Journal of Machine Intelligence and Data Science (JMIDS)

1. Introduction

Over the years, the economic impact of sporting events has become increasingly significant [1]. One of the most popular sports in Italy is football, with a national GDP impact estimated at around 11.1 billion [2].

As in all industries, planning is a fundamental activity in football: indeed, for instance, reliable stadium attendance estimates are crucial for clubs.

The reasons behind seeking an accurate prediction of this parameter are manifold: firstly, having a reasonably precise estimate of how many tickets will be sold means having a reliable estimate of the overall match revenue. Moreover, if a particular match is predicted to have low attendance, different promotional activities can be considered in order to boost it, if that is an objective.

Furthermore, there are also purely organizational reasons; clubs can plan various pre-match activities based on the estimated attendance, and they can also calculate the precise number of staff and security personnel needed for the game.

Some contributions concerning stadium attendance prediction can be found dating back to the 1970s [3, 4]. In recent years, with the advent of Machine Learning (ML), it has become possible to utilize these methodologies to achieve more accurate predictions.

Furthermore, as in all industries, having a strong knowledge of the customers is of utmost importance in predicting their behaviour. Therefore, to enhance our understanding of the customers and their preferences regarding attending matches at the stadium, we have developed a survey to be administered to fans. It includes a section of choice-based conjoint analysis, which enables us to gain a precise insight into the customer, allowing to indirectly extract their preferences regarding specific match attributes.

So, the paper’s objective is to predict stadium attendance for an Italian club competing in the top-tier football league. To achieve this, we have developed a framework consisting of two distinct phases. In the first phase, we conducted a survey among fans, which includes a conjoint analysis component, that will allow us to calculate a utility value that we will use in the predictive phase of our work.

Subsequently, we will construct various ML models using R, and starting from these, we will obtain the stadium attendance forecast.

The paper is structured as follows: in Section 2, we will provide a literature review related to football match attendance prediction. Then, in Section 3, we will delve deeper into the methodology. In Section 4, we will present the case study, while in Section 5 we will present a real case application of our proposed framework to a match of the 2023/24 season. Finally, section 6 will contain the conclusions and future work.

2. Related Work

As we have already seen in the previous section, there are several reasons why accurately predicting stadium attendance is of paramount importance in the actual football context.

The objective of our study is to create a ML model capable of predicting stadium attendance with great precision. In this specific example, achieving this goal will provide the opportunity for an Italian team, competing in the top national series, Serie A, and participating in European competitions, to plan certain activities in advance, as discussed in the previous section. Additionally, it helps in understanding how to increase profits, aided by the information derived from the conjoint analysis included in the survey conducted with fans.

In the literature, there are various examples of models designed to comprehend the impact of specific variables on stadium occupancy or simply to forecast stadium attendance based on certain factors. The innovative aspect of our work lies in the integration of conjoint analysis and ML models, enabling us to incorporate into these some insights gained directly from the fans in the survey.

In the literature, there are just a few examples of the application of conjoint analysis techniques in the football sector. For instance, the most relevant one for our study, is the work of Woratschek et al. [5], where conjoint analysis was employed to determine spectators’ willingness regarding price increases or reductions, considering competitions with different sporting significance and in different seating categories settings. In their work, the authors examined the impacts of three variables: match category (i.e., competition), ticket price, and seating category. From their analysis, it appears that the interviewees considered match category as the most important factor, followed by price, and finally, seating category. As just mentioned above this is one of the few studies that apply conjoint analysis in the domain of ticket in football events.

Regarding the prediction of match attendance, the literature provides various contributions. One such contribution is represented by the work of Fotache et al. [6], who used two R ecosystems, tidyverse and tidymodel, to develop a framework able to forecast the ticket sales of a club in the top Romanian league. They incorporated variables such as match weather conditions, kick-off time, day of the week on which the match occurred, phase of the season, opposing team, and the recent performances of the teams facing each other. They attempted to utilize both the Random Forest and Extreme Gradient Boosting (XGB) algorithms and achieved an R-squared of approximately 81%, with both algorithms.

Another noteworthy study is that of Sahin and Erol [7], who compared various ML models, including artificial neural networks (ANN), adaptive neurofuzzy inference system (ANFIS), and fuzzy rule based systems, to determine which of these methods would yield the most precise predictions in predicting match attendance. Their input variables included the match day, the distance in miles between the home and away team’s stadia, match uncertainty, and the recent performance of the teams involved in the match. They employed a dataset consisting of 236 matches of three top European clubs and used metrics such as Mean Absolute Percentage Error (MAPE) and Mean Absolute Deviation (MAD) for comparison. They found that, although all models performed well, the best was the ANN.

Another relevant study is that of Strnad et al. [8], in which the primary objective was to assess the impact of various variables, such as the home team, the away team, the rivalry between these teams, and the result uncertainty, on attendance. They evaluated the predictive quality of four different neural networks, using MAPE and mean absolute error (MAE) as metrics. Ultimately, it was revealed that neural networks are reliable in predicting stadium occupancy.

One more intriguing work is that of King and Rice [9], in which they compared the predictive performances of various machine learning models, specifically random forest, M5 prime, and extreme gradient boosting, with the accuracy obtained from traditional models like linear regression, using data from the 2014 and 2015 seasons of Major League Soccer, the top American national soccer league. In this case, the evaluation metric used was Mean Squared Error (MSE).

From their analysis, it emerged that extreme gradient boosting was the most accurate methodology.

In this section, we have thus demonstrated several examples of employing ML techniques for predicting attendance at football matches in stadiums.

