[RedDevil]

An EGR feeds exhaust air back into the air intake. It adds volume and heat to the mixture without adding oxygen. This helps the engine to run economically when on light load.

On light load the throttle plate will be almost closed, creating a strong vacuum on the rest of the air inlet trajectory. The first stroke of the Otto cycle sucks the air into the cylinder, and when that's a strong vacuum that requires more energy than when it's not; the so-called pumping loss.

When the EGR feeds warm burnt air into the inlet, the vacuum will be less strong, the heat helps complete combustion and unburnt fuel gets a second chance.

OTOH, your engine was designed to accept hot air from the EGR, so you can build a WAI or HAI instead. Clean hot air is less dense than cold air so it will reduce pumping losses.
I did plan to make a regulated WAI for some time, but I found that as my car does have EGR the added effect of the WAI becomes detrimental once the engine is fully warmed up.