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This study aims to examine the impact of the gameful experience on behavioural outcomes. Drawing from stimulus–organism–response theory, it proposes and tests a new model that investigates the relationship between the gameful experience, brand loyalty and intention to use gamified branded applications in the sports context. In addition, it explores the mediating role of customer–brand engagement (CBE) and the moderating role of self-image congruity (SIC).

A sample of 436 active users of sport-related branded gamified applications was used to test the model. Data was collected from online sports forums, brands’ Facebook communities and during sporting events.

Results indicate that the gameful experience positively and directly impacts behavioural intentions but does not directly influence brand loyalty. This relationship becomes partially significant when mediated by CBE. In addition, results show that users with high levels of SIC are more likely to continue using the gamified application, whereas users with low levels are more likely to engage with the brand.

This study expands the gamification literature in the sports sector by revealing the importance of the gameful experience in driving loyalty, behavioural intentions and CBE. It proposes a new model that sheds light on the emotional aspect of the interaction between a user and a gamified system and the importance of exploring the effects of moderators, such as SIC, in these relationships.

During rush hours, many passengers find it difficult to board the first train due to the insufficient capacity of metro vehicles, namely, left behind phenomenon. In this paper, a data-driven approach is presented to estimate left-behind patterns using automatic fare collection (AFC) data and train timetable data.

First, a data preprocessing method is introduced to obtain the waiting time of passengers at the target station. Second, a hierarchical Bayesian (HB) model is proposed to describe the left behind phenomenon, in which the waiting time is expressed as a Gaussian mixture model. Then a sampling algorithm based on Markov Chain Monte Carlo (MCMC) is developed to estimate the parameters in the model. Third, a case of Beijing metro system is taken as an application of the proposed method.

The comparison result shows that the proposed method performs better in estimating left behind patterns than the existing Maximum Likelihood Estimation. Finally, three main reasons for left behind phenomenon are summarized to make relevant strategies for metro managers.

First, an HB model is constructed to describe the left behind phenomenon in a target station and in the target direction on the basis of AFC data and train timetable data. Second, a MCMC-based sampling method Metropolis–Hasting algorithm is proposed to estimate the model parameters and obtain the quantitative results of left behind patterns. Third, a case of Beijing metro is presented as an application to test the applicability and accuracy of the proposed method.