What is the degree of state control of business?

Substantial.

Although the degree of involvement of the state in the economy does not distinguish Russia from other market economies, the manner in which that involvement is manifest does. That is to say that in strategic industries (i.e. oil, gas, power generation, aluminum, transport) the state is at the very least involved as a major shareholder / stakeholder. Often the state's involvement is more over and active, such as in instances where the government is a majority shareholder and/or exerts direct control over the conduct of businesses such as Rosneft and Gazprom.