorship, television and media rights, and sports and training rights, will be interpreted as a good quality of the sports products (their states are appropriate), and vice versa. In this case, our model has a predictive behavior, given that the states of the sports products are deduced from the current situation of the set of concepts in each dimension (their initial values describe that current situation). This set of concepts, describing the specific situation to analyze, is the only knowledge used to deduce the state of the sports products.
Case studies
Scenario 1: Professional football league
Feature: product sources in deficient conditions.
This scenario represents professional football competitions where the sources of sports products are not fully developed. Specifically, clubs do not have control of the stadiums, football academies do not work properly, nor training and sports rights of the competing players are promoted. The sports show is very basic, that is, it is limited to the football game itself, and the clubs do not have brands. This is not a typical situation in Argentina or Mexico, but it is the case of the Venezuelan Football league.
What would happen to the involved sports products in a scenario with these characteristics, under the presumption that the general context/environment is favorable?
The initial values assigned to each concept (in the MFCM model) for this first scenario are shown in Table 1.
Layer 1: competition bases. In this layer, the salary cap receives a low value, transfers a high value, and rules a mean value. This is based on a professional football tournament that does not work under the standards of a league, but is governed by international transfer regulations that are favorable to its interest. Layer 2: product sources. In this layer, concepts receive low values. This refers to a scarce development of the product sources, which are the strategic basis for the conception and management of commercial sports products. Layer 3: sports products. All concepts in this layer start at zero, since they are the ones to be inferred. Layer 4: environment. All concepts receive high values, denoting favorable conditions for the development of business. This means that society has a high degree of well-being, and the sport is well-rooted.
Initial values of the concepts for scenario 2
FCM inference process for scenario 1.
The iterative process of this FCM is shown in Fig. 3.
Figure 3 shows the high variability of the values of the concepts in the initial iterations: in the first iteration, all of them increase, but then, in the second iteration, most of them decrease, until stabilizing in the following iteration. The final values of the concepts inferred for layer three are shown in Table 2.
The resulting values in scenario 1 show a clear predominance of the concept of sports and training rights, as the central axis of the management of the commercial sports products in this professional discipline. This is due to the influence of a clear and favorable regulation of the transfer of players from one club to another, which is regulated by a supra sporting entity, such as the International Federation of Associated Football. Similarly, the favorable conditions of the business environment, as well as social and economic situations, coupled with the high social roots of the discipline, offer an opportunity to generate a satisfactory management of the commercial sports products.
Feature: unfavorable context for a well-structured league
This scenario considers a league of professional baseball, where regulations are well developed, there are favorable policies regarding salary caps, transfers among players are well established, and product sources are well developed. However, regarding the variables of context, the reality of the country where this league operates is not favorable, because of a bad socio-economic situation. The economic activity has strongly decreased in the last five years, while advertisers and sponsors have stopped investing in sports. Consequently, fans have stopped attending stadiums. In politics, un-governability is permanent, society lives in conflict, and there is no legal security. Culturally, the sports discipline has deep roots in the country’s population. This is the current situation of the Venezuelan baseball league.
What would happen to the sports products in a scenario with these characteristics?
The initial values assigned to each concept are shown in Table 3.
Layer 1: competition bases. In this layer, all concepts receive high values, which denotes full development of the regulations, as well as the establishment of salary caps and bases of competition that promote uncertainty in the result, strengthening the commercial and sports appeal. Layer 2: product sources. The concepts in this layer receive high values. This corresponds to a high development of the product sources, which are the strategic basis for the conception and management of commercial sports products. Layer 3: sports products. All concepts in this layer start at zero, given that they are the ones to be inferred. Layer 4: environment. All concepts of this layer receive low values, with the exception of the cultural concept, due to the high level of the rootedness of the discipline in this scenario. The low values for these concepts denote unfavorable conditions for the development of business, in a society with a low degree of well-being.
The final values of the concepts in layer three are shown in Table 4.
