Analysis of the potential of Russian universities due the Project 5-100 implementation

The presented study analyzes the possibility of Project 5-100 implementing, initiated by the Decree of the President of Russia. It is aimed at increasing the competitiveness of leading Russian universities in relation to the world's leading scientific and educational centers and solving a number of other important tasks in the development of education and science in Russia. The main rankings evaluating higher educational institutions have been studied, among them the most authoritative universities in the world have been identified. A list of Russian higher education institutions that are assessed or have a chance to be included in these ratings has also been established. It was revealed that as of 2020, the only Russian university that consistently occupies a worthy place in one of the generally recognized world rankings is the Lomonosov Moscow State University. At the same time, the authors have made a quantitative assessment of the likelihood of inclusion of Russian higher educational institutions in the world university rankings. It has also been established which of the world rankings domestic universities can reach high places as quickly and successfully as possible. As a result, the objectives of Project 5-100 seem to be the most attainable within the framework of this rating. To solve such an important task, it was proposed to analyze in detail the methodology for giving marks to higher educational institutions present in it. In addition, it has been proven that it is necessary to develop measures to improve the assessment of domestic universities in a number of world research and educational centers.


Introduction
Since 2012, the Russian system of higher professional education (HPE) has been implementing the Project to improve the competitiveness of leading Russian universities among the world's leading research and educational centers (hereinafter -Project 5-100), initiated by the Decree of the President of the Russian Federation №599 dated 07.05.2012. The goal of the Project is to enter at least five of the best Russian universities in the top 100 leading world university rankings. In November 2019, it was decided to expand the number of Project participants to 30, starting in 2020, and for the next 6 years. This measure, apparently, is due to the fact that the declared goal of the Project was not achieved for a number of reasons. So, of the domestic universities, only the Moscow State University. M.V. Lomonosov is relatively confident in the top 100 of only two rankings recognized in the world university community -Shanghai and QS (the best result is 74th position in 2020). In this regard, when determining the potential of Russian universities, identifying the world's leading university rankings, in which Russian universities have the greatest chances of entering the top 100, is a priority and urgent issue.

Problem Statement
Traditionally, the following ratings are considered the most authoritative in the world educational community: - -Leiden University Center for Science and Technology Research (CWTS) rankingthe so-called The Leiden rating, which was first compiled in 2007, and has been published in its current form since 2011. [4].
It is necessary to consider the position of the leading Russian universities in the listed ratings.

Materials and Methods
Consider the position of the leading Russian universities in the listed rankings -it was compiled by the authors of the article on the basis of sources [1-4] and is presented in Table  1. Already at the stage of preliminary analysis of the table data, the following dependence was noted. In order of magnitude (10 3 ) the number of universities, included in the ratings under consideration, coincides with a slightly larger (about 17%) number of participants in the CWTS rating. At the same time, the number of Russian universities included in the QS ranking is 1.7 times more than in THE, 2.3 times more than in ARWU and 3.6 times more than in CWTS. It should also be noted that the best national university is Moscow State University. M.V. Lomonosov, occupies the highest position (84) in the QS rating, close to her (93) in the ARWU rating, and in the THE and CWTS ratings, his position is significantly lower -189 and 250 positions, respectively. At first glance, Russian universities are best represented in the QS-rating, but it is desirable to operate with a specific quantitative assessment. To obtain it, we use the methodology proposed by the authors of the article. We will assign points to each university participating in the rating according to the place occupied. Taking into account the fact that the goal for Russian universities is to enter the top 100, the scale of the assigned points may look as follows, presented in Table 2.  For each rating, a corresponding assessment can be obtained in the form of the sum of points scored by the universities included in the rating. The value of this estimate will depend on two factors: 1) the number of universities included in the ranking; 2) the places occupied by universities in the ranking. Obviously, the most promising from the point of view of Project 5-100 implementation is the rating with the highest point score. Mathematically, the proposed score can be expressed as follows: (1) where: О -rating score; N -number of universities included in the ranking; Bi -the point awarded to the i-th university in accordance with the place in the ranking (see Table 2).
To improve the accuracy of the proposed quantitative assessment, we introduce a correction factor that takes into account the proximity of the location of universities to the top 100 ranking. Let us explain the necessity of introducing a correction factor using the following example. Suppose 5 Russian universities are included in the top 100 of a certain rating. An appropriate rating score will matter: О1 = 5*10 = 50 points ( Table 2). Another ranking includes 7 universities in positions 101-200, the score will be: О2 = 7*8 = 56 points. The third rating includes 10 universities in positions 201-300, respectively, the rating for the rating will be equal to: O3 = 10 * 6.5 = 65. You can see that the first rating, for which the task of Project 5-100 can be considered completed, has an estimate lower than the other two. At the same time, the score of the second rating is lower than that of the third, in which all universities occupy significantly worse positions. There is a contradiction between the categories of quantity and quality, which can be removed by a correction factor calculated by the formula: where: Fcorr. -dimensionless correction factor; Uav.
-the average score of the university in the ranking, defined as the ratio of sum of points ∑Bi, received by universities included in the ranking to the number of universities N in it; Umax. -the maximum score for a place in the rating, in this example Umax. = 10 ( Table  2).
The calculated values of the correction factors for the three ratings will be: The above estimates for the ratings, taking into account the correction factors, will take the values: Acorr.1 = 50*1= 50,00 Acorr.2 = 56*0,80 = 44,80 Acorr.3 = 65*0,65 = 42,25 It can be seen that the adjusted scores more accurately reflect the compliance of the ratings with the criteria of the Project 5-100 problem, since the score of the first rating, for which the problem is solved, is the highest.
Thus, the final calculation formula for the adjusted rating assessment will take the form: In accordance with the proposed methodology, based on the materials in Table 1, the authors performed calculations using formulas (1), (2), (3). The calculation results are presented in Table 3. Note that the average score in the ranking can serve as an estimate of the average position occupied by universities. Assuming that the scale of points is piecewise linear between its reference points, we can conclude that when moving along positions 101-1, there is an increment of 2 points (from 8 to 10 -see Table 2, lines 1,2), which corresponds to the scale division price in this area of 0.02 points. When moving through positions 201-101 and 301-201, the increments are 1.5 points (from 6.5 to 8 and from 5 to 6.5 -see Table  2