3. Methodology

The methodology we intend to present consists of two distinct steps. Initially, the idea is to administer a survey to customers, which includes a conjoint analysis dedicated section, aiming to deepen our understanding of the customer. Conjoint analysis is a decompositional method introduced in the 1970s, that allows to assess trade-offs among various product characteristics [10, 11, 12]. To use this technique, it is necessary to define in advance the attributes that need to be evaluated and the levels of these attributes, which refer to the values these attributes can assume.

It is the task of the analyst to include the product characteristics they consider most relevant, also called attributes, and to include all possible levels of these characteristics. Once this is done, the so-called “cards” are created, which are particular combination of the attributes’ levels. Then, these profiles must be evaluated by the respondent and then statistically analysed to determine the customer preferred levels for the various characteristics.

The advantage of this technique is that being an indirect method for eliciting preferences, the results are not influenced by socially desirable responses. Moreover, it is important to emphasize that there are various types of conjoint analysis. In traditional conjoint analysis, respondents are asked to evaluate different profiles by assigning a rating to each profile or by ranking the various profiles. In 1983, Louviere and Woodworth [13] combined conjoint analysis and choice evaluation, creating choice-based conjoint analysis, where the respondent no longer needs to rate or rank each profile but is asked to choose between sets of profiles. This approach has two main advantages, as presented in the work of Raghavarao et Al. [14]: firstly, the choice is conceptually similar to making a purchase, and secondly, the respondent must consider the other alternatives in the choice set when making a selection, thus having a more comprehensive view of the alternatives at the time of choice.

Through traditional conjoint analysis techniques, such as the logit model, it is possible to estimate utility values for each level of each characteristic evaluated by the customer.

The second phase consists in modelling the data with ML algorithms in order to obtain a classification model capable of predicting, starting in particular from match and match day characteristics, if a stadium seat will be sold or not.

What is essential to emphasize, in our framework, is that the utility values of the levels of the various product characteristics obtained through conjoint analysis are condensed into a single indicator.

Our idea is to include this indicator among the predictive variables of the ML model we intend to develop, serving as the link between the two phases.

This choice is motivated by the idea that by implementing this variable into the ML model, we can include customer preferences in the ML model, considering not only historical data but also customer preferences, resulting in a model that can more accurately predict population behaviour.

4. Case study

As already mentioned, we have tested the approach we proposed in section 3 on a real case study developed in collaboration with an important football team competing in the Italian top division.

So, in the subsequent paragraphs we will present the settings of the case study and we will explain deeper how we implemented each phase of the proposed framework.

4. 1. Aim and data collection

In this case study, we collaborated with an Italian Serie A football team with the aim of creating predictive models for stadium attendance.ted by the data cleaning phase, which is followed by the clustering phase.

As previously mentioned, the work was structured following the methodology presented in Section 3. Firstly, we created a survey to be administered to the fans, which included a conjoint analysis section. Subsequently, we analysed the results and, based on these findings, we created a variable that was later incorporated into the ML models.

It’s important to highlight that we partnered with this team as they provided us with historical data concerning the team stadium attendance over the 2018-19, 2021-22, and 2022-23 seasons. Such choice has been derived by the fact that, due to COVID-19 pandemic, season 2020-2021 was not regularly disputed, especially in terms of fans’ attendance. The selected seasons represented the three last season for which the stadium ran at full capacity for all the season matches.

Furthermore, in the models, we also included variables, which will be presented in the following sections, obtained through web scraping, such as weather data related to the match or the performance of the home and away teams.

4.2 Conjoint analysis

In this initial phase, we created two surveys, very similar to each other, and, in particular, identical in the conjoint analysis section, to be administered to two distinct groups of fans.

The first group to whom we administered the survey consists of loyal fans, those who hold the team membership card, and have presumably attended the stadium at least once in their lifetime, and, most importantly, are devoted fans of the team. Regarding this group, for which we had email contact, we sent an email with an access code for the survey.

Regarding the second group, we decided to conduct the survey among those who follow the team on social media. In collaboration with the football club’s social media team, we created posts and stories dedicated to the survey. In this case, there was no need for a code to respond to the survey.

To streamline this section, we will not present the whole survey; instead, we will focus only on the conjoint analysis part, which is the aspect of primary interest in this work.

Regarding the attributes of the conjoint analysis, we have included six: stadium sector, opposing team category, game day, time slot, football season period, and weather.

We must clarify something that regards the stadium sectors: indeed, in this study, we aimed to predict fan attendance for home games played in a stadium, which is composed of 14 sectors. Clearly, we could not include an attribute with 14 levels in the conjoint analysis. Furthermore, it would not have made much sense as if we had included all the sectors in the same analysis; people would likely have chosen the best sector consistently, as we don’t consider the price in the attributes of our analysis. Therefore, we aggregated the sectors into six macro-sectors (comprising similar sectors) and, in a section prior to the conjoint analysis in the survey, we posed a question asking: “Considering the average price of the indicated macro-sector, please indicate in which macro-sector you have attended, or you could attend a league match.” This allowed us to create six different conjoint analysis, one for each macro-sector, with the same attributes mentioned earlier, but with different levels of the attribute stadium sector: indeed, for example macro-sector A included sector 1, sector 2 and sector 3, while macro-sector B included sector 4, sector 5 and sector 6, and so on.

In Table 1, we present the various levels that the six attributes listed earlier can assume, with the values of the stadium sectors reported here generally as sector 1, sector 2 and sector 3.