As I understand it, the main benefit of PEDs is improved recovery times. Regardless of the extent to which it affects the first race / game / training session, it permits your body to get back to peak condition more rapidly. The incremental gains from spending more time in the optimal performance window quickly compound.
There is a huge universe of PEDs, legal and otherwise. Some improve recovery times. Some accelerate muscle growth. Some, like EPO, directly boost aerobic capacity.