Final values of the concepts in layer 3 for scenario 2
Configurations of layer 4 for which optimal conditions for scenario 2 are reached
The resulting values for scenario 2 describe the projection of an unfavorable behavior in the results of the management of the commercial sports products in the sports league. With these values, it is deduced that the sports products will have problems in their development, due to the negative environmental conditions for business, which show that, despite maintaining organizational strengths, and having a deeply rooted sport, the commercial success of a sport is closely linked to a favorable context.
For this scenario, we have added an exhaustive evaluation to determine for which values of the concepts of this layer, an optimal condition for the sports products is reached (i.e., the values of the concepts of layer 3 are high: above 0.6). The exhaustive evaluation consists of incrementing (varying) by 0.1 the values of the concepts of Layer 4, until the desired condition is reached. Table 5 shows some of the configurations of the values of the concepts in layer 4 for which this condition is reached.
Relevance of the concepts of the model: Concepts in red have a stronger impact on the commercial success of the sport, than those in black
According to Table 5, “Fans” and “Demographic” concepts have low influence to achieve optimal conditions for the sports products of the Venezuelan Baseball League. The synchronized improvement of several other concepts allows reaching the optimal conditions of the sports products. For example, high values of “Business executives”, “Political” and “Legal” concepts that denote a secure situation for the investments; or high values of the “Economic”, “Political”, “Social” and “Legal” concepts that denote a nation with an ideal social, political and economic situation. In general, high values of the “Social” and “Legal” concepts are critical to obtain good ideal conditions for the sports products.
This section examines the results of the experiments, and in light of this, the advantages and potential of MFCMs.
Discussion
The application of the MFCM model in the previous scenarios allows verifying the existing correlation between the sports products (layer 3) and the context or environment (layer 4), evidencing that, the better the conditions of the environment (expressed by high values in the concepts representing it), the greater the potential, and probability of an attractive and successful commercial portfolio. Also, our model describes the natural correlation between the competition bases (layer 1) and the sports products (layer 2) in its definition, in order to use the “par conditio” principle for the management of professional football and baseball leagues. This is not the case between the sources of the product (layer 2) and the product forms (layer 3). The scenarios show that in some cases where the product sources (layer 2) have not been fully developed, favorable results can be obtained in the commercial management of the sports product portfolio (layer 3), when the context is in a good state. This shows the higher relevance of the context (layer 4) than that of the sources of the product (layer 2), for a good state of the sports product portfolio, as it could be expected.
With respect to the convergence of our MFCM model into a stable state implemented in the experiments above, the behavior of the model consisted of assigning specific values to the different concepts in each of the layers, except to the concepts of layer 3, and then analyze the resulting values of the concepts in this layer, once the model converges. The model converges (it reaches a stable state) when the concepts stop changing over time, that is, through the iterations. The concepts of layers 1, 2 and 4 were defined according to the case study, in order to describe a possible configuration of it (this specific configuration represents an instantiation of the model (scenario)), to analyze the inference capabilities on the concepts that represent the sports product portfolio (these were initialized to 0). In general, each instantiation of the model was run 30 times, and the behavior of the model was evaluated, achieving the required stability after a number of given iterations (in each case study, the stability/convergence is reached in different numbers of iterations). The model stabilized for all explored scenarios, then the inferred values were analyzed (above).
In the field of commercial product management in professional sports, the proposed model allows us not only to discriminate among the most important and the least important layers to promote the professional sport, as seen above, but also to signalize the concepts to which more attention should be given, due to its potential influence on commercial results. Table 6 indicates, for each of the layers of the model, the potential influence of the concepts. This influence is determined experimentally, modifying the concepts and verifying their impact on the final results. The most relevant concepts are shown in red. A modification of the values of these concepts generates important fluctuations in the concepts of the inferred layer (layer 3). In layer 1, salary caps have a decisive impact on the commercial success of a league, due to its contribution to the competitive equilibrium among participating clubs. In layer 2, the brand is decisive, because of its ability to expand the business options of a professional league. In layer 4, the economic, social and cultural concepts are decisive in the success of any league, because they provide business opportunities, connected with necessary aspects, such as the cultural adoption of the sports discipline, and the degree of emotional connection that can be generated, which affects the size of the market and the attractiveness of the league as a commercial product. In general, concepts of layer 4 have a high effect on the concepts of the rest of the layers. In particular, at the end of section 5.2.2, via a systematic exploration of the values of some concepts, we have proved that: “High values of the Social and Legal concepts are critical to obtain good ideal conditions for the sports products”. This shows the capabilities of our approach for theorem proving and deduction of strong propositions.
