The review article shows the evolutionary path that turnover frequency (TOF) and turnover number (TON) have passed from "Boreskov`s Rule" to their modern definitions. From the equation catalysis rate, the second method for calculating TOF is obtained using the characteristics of catalyst material. Was prooved the possibility of obtaining TOF in two ways - using the characteristics of catalysis process and using the characteristics of the catalyst and reagents. The equivalence of two methods of TOF calculation is proved. It turned out that TOF is not a complete and unambiguous characteristic of the catalyst, as it was usually believed. TOF is only partially dependent on the characteristics of the catalyst material. It turned out that TOF is not a characteristic of a catalyst, but of a "catalyst + reagents" system, and its value directly depends on the state of their oxidation. It is proposed to use the list of oxidation states of chemical elements as the main tool in the selection of catalysts. The Sabatier principle limits the TOF and TON values by limiting the multielectron transitions when the oxidation state of the active sites of the catalyst changes. An explanation for the effect of overcoming the Sabatier prohibition is given, in which external synchronous action on the catalyst makes it possible to achieve a catalytic reaction speed higher than the Sabatier maximum.