Mathematical model for the integral assessment of team sport athletic readiness, Математическая модель интегральной оценки готовности спортсменов командных видов спорта, Математична модель інтегральної оцінки готовності спортсменів командних видів спорту

<jats:p>Background and Purpose  Modern digital technologies enable the continuous monitoring of various components of preparedness of team sport athletes. However, the existing approaches focus primarily on analyzing individual indicators and do not allow to obtain the objective, integral assessment of athletic readiness. Differences in units of measurement, directionality of indicators, and their multi-component character hinder significantly the comprehensive interpretation of the results and well-founded coaching decision-making. In this regard, the development of a universal mathematical model is a matter of current importance, which integrates diverse characteristics of preparedness into a unified quantitative indicator. Materials and Methods The study is methodological in nature and relies on mathematical modeling, systems analysis, and multi-criteria assessment methods. The proposed model involves the sequential normalization of heterogeneous indicators, converting them to a unified 100-point scale, the formation of five specific indices (Physical Readiness Index, Technical Readiness Index, Tactical Readiness Index, Psychological Readiness Index, and Functional Readiness Index), and their subsequent integral aggregation using the weighted geometric mean. Results The universal mathematical model for the integral assessment of team-sport athletic readiness has been developed, and the integral indicator Athlete Readiness Index (ARI) has been proposed. It has been shown that the use of geometric aggregation reduces the mutual compensation effect among sub-indices and provides more objective assessment of athletic readiness structure as compared with arithmetic averaging. Conclusions The developed mathematical model enables a comprehensive assessment of athletic readiness within the framework of a single integral indicator. The universal structure of the model allows adaptation to various team sports by modifying the set of primary indicators without deviating from the principles of normalization and aggregation. The proposed approach can serve as the mathematical basis for digital systems designed to monitor athletes and support coaching decisions, as well as a tool for the objective assessment of athletic readiness and optimization of training process management.</jats:p>