Qualitative comparison of a diversity of research works (in rows) by using several criteria (in columns)
Qualitative comparison of a diversity of research works (in rows) by using several criteria (in columns)
In this section, we carry out a comparison of different works based on the next set of properties: i) they propose approaches for Latin American sports management; ii) they analyze the relationship between sports and the competitive equilibrium; iii) they propose schemes for sports marketing; iv) they propose approaches for the management of sports, from the economic, planning and financial point of view; and, v) they propose approaches for the management of sports products. Table 7 presents the qualitative comparison.
Examples of initialization of the concepts of our model using text mining on the dataset
Examples of initialization of the concepts of our model using text mining on the dataset
Table 7 shows that the majority of the previous works are very specific, analyzing a single aspect: the competitive equilibrium in the sports discipline, or how to manage a sports organization, etc. There are no previous approaches for the management of sports products, based on the “par conditio” concept, for Latin American sports disciplines. Particularly, our approach has been defined according to the opinion of experts in the baseball and football leagues of Latin America. Our work is the only one proposing a model for inferring knowledge, based on a representation of the process of influence of different aspects in the sports products. Additionally, our model can determine the quality of a sports product. There are no previous works proposing systems that can be used in these two ways, in order to analyze a sports product in a specific situation. Additionally, our theoretical model considers the Latin-American expert opinion in order to define the MFCM holistically, considering the behavior of the modeled sports league and its context.
Table 7 shows that the majority of the previous works are very specific, analyzing a single aspect: The competitive equilibrium in the sports discipline, or how to manage a sports organization, etc. There are no previous approaches for the management of sports products, based on the “par conditio” concept, for Latin American sports disciplines. Particularly, our approach has been defined according to the opinion of experts in the baseball and football leagues of Latin America. Our work is the only one proposing a model for inferring knowledge, based on a representation of the process of influence of different aspects in the sports products. Additionally, our model can determine the quality of a sports product. There are no previous works proposing systems that can be used in these two ways, in order to analyze a sports product in a specific situation. Additionally, our theoretical model considers the Latin-American expert opinion in order to define the MFCM holistically, considering the behavior of the modeled sports league and its context.
As far as we know, there is no other model in the literature for inferring knowledge based on the process of influence of the “par conditio” paradigm in the sports product. Even more, we have not found a similar model to describe the state of a sports product, or publicly available datasets to test our model. Thus, we are unable to compare the outcomes of our model with previous works.
Classes based on the values of the concepts in layer 3
Classes based on the values of the concepts in layer 3
In any case, we will test the prediction capability of our model with respect to the state of the sports products. For that, we generate a dataset containing around 1,200,000 sport articles of the main newspapers of four Latin-American Countries, choosing the dominating sport in each country. Sports articles about baseball were taken from two countries, Dominican Republic and Venezuela, and sports articles about football were chosen from the two other countries, Mexico and Argentina. All articles were published between January 1
We are going to evaluate the capability of prediction of our model with a k-fold-cross-validation process, using classical performance metrics: F-measure (it is the combination of the precision and recall metrics) and accuracy (it describes the closeness of a measurement to the true value).
