Stupid Question
Compression ratio is a mechanical ratio of the cylinder & combustion chamber and is set. Cylinder pressure is just that, pressure while the engine is spinning and is variable depending on camshaft opening and closing rates for example.
The two aren't exactly connected but, here is a chart that shows compression ratio vs cylinder pressure. I have checked this chart against "real" engines that I have built and it is about 95% accurate. Using this chart an 8:1 compression ratio motor should have somewhere between 125 to 150 psi cranking pressure.
http://www.moparts.com/Tech/Archive/clutch/1.html
Chuck