## 1 Introduction  
Referees are expected to make over a hundred decisions during a football match [1]. During these decisions, however, match officials can be influenced by many factors, such as the team's ability, the crowd noise, and social pressure [2, 3, 4, 5]. This can result in significant mistakes that can affect the match results. For this reason, different technological official aids, such as goal-line technology [6], referee microphone systems, and additional assistant referees [7], have been introduced to increase the accuracy of referee decisions and avoid major mistakes. Although these technological aids have their benefits, they have not been without controversy [8]. Nevertheless, the implementation of these technological aids has improved the accuracy of referees' decisions and thus the fairness of sports competitions. In this context, the Video Assistant Referee (VAR) represents the most substantial and transformative innovation in football officiating in recent decades. Introduced with the objective of minimizing human error in critical match situations, VAR was officially approved by the International Football Association Board (IFAB) for use in the laws of the game during the 2018/19 season. Since then, it has been widely adopted in top-tier competitions such as the FIFA World Cup, UEFA Champions League, and numerous national leagues [9]. VAR is designed to assist the on-field referee in correcting \"clear and obvious errors\" or serious missed incidents in four key situations: goals, penalty decisions, direct red card incidents, and cases of mistaken identity. Its core purpose is to increase decision-making accuracy while maintaining the flow and integrity of the game. The implementation of VAR has stimulated a substantial body of academic research seeking to evaluate its influence across various dimensions of football. Previous studies have focused on its statistical impact, reporting significant changes in key performance indicators such as the number of goals, offsides, penalties awarded, yellow and red cards, fools, and overall match duration [10; 11; 12; 13; 14; 15]. After the introduction of VAR, both the Italian and German top divisions reported a reduction in the number of offsides, fools, and yellow cards. Additionally, there was an increase in the number of minutes added to the end of the first half and the full match duration, though this was not observed in the second half alone [10]. In Spain, the implementation of VAR led to a significant decline in offsides [11]. A similar trend was observed in the World Cup, where the number of offsides notably dropped following the adoption of VAR. Furthermore, the duration of the first half, second half, and total match time significantly increased [12]. In Brazil's top men's football league, the use of VAR also resulted in fewer fools and disciplinary cards [13]. Specifically, VAR has been linked to a reduction in the frequency of certain infractions, such as simulation and offside infringements, due to increased detection and accountability [10; 13; 16; 17]. In addition, some evidence suggests that VAR contributes to improved decision-making consistency and a decrease in referee bias [18; 19]. Beyond performance metrics, scholars have explored the psychological and behavioral implications of VAR for players, referees, and fans. The presence of video review may alter players' tactical approaches and reduce unsporting behavior, given the increased risk of retrospective sanctions [20; 21]. Moreover, VAR has been found to affect perceptions of fairness and legitimacy in match officiating. On the one hand, it reinforces trust in the objectivity of decisions by offering referees technological support in critical moments. On the other hand, it has generated new forms of controversy and resistance.