In our case, the values of the concepts of layer 3 inferred by our MFCM are the predicted values and the values of the concepts determined by the analysis of the articles contents (by using the frequency of the words, in each one) are the correct results. Accuracy is the ratio of number of correct predictions to the total number of inputs, where there is a correct prediction when the differences of the inferred and correct values for all concepts is
Now, we can use F-measure to determine the quality of the classification inferred by our model. In our case, a True Positive result occurs when our model predicts this correctly, indicating that it pertains to a certain class when in fact it is part of it. A True Negative result happens when our model does not predict it as correct, and it is incorrect. A False Positive result occurs when our model wrongly predicts it as correct. Finally, a False Negative result occurs when our model does not predict it as correct and it is correct. F-measure Score is the Harmonic Mean between precision and recall:
Where Precision is the number of True Positive cases divided by the total of positive results predicted by our model (True Positive
Results
These results show that our approach can predict very well the behavior of the sports products in different contexts, with accuracy and F-measure values over or equal to 0.9. Table 10 shows that the best prediction occurs for the case “Football (Mexico)”. The reason for this seems to be that for the Mexican Football case we were able to generate the best (accurate) initialization of concepts, due to the high number of sports articles available (and effectively used) to define this context. As it can be noted our approach is helpful not only to predict the behavior of the sports products, but also to analyze their context (e.g., environmental conditions, “par condition” paradigm fulfillment), facilitated by the holistic consideration of the commercial sports products.
The case study has illustrated the main points about MFCM set in Section 3.2.2. Let us examine some of them, based on the previous analysis (Sections 5 and 6.1 to 6.3):
The model was fed both by domain expert knowledge and from text mining. From the case study, it is also obvious that we could have used historical data. This shows the high flexibility of the MFCMs in this respect. The model permitted us to verify the correlation among various layers, each resting on a particular conceptual formulation, and to conclude about how changes on particular concepts or layers can impact on other concepts or layers (Section 6.1). Exploration of scenarios can determine that concepts or layers have a stronger impact on the MFCM; i.e., to which concepts or layers the MFCM is more sensitive (Section 6.1). An exhaustive exploration of values of concepts allowed us to prove the following fact: “high values of the Social and Legal concepts are critical to obtain good ideal conditions for the sports products” (reported at the end of Section 6.1). MFCM is useful for analyzing diverse aspects of a situation, beyond traditional tools that examine a single aspect, as Table 8 shows in the case of sport management (Section 6.2). MFCM can be used to infer knowledge and predict issues related to the modelled situation. Even more, it has proved to be more precise than some text mining tools (TF-normalized) to infer and predict knowledge, by using two metrics: F-measure and accuracy (Section 6.3).
The exploration of scenarios required for characteristics iii) and iv) were made via a systematic exploration of scenarios, based on a sequence of values given to the relevant set of concepts, and then the results were observed to verify what the fact or tendency held. In a more advanced experiment, emergent tendencies could be discovered by the system running of the MFCM, by checking the facts occurring in the explored scenarios. Such tendencies would be valid in the subspace of the theory systematically explored (for more details about this, see, e.g., [38]). In this sense, MFCMs can be used as an alternative or as the main tool to perform similar duties to those of diverse simulation approaches and languages, for instance, Multi-Agent Based Simulation, Events Driven Simulation, among others, or even more, as a theorem prover and a theorem searcher.
This paper has reviewed MFCMs and their applications in order to show their novelty and potential related to the analysis of situations and decision making, as well as proposed an MFCM model for the sports product management of Latin American professional sports leagues, based on the “par condition” principle, where several levels or layers representing aspects of the modelled situation were identified. In each layer, relevant variables or concepts were identified. The model was successfully used as a case to show the characteristics and potentiality of MFCMs for future applications.
Our model has a holistic view of the situation of a professional sports league, which allows us to analyze not only the sports product and commercial issues, but also the context where the professional sports league develops. As far as we know, there are no models of this type or with such a holistic view and analytical capabilities in the literature, for representing a professional sports league. The model was raised having in mind two goals: First, to systematize the aspects to be considered when characterizing the management of the commercial sports products in order to understand the overall behavior of the involved system; and, second, to help in the decision-making processes occurring in the modelled system.
