By the method of semi-tensor product of matrices, state based potential games are investigated. Firstly, using the potential equation, a necessary and sufficient condition and a sufficient condition are proposed, respectively, to verify whether a state based game is potential. Then two static equivalence conditions of state based potential games are presented. Furthermore, the dynamic equivalence is given such that the state based games dynamically equivalent to the state based potential games have similar dynamic properties. Lastly, the concept of state based networked evolutionary games is proposed. A necessary and sufficient condition is given to assure a state based networked evolutionary game is potential.