Application and Computer Implementation of Transfer Matrix Decision Method in Sports Training Efficiency

Abstract

Sports training efficiency is a critical indicator for measuring the level of coaches and training effects. Due to differences in athletes' initial levels upon joining a team and the diversity of training environments, accurately assessing the training level of coaches is a complex and challenging task. This study aims to establish a scientifically sound mathematical model for evaluating coach training efficiency by applying the "one-step transfer probability matrix" method from Markov chains. This model aims to eliminate unfair judgments caused by differences in athletes' baseline abilities and objectively reflect the actual training level of coaches. The study defines concepts such as initial state vector of athletes, state transition matrix, state transition rate matrix, and efficiency, constructing a mathematical model for evaluating coach efficiency. Computational programs were developed in MATLAB to calculate efficiency, taking into account differences in athletes' baseline abilities and changes in states during training, thereby providing a comprehensive evaluation method. Through case studies and program validation, the research found that the model effectively eliminates unfair judgments caused by differences in athletes' baseline abilities and quantifies the contribution of coaches to athletes' progress. The results show that the first coach has the highest training efficiency, and the evaluation results provided by the model are scientifically and practically robust. This study proposes a coach training efficiency evaluation model based on the "one-step transfer probability matrix" method from Markov chains, which objectively evaluates coach training efficiency through scientific quantification. The model demonstrates significant advantages in fairness, scientific rigor, and practicality, though practical application requires consideration of factors such as individual differences among athletes, training environments, conditions, as well as coaches' experience and strategies.