Layer 4 (representing the cultural, social, political, and economic environment) is made up of independent variables, layers 1 (characterizing the “par conditio” principle) and 2 (representing the product sources) comprise independent and dependent variables, and layer 3 (describing the sports products) is comprised of dependent variables. Although the developed model does not generate specific decision alternatives for managers of commercial products in professional sports, it allows them to clarify the context, the relative importance among layers and variables, and so to guide decisions, helping in discriminating among aspects that influence behavior (quality) of the commercial products, and even to infer what will happen in case of taking certain decisions. In relation to this inference capability the model, through the configuration of cause-effect relationships, creates a practical framework to deduce possible behaviors from a given scenario, enabling scenario analysis to inform managers and stakeholders, facilitating better decisions in favor of the sports leagues.
In general, the implementation of MFCMs based on layers to model the state of sports products in professional leagues, permits not only a holistic view, but also a detailed analysis of the situation of the professional sports league. For example, to infer the quality of a sports product in a particular context, and to identify the most influential aspects (concepts) for improving the professional sports league. It has been shown that the specific developed model can be used as a tool to support decision-making in the management of sports products, for the professional football and baseball leagues in Latin America. In the tests, several real cases were analyzed in the Latin American context, showing us what may happen in the immediate future. The model raises the need for the leagues to promote competitive equilibrium, as a means to improve the commercial appeal of the competition. If this purpose is achieved, the attractiveness of the sports products from a commercial perspective is strengthened, allowing greater benefits, which in turn favorably impacts the promotion of the best products in the long term by allowing better product sources.
The previous general conclusions about the evolution of the state of the sports products, derived from the generic MFCM proposed in this work, demonstrate the capacity of the MFCM for analyzing professional sports league products and their context, and for guiding strategic sports marketing decision making. Our model allows determining the relevant aspects to consider in a sports product, identifying its current state and the causes that have generated it, more holistically analyzing this kind of process than previous studies, by considering the “par condition” paradigm, the environment and the product sources. The comparison of our model with previous research works in the area has demonstrated that our model is the only one that permits analyzing the sports products to determine their quality. The capabilities of our model to predict the state of a sports product in specific Latin-American sports contexts, for football and baseball, with high values of F-measure and accuracy, has been demonstrated.
The inferential and predictive capacities of MFCM turn it into a valuable method for future decision-making applications in complex contexts, becoming an alternative to various other approaches, including simulation methods. Even more, it can be applied in a large diversity of areas where current modeling approaches have difficulties; for example, to combine qualitative and quantitative data, or as a theorem prover of hypothetical or of emergent tendencies (For example, it was proved in the paper that: “high values of the Social and Legal concepts are critical to obtain good ideal conditions for the sports products”). Additionally, the high flexibility of our method to be fed by a variety of data sources, such as data mining (e.g., text mining), expert domain, and historical data, has been shown.
Future work will continue testing the tool in other contexts, aiming at facilitating the modeling process, for instance, to automate the process of instantiation of concepts. The ideal case would be to be able to automatically instantiate the concepts of the MFCM without passing through the human subjectivity to define the values. For example, regarding the case of the present paper, text mining in social networks could be carried out to determine the competitive equilibrium in a league, by checking whether a concept is in a certain range. In this way, every mining can be helpful to analyze the information from different sources, in order to instantiate the MFCM for the sports league under study. Based on the same idea, similar models will be developed for analyzing i) the actual and future possibilities for economic development in Latin-American countries, and ii) the quality of democracy, in diverse socio-political contexts, and in particular, how “fake news” impacts it.
Footnotes
Annex 1. Causal relations between concepts
Concept of origin
Destination concept
Causal relationship
Value
Salary caps (Layer 1)
Game (Layer 2)
The salary cap seeks to maintain balance in the hiring of athletes, Giving all the clubs in the league a similar possibility to access Players of the same level, and thus keeping a good level of Uncertainty in the results (similar chance for any team). This Favors The appeal of the show.
0.11
Salary cap (Layer 1)
Promotion of talent (Layer 2)
The salary cap, as a regulatory principle, motivates clubs to work On generating their own talents, whom they can contract at a Relatively lower cost than the value of contracting other Professionals in the market.
