The article attempts to build up a hierarchy of performance indicators of scientific activity, the upper part of which was exactly the same for all fields of science. A proposal for optimal approaches and tools for assesing effectiveness of science was made for the scientific community and for government as well. Also an approach was proposed to evaluate efficiency of scientific activity that allows to quickly evaluate this activity for large research organisations, entire regions and countries on the basis of macroeconomic indicators. It is suggested that decisive factor of effectiveness of science is quantitative and qualitative state of the layer of its leaders. Using Pareto principle and Russian research data carried out previously we show that today’s quantity is considerably less than would be expected basing on total number of scientists. Proposed are some approaches for government agencies to overcome this situation.