The term pilot ratio refers to the ratio of two, discrete areas of a piston, spool or poppet on which opposing pressures act. The pilot area, on which pilot-pressure acts, is always the larger of the two areas. Working or system pressure acts on the smaller, opposing area. This means a relatively small pilot-pressure can overcome a much larger working or system pressure. In other words, pilot ratio is the hydraulic equivalent of mechanical advantage.
For example, consider a pilot-operated check valve with a pilot ratio of 4:1. If working or system pressure acting on the smaller poppet area, which opposes the larger pilot-piston area, is 3,000 PSI, it means pilot pressure of just greater than 750 PSI is required to overcome the working pressure and open the poppet (3000 / 4 = 750 – this assumes the pressure in the downstream port in the reverse flow direction is negligible, otherwise the effective pilot area is reduced).
Pilot ratio is an inherent characteristic of pilot-operated check valves, over center counterbalance valves (externally piloted) and brake valves (internally and externally piloted). But it also finds application in other situations, including variable pump and motor controls.
In the case of pilot-to-open check valves, it is important to consider the piston-to-annulus area ratio when applying these valves to the rod-side of a double-acting cylinder. For example, if the cylinder has a piston-to-annulus area ratio of 2:1, the piloted-operated check valve must have a pilot ratio of at least 3:1 (or higher if there is a negative load on the piston rod), otherwise it will not open. And you can watch a simulation video that explains this phenomenon, here