There are several options for constructing a rating scale, which involves many solutions to the problem. The most convenient is a solution that can be written down in an analytical form (do without tablets), consisting of the minimum number of only arithmetic operations in recounting the rating in a well-known way. The rating scale should be constructed on the basis of the concept definition of the concept of rating and a number of generally recognized principles that specify each element of its structure. The principles should be transcended from the specific formulas. Their list will be constantly updated with new items, updated and detailed. This will lead to a common denominator of all previous proposals within the general case, which will significantly increase the effectiveness of work on this topic.

We call the rank of the participant of the universal hypothetical circular macro-pattern shifted to the region of positive integers. We call a macro tournament any tournament with an arbitrary form of holding it among all participants, in which there are no isolated microtournament. An isolated microtournament is a tournament in which a smaller part of the competitors takes part, who has no formal meetings with the remaining majority of participants. Participants in the isolated microtournament (hereinafter MI) can not be assigned a rating. We call game sports (hereinafter ITT) those team types in which the ball is involved and there is a distribution by role.

The rating scale is based on the following principles:

Goal priority over the point. Information basis of the rating in the sport are scored and missed balls or other realized actions. Points – this is a result shifted to the field of positive integers, determining the participant’s place in a circular microtournament of a certain level, which occupies the corresponding sequence of places in the hierarchy of a longer macro-tournament. The perspective of the point system is seen in its gradual transformation into the scoring scale until they are completely merged. For example, teams play up to a certain amount of goals and the number of points scored by them is equal to the number of goals scored by them. In this case, the complication in calculations is justified only with a very significant optimization of the macro-pattern.Nevertheless, in future decisions it is possible to use the points (M, N) instead of the heads (З, П) because of the similarity of the transformations, which allows to form and use both scoring and scoring scales of the rating.
Selection of the type of functional dependence. The selected function must:
2.1. To have the anticommutativity property: F (3, P) = -F (II, 3).

2.2. Work in a certain numerical interval, and not over the entire scale.

2.3. Do not go beyond the four arithmetic operations and ensure the minimum number of arithmetic operations in recounting the rating.

2.4. Minimize the total difference between the results of the participants in the personal meeting and their common results. The absence of this principle leads to unsustainable behavior of the rating.

3. The principle of transitivity states that if participant A is stronger than participant B, and B is stronger than C, then A is stronger than C. It is implied that it is not just A who has won from B, but that A is preferable to B by the combination of results. It allows you to hold a macro tour without having to meet everyone with everyone; Makes it possible to turn a circular macro-market into a hypothetical one, in which the obtained part of the results is extrapolated to the whole sum of the games. The absence of this principle means the requirement of meeting each participant of the macro-tournament with all the others, which seems to be a matter without perspective.
3.1. For each pair of participants in the macro-tournament A and E, you can determine the number of the result chains connecting them: A-B-E, A-C-D-E, etc. Any pair of participants must be connected by a set of the shortest links.

4. The principle of depth translation is designed to ensure that the method of rating recalculation during the transition from the macrolevel to the next lower layers is unchanged, allowing to spread the obtained data into private ratings: the rating of the team is based on the ratings of its constituent players, the players ‘ratings are based on the players’ ratings on the base components of the game and vice versa . He also suggests the possibility of replacing several rivals with one equivalent to them.Rejection of this principle leads to loss of interaction between different levels.
5. The principle of asymptotic stability of results means the possibility of obtaining a unique solution in the distribution of ratings, based on the results obtained, regardless of their initial values. The most convenient way to implement this principle is to compile and then solve the corresponding system of linear equations (hereinafter referred to as SLR). If the determinant is not equal to zero, the CML always has a unique solution.The absence of this principle leads to the existence of a set of solutions with the same results of the macro-pattern, which is equivalent to the absence of a solution as such.
6. The average macro tour rating is adjusted based on the fact that the progress of independent participants is not synchronous and is chosen so that the sum of the deviations by the modulus of participants’ results for the past and current seasons within the macro-tournament is the smallest. To do this, all participants are successively moved in order of increasing such deviations, followed by the determination of the average rating of the new macro-market, the ratings of the remaining participants, and proceeding from this – the magnitude of the deviations throughout the macro-market.
7. Factor compensation. There are factors that affect the final result and create unequal conditions for participants. Compensation for the amount of such independent, non-interacting factors should be equal to the sum of their compensation. It is possible to extract from this result one or another factor. However, there are more promising changes in the conditions of the game, in which this compensation occurs automatically. For example, you can change the ratio of badminton or volleyball grounds so that the factor of another’s field will be leveled.

Polozov A.A. Ranking system when holding a personal championship in the team sport without changing the structure of the game. // Abstract on the competition .. kan. Ped.Sciences, 1999, 26c. Tyumen