How to rate numerical packages? Foundations of ratings, and their possible use in numerical mathematics, in education, and in military design

One of the major human activities is solving problems. It is desirable to be able to predict whether a problem will be solved or not or, more precisely, the probability that a person can solve a problem. This probability can be estimated based on previous experience of people solving similar problems.Then, it is necessary to somehow describe the ability of the problem-solvers as well as the difficulty of the problems. This can be done by assigning to each problem or problem solver a rating, i.e., a number that represents the skill of the problem solver or the difficulty of the problem.In this paper, we propose to use a rating system developed in sports to other real-life problems, including rating of numerical packages.