Learning about Corner Kicks in Soccer by Analysis of Event Times Using a Frailty Model

2026-02-26

AI Summary

This study addresses the intra-team dependence among corner kick event times within the same football team—a dependency structure commonly overlooked by existing models. To account for this correlation, the paper introduces a frailty model into the analysis of corner kick timing, formulated within a right-censored event time framework. Parameter estimation is carried out via a Monte Carlo Expectation–Maximization (MCEM) algorithm. Empirical analysis based on data from the 2019 Chinese Super League demonstrates that the proposed model significantly outperforms the benchmark approach of Peng et al. (2024), offering more accurate insights into the temporal patterns of corner kick occurrences. This work thereby extends the application of mixed-effects event time models to sports analytics, particularly in modeling correlated event times in team-based settings.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Corner kicks are an important event in soccer because they are often the result of strong attacking play and can be of keen interest to sports fans and bettors. Peng, Hu, and Swartz (2024, Computational Statistics) formulate the mixture feature of corner kick times caused by previous corner kicks, frame the commonly available corner kick data as right-censored event times, and explore patterns of corner kicks. This paper extends their modeling to accommodate the potential correlations between corner kicks by the same teams within the same games. We con- sider a frailty model for event times and apply the Monte Carlo Expec- tation Maximization (MCEM) algorithm to obtain the maximum like- lihood estimates for the model parameters. We compare the proposed model with the model in Peng, Hu, and Swartz (2024) using likelihood ratio tests. The 2019 Chinese Super League (CSL) data are employed throughout the paper for motivation and illustration.

Problem

• corner kicks
• event times
• frailty model
• within-game correlation
• soccer

Innovation

• frailty model
• corner kicks
• event times
• MCEM algorithm
• right-censored data