0.10
Salary cap (Layer 1)
Brand (Layer 2)
The possibility that clubs can hire players of a similar sporting Level, in addition to guaranteeing the uncertainty in the results, Contributes to the competitiveness of clubs, so that they are able to Attract and maintain a significant number of fans, becoming a Well-positioned brand.
0.05
Transfers (Layer 1)
Game (Layer 2)
The transfers of players among clubs promote the competitive Equilibrium among them, increasing the uncertainty in the result, Making the show more attractive.
0.25
Transfers (Layer 1)
Promotion of talent (Layer 2)
The possibility of transferring players from one club to another, and Receiving a financial return for it, motivates that clubs in a League focus on developing their own sports talents, with a view to employ them in their clubs or transfer them to other teams, Getting a monetary benefit or other players whose abilities Increase the competitiveness of the team.
0.50
Transfers (Layer 1)
Brand (Layer 2)
The facilitation of players transfers increases the attractiveness of Clubs for the public, and makes them stronger brands, while Allowing them to be recognized by outstanding athletes, with high Sports performance.
0.30
Rules (Layer 1)
Game (Layer 2)
The rules regulate the show in all its aspects, always trying to Make it more attractive.
0.07
Rules (Layer 1)
Stadium (Layer 2)
The rules establish the minimum conditions that a stadium must Meet to be used as a venue by a club that will compete in the League.
0.30
Rules (Layer 1)
Promotion of talent (Layer 2)
The rules generally demand the clubs of the leagues to have their Own process of generation of sports talent.
0.40
Rules (Layer 1)
Brand (Layer 2)
The rules establish minimum operating conditions, impacting the Club, and outlining it as a brand.
0.20
Game (Layer 2)
Sports and training rights (Layer 3)
The game is the ultimate showcase for clubs to expose their sports Talents, allowing them to promote them and place them in other Clubs, via transfer.
0.05
Game (Layer 2)
TV and media rights (Layer 3)
The quality of the show determines the interest and value of its Broadcasting rights, through the different means of Communication.
0.01
Game (Layer 2)
Sponsorship (Layer 3)
An attractive game arises more interest in potential sponsors and/or Advertisers.
0.01
Game (Layer 2)
Licensing (Layer 3)
When the show is attractive, fans become followers of this, so that Opportunities are generated for the commercialization of derivative Services, under the modality of licensing.
0.01
Game (Layer 2)
Hospitality (Layer 3)
Attractive shows attract a greater number of fans, who will require Specific services (hospitality) at the stadium.
0.99
Stadium (Layer 2)
TV and media rights (Layer 3)
Adequate facilities, in perfect condition, with the spaces available for the media, will allow the use of this form of sports product.
0.49
Stadium (Layer 2)
Sponsorship (Layer 3)
The stadiums must provide adequate spaces, which can be used as Advertising options for the exhibition of the brands of sponsors and/or advertisers.
0.39
Stadium (Layer 2)
Licensing (Layer 3)
The stadiums limit or facilitate the commercialization of different Types of licenses, depending on the availability of usable spaces.
0.48
Stadium (Layer 2)
Hospitality (Layer 3)
The hospitality services are conditioned to the availability of Adequate facilities.
0.01
Concept of origin
Destination concept
Causal relationship
Value
Promotion of talent (Layer 2)
Sports and training rights (layer 3)
Clubs that have their own sports talent factories have the Possibility to place them in the athletes’ market, Commercially exploiting their training and sports rights.
0.70
Promotion of talent (Layer 2)
TV and media rights (Layer 3)
Television and media rights become more commercially Attractive when clubs have high-level sports talent.
0.50
Promotion of talent (Layer 2)
Sponsorship (Layer 3)
Having high-level sports talent makes sponsorship and Advertising products more attractive.
0.60
Promotion of talent (Layer 2)
Licensing (Layer 3)
Having high-level sports talent makes offers of licensing of various kinds more attractive.
0.50
Brand (Layer 2)
TV and media rights (Layer 3)
Clubs or leagues of greater renown and commercial Reputation will be more likely to negotiate favorably Their TV and media rights.
