The influence of the field factor in a linear and nonlinear formulation

Aim. The aim of the paper was a theoretical substantiation of rating calculation using numerical methods, as well as the description of the rating determination system based on the factor of own field in team sports. Materials and methods. The data of ice hockey team performance during the Regular Championships of the National Hockey League from December 19, 1917 to March 11, 2020 were used. The research process included three calculation options: the first and second options assumed the calculation of a unified system of equations with/without field factor; the third option implied the calculation of the field coefficient for each individual season. Results. The system of linear equations with a single solution was presented. Mathematically grounded formulas for rating calculation were given. Conclusion. The proposed rating system satisfied the requirements for the accuracy of predicted results, the convergence of the computational process, and the level of compliance with the match result. The data obtained allowed us to conclude that the developed system helped to identify team strengths and increased the reliability of team performance prediction. The developed rating calculation system can become a methodological basis for the formation of team rating for all team sports.