Typical compression ratio in a Diesel engine is somewhere around 20:1, vs a gasoline engine that's running 10:1 or there about.
Basically this is displacement/cylinder * compression ratio * RPM * number of intake strokes per revolution.
The compression ratio is a function of the head volume and the cylinder volume. It has nothing to do whatsoever with determining how much air is drawn into the engine, which is defined by speed, bore, stroke, and intake efficiency. It is rather determined by how much air is drawn into the engine, and how much space you have left for air at the end of a compression stroke.
Ever wondered why diesel tail pipes are a lot larger than gasoline ones? This is why, diesels move a lot more air.
Diesel tail pipes are a lot larger than gasoline ones because diesels shit the bed when you have backpressure. It ruins their efficiency and you have to play tricks to get it back. Turbocharging is worth it anyway because it's turbocharging. Now, pay attention to this part, because it's important: exhaust gas volume is proportional to load. Diesels have bigger exhausts because they have more torque. This is also why turbochargers and diesels go together so well. Turbochargers are driven by exhaust gas expansion, which as mentioned, is proportional to load.
If you carve the piston out, you lower the compression ratio, and you increase the amount of air the engine consumes. You in fact have this exactly backwards.