0.01
Brand (Layer 2)
Sponsorship (Layer 3)
Clubs or leagues of greater renown and commercial Reputation, will be more likely to negotiate favorably Their sponsorship and advertising products.
0.01
Brand (Layer 2)
Licensing (Layer 3)
Clubs or leagues of greater renown and commercial Reputation will be more likely to favorably negotiate Their Licenses.
0.01
Fans (Layer 4)
Salary cap (Layer 1)
The fans, by demanding greater quality in the sports Spectacle, encourage leagues and clubs to establish Salary Caps, so that everyone can hire athletes of sa imilar level, Seeking to maintain uncertainty in the result.
0.10
Fans (Layer 4)
Transfers (Layer 1)
The fans, by demanding greater quality in the sports Spectacle, encourage leagues and clubs to establish Transfer rules, in order that they can negotiate athletes of a similar level, from one club to another.
0.50
Fans (Layer 4)
Rules (Layer 1)
Leagues and clubs establish bases of competition that Guarantee the good sports spectacle, seeking to satisfy the needs of recreation of fans. The larger the number of Fans, then the stronger the pressure over leagues and Clubs to establish and follow appropriate rules.
0.20
Fans (Layer 4)
Game (Layer 2)
The fan requires leagues and clubs to organize quality Shows, suppliers of high levels of satisfaction.
0.20
Fans (Layer 4)
Stadium (Layer 2)
The fan requires leagues and clubs to organize shows in Appropriate, comfortable, safe, and well located Stadiums.
0.25
Fans (Layer 4)
Brand (Layer 2)
Clubs and leagues must focus their product management on developing a brand that captivates and please their Fans so as to capture and maintain their loyalty.
0.30
Fans (Layer 4)
TV and media rights (Layer 3)
The more active and devoted the fans are, the more loyal They are to their brands, then the more necessary and Attractive the TV and media rights will be.
0.01
Fans (Layer 4)
Sponsorship (Layer 3)
The more active and devoted the fans are, and the more Loyal they are to their brands, then the more attractive the Sponsorship and advertising products will be.
0.01
Fans (Layer 4)
Licensing (Layer 3)
The more active and devoted the fans are, and the more Loyal they are to their brands, then the more attractive and necessary the licensing products will be.
0.01
Fans (Layer 4)
Hospitality (Layer 3)
The existence of fans makes hospitality services Necessary.
0.01
Business executives (Layer 4)
Salary cap (Layer 1)
The need to attract business executives motivates leagues and clubs to apply salary caps to promote a more Balanced and attractive show.
0.30
Business executives (Layer 4)
Transfers (Layer 1)
The need to attract business executives motivates leagues and clubs to apply the rules of athlete transfers, Promoting a more balanced and attractive show.
0.20
Business executives (Layer 4)
Game (Layer 2)
The need to attract business executives motivates leagues and clubs to organize and promote a high level sporting Event.
0.03
Concept of origin
Destination concept
Causal relationship
Value
Business executives (Layer 4)
Brand (Layer 2)
The need to attract business executives motivates leagues and clubs to properly position themselves, and increase the number of followers.
0.05
Business executives (Layer 4)
Sponsorship (Layer 3)
The requirements of business executives, in terms of Marketing, promotion and advertising, influence the Configuration of the sponsorship and advertising products of the league or club.
0.01
Business executives (Layer 4)
Hospitality (Layer 3)
The demands of business executives, in terms of Marketing and customer service, influence the Configuration of the hospitality services of the league or Club.
0.01
Economic (Layer 4)
Salary cap (Layer 1)
The economic situation in the country or region where the league is held determines the extent to which salary Caps are applied, seeking to maintain the competitive Equilibrium.
0.15
Economic (Layer 4)
Transfers (Layer 1)
The economic situation in the country or region where the league is held influences how and the extent to which the transfer rules are applied, in order to maintain the Competitive equilibrium.
0.13
Economic (Layer 4)
Game (Layer 2)
The diverse aspects of the economic sphere of the league or club directly related to the show, including prices of Tickets, are influenced by the prevailing economic Situation.
