Data-based methods and statistical models are given special attention to the study of sports injuries to gain in-depth understanding of its risk factors and mechanisms. The objective of this work is to evaluate the use of shared frailty Cox models for the prediction of occurring sports injuries, and to compare their performance with different sets of variables selected by several regularized variable selection approaches. The study is motivated by specific characteristics commonly found for sports injury data, that usually include reduced sample size and even fewer number of injuries, coupled with a large number of potentially influential variables. Hence, we conduct a simulation study to address these statistical challenges and to explore regularized Cox model strategies together with shared frailty models in different controlled situations. We show that predictive performance greatly improves as more player observations are available. Methods that result in sparse models and favour interpretability, e.g. Best Subset Selection and Boosting, are preferred when the sample size is small. We include a real case study of injuries of female football players of a Spanish football club.