The cranking compression has nothing to do with what octane fuel the engine needs.  The pressure in the cylinder near TDC or about the time spark needs to occur has a lot of influence, as well as a few other things, on what octane fuel your engine requires.  The temperature of the piston crown, the ground strap on the spark plug, the surfaces of the combustion chamber, and carbon deposits have an effect on what octane fuel your engine requires.

An engine with very high cranking compression with a lousy pipe and bad ports will often run detonation free on low octane fuel.  A highly developed engine and pipe with low cranking compression will most often require high octane fuel.

A low compression four stroke that was originally made to run on 87 octane fuel will require higher octane fuel as the intake manifold pressure is increased when a supercharger or turbocharger is added.  The temperatures of the mixture in the cylinder and pressure in the cylinder near TDC will increase as boost pressure is increased. 

I hope you can see the trend that it is density and temperature of the trapped mixture in the cylinder near TDC that has the largest influence on the engines octane requirements. 

I remember some of the first jet ski engines we modified in the mid to late 1970s had very crude ports and pipes.  We could run over 200 psi cranking pressure on 87 octane pump gas detonation free.  Our current 45 to 50 hp 125cc road racing engines with around 150 psi cranking pressure needs over 115 octane fuel to keep them detonation free.

The cylinder pressure near TDC on engines with poorly developed ports and pipe goes down as the engine RPM increases. 

The pressure in the cylinder near TDC on engines with highly developed ports and pipe goes up when the engine is in the RPM range where the ports and pipe are working together.  A  tuned pipe will actually charge the cylinder with more mixture than what the engine displacement could pump without the assistance of the pipe.  A supercharger or turbocharger also makes a engine consume more air than the engine's  displacement.