0.15
Economic (Layer 4)
Stadium (Layer 2)
The economic situation in the country or region where the league and its clubs are managed, influences the Maintenance or adaptation of the stadiums chosen for the Competition.
0.10
Economic (Layer 4)
TV and media rights (Layer 3)
The economic situation in the country or region where the league is held, directly influences the negotiations of This type of rights, as well as their monetary values.
0.10
Economic (Layer 4)
Sponsorship (Layer 3)
The economic situation in the country or region where the league is held, influences the commercialization of Sponsorship and advertising products.
0.01
Economic (Layer 4)
Licensing (Layer 3)
The economic situation in the country or region where the league and its clubs are managed influences the Commercialization of licensing products.
0.01
Demographic (Layer 4)
Game (Layer 2)
A higher level of population makes the game (show) Much more marketable, i.e., increases its profitability.
0.05
Demographic (Layer 4)
Stadium (Layer 2)
The larger the population, the higher the demand for Large stadiums and good services.
0.25
Demographic (Layer 4)
Brand (Layer 2)
A high level of population makes the brand more Marketable.
0.05
Demographic (Layer 4)
TV and media rights (Layer 3)
The larger the population, the more marketable the TV and media rights will be.
0.01
Political (Layer 4)
Rules (Layer 1)
The level of governability influences the configuration of the rules governing the operation of sports leagues.
0.30
Political (Layer 4)
Stadium (Layer 2)
The level of governance influences the access to adequate Facilities for the realization of the sports spectacle.
0.10
Political (Layer 4)
TV and media rights (Layer 3)
The level of governance influences the Commercialization of TV and media rights.
0.01
Social (Layer 4)
Rules (Layer 1)
The social situation influences the regulations of leagues and tournaments.
0.20
Social (Layer 4)
Game (Layer 2)
The social situation influences the organization and Development of the game.
0.05
Social (Layer 4)
Brand (Layer 2)
The values of the society, associated with the sports Discipline, influence the principles that the brand Projects.
0.15
Social (Layer 4)
Sports and training rights (layer 3)
The values of the society, associated with the sports Discipline, will directly influence the commercialization of sports and training rights.
0.05
Concept of origin
Destination concept
Causal relationship
Value
Social (Layer 4)
Hospitality (Layer 3)
The conception of service that a society has, influences the hospitality strategy in the leagues and their clubs.
0.01
Legal (Layer 4)
Salary cap (Layer 1)
The current legal norms impact on the establishment of Salary cap regulations.
0.45
Legal (Layer 4)
Transfers (Layer 1)
The current legal norms influence the establishment of Regulations for athlete transfers.
0.17
Legal (Layer 4)
Rules (Layer 1)
The current legal norms affect the establishment of competition rules for leagues and tournaments.
0.30
Legal (Layer 4)
Brand (Layer 2)
The current legal norms condition the commercial exploitation of the Club or league, from its brand perspective.
0.05
Legal (Layer 4)
Sports and training rights (layer 3)
The current legal norms influence the establishment of rules for sports and training rights.
0.05
Legal (Layer 4)
TV and media rights (Layer 3)
The current legal norms constrain and give a mark for the definition of TV and media rights in a league or club.
0.01
Legal (Layer 4)
Sponsorship (Layer 3)
The current legal norms influence the establishment of sponsorship and publicity agreements.
0.01
Legal (Layer 4)
Licensing (Layer 3)
The current legal norms impact the establishment of brand licensing Agreements.
0.01
Cultural (Layer 4)
Game (Layer 2)
The degree or level of rooting of the sports discipline influence the Market of users and consumers of the game (show).
0.09
Cultural (Layer 4)
TV and media rights (Layer 3)
The degree or level of rooting of the sports discipline has an effect on the commercial appeal of TV and media rights.
0.01
Cultural (Layer 4)
Hospitality (Layer 3)
The degree or level of rooting of the sports discipline influences the Need and the magnitude of the hospitality services provided to the fan.
0.01