The problem of finding measurable indicators reflecting the quality of education at universities is considered. It is shown that the existing methods of compiling university rankings are guided de facto by the analysis of the prerequisites for obtaining a quality education, but not by the actual result. The problem of finding a measurable indicator that reflects the level of competence of university graduates remains unresolved. It is shown that the solution to this problem can be found through finding the optimal distribution of students by competence levels, which, in turn, can be established using classical methods of statistical physics. It is shown that it is possible to find an analog of the Boltzmann distribution, reflecting the distribution of students by competence levels for given macroscopic parameters, which are the characteristics of a particular university (by analogy with such macroscopic parameters as temperature and pressure). Using the reference theoretical distribution of students by competence levels, we can offer a measurable indicator, which is a measure of the deviation of the real distribution of grades received by students at exams from the theoretical optimum. The influence of subjective factors on the result of calculating the specified measurable indicator is discussed. It is shown that even with attempts to artificially distort the result, its impact on the quality of the educational process remains positive.