Results
Analysis of the data in the table shows that in all quantitative indicators, the QS rating is significantly superior to other ratings. Accordingly, the objectives of Project 5-100 seem to be the most attainable within the framework of this rating. To confirm this assumption, we will conduct a time-based analysis, considering the results of the ratings of 2012 (start of Project 5-100) and 2016 (the middle of the time interval between the start and the current year) -tables 4, 5. Table 4. The position of Russian universities in world university rankings in 2012 (compiled by the authors of the article based on sources [5][6][7][8]  The table shows that in terms of the number of universities included in the rankings and the places they occupy, the most advantageous position of Russian universities appears in the QS ranking. The only exception is the higher position of the Moscow State University. Lomonosov in the ARWU rating, but this is the only Russian university that occupies a worthy place in this rating. Quantitative estimates calculated by the authors using formulas (1), (2), (3) are presented in Table 6. The calculated data are in good agreement with the results obtained for 2020 (Table 3)the adjusted estimate (line 6) of the QS rating is significantly higher than that of all other ratings. The fact that the average score of participants (row 4) and the conditional average position (row 8) for QS turns out to be significantly lower than for ARWU is explained by the small number of participants in the last ranking (only 2 and 3 universities in 2012 and 2016, respectively). Due to this, the high position of Moscow State University "pulls" the indicator for the rating as a whole. It should also be noted that a stable trend over the entire considered time interval 2012-2020 is a constant increase in the number of universities included in the rankings with a parallel decrease in the average score of participants. Obviously, the expansion of the list of participants is due to not the strongest universities, for which the very fact of being included in the prestigious world rankings is the primary task. At the final stage of the analysis, to assess the dynamics of the process, we will calculate the average annual growth rates of the main quantitative indicators determined in tables 3 and 6. The calculations were performed by the authors for the time intervals 2012-2016, 2016-2020 and 2012-2020, and their results are presented in table 7. The sum of points in accordance with the places in the ratingthe average annual growth rate, %

Discussion
Thus, the calculations show that the growth rates of almost all indicators in the time interval 2012-2020 are values that are not only the same in order, but also quite close in value (the difference in relative terms does not exceed 10%). Decrease in the average score (line 3) is characteristic, which is a consequence of the expansion of the list of participants at the expense of relatively weak universities. It should also be noted that the adjusted score for the ARWU and CWTS ratings in 2012-2020 does not grow, while QS and THE show an average annual growth of about 10% (row 4). This suggests that in these ratings, the positions of Russian universities tend to improve. Based on the value of this indicator achieved by 2020 (QS -44.5 points, THE -16.2 points - Table 3, line 6), we can conclude that domestic universities have the best prospects for achieving high places in the QS ranking. Accordingly, it seems appropriate to focus efforts on promoting Russian universities in this particular rating, for which it is necessary to analyze in detail the system of grading in it and develop measures to increase them for domestic participants in the rating.

Conclusion
The performed analysis and the calculations made it possible to draw certain conclusions regarding the possibility of implementing Project 5-100 and the feasibility of taking into account the rating methodology, which can contribute to solving this important task. Therefore, it seems appropriate to focus efforts on promoting Russian universities in this particular ranking. For this purpose, it is necessary to analyze in detail the system of grading in it and develop measures to increase them for domestic participants in the rating.